Combining Fuzzy Logic and Genetic Algorithms to Optimize Cost, Time and Quality in Modern Agriculture

Abstract

This study presents a novel approach to managing the cost–time–quality trade-off in modern agriculture by integrating fuzzy logic with a genetic algorithm. Agriculture faces significant challenges due to climate variability, economic constraints, and the increasing demand for sustainable practices. These challenges are compounded by uncertainties and risks inherent in agricultural processes, such as fluctuating yields, unpredictable costs, and inconsistent quality. The proposed model uses a fuzzy multi-objective optimization framework to address these uncertainties, incorporating expert opinions through the alpha-cut technique. By adjusting the level of uncertainty (represented by alpha values ranging from 0 to 1), the model can shift from pessimistic to optimistic scenarios, enabling strategic decision making. The genetic algorithm improves computational efficiency, making the model scalable for large agricultural projects. A case study was conducted to optimize resource allocation for rice cultivation in Asia, barley in Europe, wheat globally, and corn in the Americas, using data from 2003 to 2025. Key datasets, including the USDA Feed Grains Database and the Global Yield Gap Atlas, provided comprehensive insights into costs, yields, and quality across regions. The results demonstrate that the model effectively balances competing objectives while accounting for risks and opportunities. Under high uncertainty (α = 0\alpha = 0α = 0), the model focuses on risk mitigation, reflecting the impact of adverse climate conditions and market volatility. On the other hand, under more stable conditions and lower market volatility conditions (α = 1\alpha = 1α = 1), the solutions prioritize efficiency and sustainability. The genetic algorithm’s rapid convergence ensures that complex problems can be solved in minutes. This research highlights the potential of combining fuzzy logic and genetic algorithms to transform modern agriculture. By addressing uncertainties and optimizing key parameters, this approach paves the way for sustainable, resilient, and productive agricultural systems, contributing to global food security.

1. Introduction

Agriculture is currently facing a range of challenges, including limited resources, environmental uncertainties, and market volatility. Addressing the critical triad of cost, time, and quality (CTQ) is essential for ensuring both sustainability and profitability within the sector. Traditional optimization techniques often fall short in managing the complexities and unpredictable nature of agricultural systems [1]. Recent research has highlighted the potential of genetic algorithms as a promising approach to optimize key aspects such as water usage, nutrient management, and crop rotation strategies, further advancing the field of precision agriculture [2,3].

The evolution of modern agriculture from traditional methods to a technology-driven industry is largely driven by the need to meet the increasing global food demand, manage finite resources effectively, and adapt to the impacts of climate change [4]. This transition highlights the importance of balancing CTQ parameters—reducing operational costs, ensuring timely execution of tasks, and preserving the quality of agricultural products [5]. In this context, computational techniques such as fuzzy logic and genetic algorithms emerge as powerful tools to address these challenges. Fuzzy logic, known for its ability to manage uncertainties like weather fluctuations and soil conditions, provides a valuable framework for agricultural decision making [6]. On the other hand, genetic algorithms offer solutions for optimizing multi-objective problems, offering novel approaches to the management of CTQ parameters in agriculture [7].

This integrated approach, combining fuzzy logic and genetic algorithms, holds significant potential for addressing the complex issues facing modern agriculture and promoting sustainable practices.

1.1. Complexity in Agriculture

Agriculture involves a complex array of interconnected factors, including crop selection, irrigation practices, pest management, and harvesting strategies. These factors are further influenced by external elements such as climate conditions, soil properties, market demands, and regulatory policies [8,9]. The advent of advanced technologies, such as precision agriculture and IoT-enabled devices, has added a new layer of complexity to agricultural decision-making [10]. Furthermore, the growing influence of artificial intelligence (AI) in agriculture offers new opportunities to enhance production efficiency and resource management [11].

Traditional decision-making methods, which often rely on heuristics or statistical models, are increasingly inadequate for addressing the dynamic and unpredictable nature of modern agriculture. As a result, computational tools have become essential for managing large datasets, handling uncertainties, and optimizing multiple objectives simultaneously [12]. These tools help farmers adapt to fluctuating conditions, enabling agriculture to become more adaptive to environmental changes and market shifts [13].

1.2. Cost, Time, and Quality Management in Agriculture

The effective management of cost, time, and quality (CTQ) is crucial for evaluating and improving agricultural operations. Farmers, agribusinesses, and agricultural supply chains must navigate a complex environment where these three elements often interact in unpredictable ways. The agriculture industry is unique because it is affected by both natural and economic forces that make managing these parameters even more challenging [14]. Understanding the impact of cost, time, and quality on production can help in making informed decisions that boost efficiency, profitability, and sustainability. This section delves deeper into how cost, time, and quality are managed in agriculture and how they are interlinked [15]. The following key dimensions play a central role in managing this:

• Cost: This refers to expenses related to labor, machinery, fertilizers, and energy. Minimizing costs without sacrificing productivity or quality is a primary goal for agricultural enterprises [16,17]. Cost management involves analyzing both fixed and variable costs to identify areas for potential savings. For instance, the adoption of renewable energy sources, such as solar-powered irrigation systems, can reduce long-term energy costs, although the initial investment might be high. Furthermore, implementing crop rotation and integrated pest management strategies can help reduce the need for expensive chemical inputs, leading to cost savings [18].
• Time: Time management pertains to the duration of various processes, from planting to harvesting. Efficiently managing time is essential to synchronize operations with seasonal cycles and market demands [19]. Automation, such as the use of drones for crop monitoring and automated harvesters, can significantly cut down on labor hours, improving efficiency. Furthermore, technology-driven solutions like predictive analytics can assist in anticipating optimal harvest times, minimizing the risk of spoilage, and ensuring that crops are delivered to market at peak freshness [20]. However, the challenge remains in aligning the timing of these operations with unpredictable environmental factors, such as sudden weather changes, which can disrupt well-planned schedules [21].
• Quality: Quality encompasses attributes like nutritional value, appearance, and shelf life, all of which influence market pricing and consumer satisfaction. Effective quality management is crucial for ensuring product consistency and meeting consumer expectations [22,23]. Quality management systems, such as ISO certifications and Good Agricultural Practices (GAP), guide farmers in maintaining high standards of production. Additionally, innovations in genetic modification and selective breeding are allowing for crops that are not only more resistant to pests and diseases but also better suited to environmental conditions, thereby improving overall product quality [24]. However, these advancements must be balanced with consumer preferences for organic and sustainably produced goods, which may require additional effort and resources but offer higher returns [25].

Achieving a balance between these CTQ parameters presents a considerable challenge due to their interconnectedness. For instance, efforts to reduce costs may adversely affect quality or lead to production delays, while improving quality may require additional resources and time [26,27]. To manage this complexity, advanced optimization models that integrate multiple variables, including environmental and economic factors, are vital. These models provide agricultural managers with the tools to make informed decisions that optimize cost, time, and quality simultaneously. By simulating different scenarios, farmers can forecast the impacts of various management strategies and select the most effective solutions for their unique circumstances [28].

Technological advancements in precision agriculture are proving invaluable in this regard. Through data collection and analysis, these technologies help farmers make precise decisions about when to plant, irrigate, fertilize, and harvest. For example, soil sensors can monitor nutrient levels and moisture content in real-time, ensuring that fertilizers and water are used only when necessary, which not only saves costs but also helps maintain crop quality [29]. Furthermore, blockchain technology is being explored for improving traceability in the agricultural supply chain, which can ensure that products meet quality standards and reach consumers faster, with reduced waste [30]. Integrating cost, time, and quality management in agriculture requires a comprehensive approach that combines technology, strategic planning, and continual adaptation. By leveraging innovative tools and techniques, agricultural enterprises can achieve greater efficiency and sustainability, ensuring that they meet both economic and consumer demands while minimizing environmental impacts.

1.3. Computational Methods in Decision Making

1.3.1. Fuzzy Logic

Fuzzy logic, introduced by Lotfi Zadeh in 1965, offers a mathematical approach to handling uncertainty and imprecision, closely simulating human decision-making processes [31]. It is particularly effective in agricultural tasks that involve inherent variability and complexity, such as predicting crop yields, scheduling irrigation, and managing pests. In agricultural decision making, traditional binary logic (true/false, yes/no) often fails to address the nuanced and uncertain nature of real-world data. Fuzzy logic, however, allows for the representation of concepts such as “high”, “medium”, or “low” rather than relying solely on rigid classifications, making it more suited to the dynamic and imprecise nature of agriculture [32,33]. Recent advancements in fuzzy logic have demonstrated its effectiveness in optimizing irrigation schedules. By integrating weather forecasts, soil moisture levels, and plant growth stages, fuzzy systems can determine the appropriate amount of water needed, reducing waste while ensuring crops receive adequate hydration [34]. The ability to process and reason with uncertain or imprecise inputs is especially beneficial in regions with erratic weather patterns, where traditional irrigation systems may fail to adapt quickly enough to changing conditions. The flexibility of fuzzy systems allows for more personalized and adaptive solutions in irrigation management, which can contribute to increased crop yields and reduced resource consumption [35]. Fuzzy logic has also found application in pest management, where predicting pest outbreaks can be highly uncertain due to varying environmental factors. By utilizing fuzzy systems, farmers can assess the risk of pest infestations based on factors such as temperature, humidity, and crop vulnerability, thereby facilitating timely intervention and minimizing the use of pesticides [36]. This not only helps in reducing costs but also minimizes the environmental impact of chemical use in agriculture. Furthermore, fuzzy logic-based models can be used to predict the effectiveness of different pest control strategies, optimizing resource allocation and enhancing pest management outcomes [37,38]. In addition to its application in irrigation and pest control, fuzzy logic is also widely used in precision agriculture for crop yield prediction. By analyzing factors like soil properties, weather conditions, and crop health, fuzzy logic systems can provide more accurate and adaptable predictions compared to traditional methods, which often rely on deterministic models that fail to account for uncertainty [39]. As precision agriculture continues to grow, the role of fuzzy logic in integrating diverse data sources and improving decision making may become increasingly significant, helping farmers optimize production and achieve sustainable agricultural practices.

1.3.2. Genetic Algorithms (GAs)

Based on the principles of natural selection, genetic algorithms (GAs) were popularized by Goldberg in 1989 as optimization techniques [40]. These algorithms excel at solving multi-objective optimization problems, such as balancing cost, time, and quality (CTQ) within agricultural systems. GAs have been successfully applied to a variety of agricultural tasks, including resource allocation, crop planting schedules, and supply chain management. By simulating the process of natural evolution, genetic algorithms use a population of potential solutions, applying operators like selection, crossover, and mutation to generate improved solutions over time [41,42]. One of the most prominent applications of GAs in agriculture is optimizing resource allocation. In agriculture, there are numerous variables involved in the efficient use of resources such as land, water, fertilizers, and labor. Genetic algorithms can be applied to these problems to find optimal strategies for allocating resources in a way that maximizes yield and minimizes waste [41]. These algorithms are particularly valuable in large-scale farming, where manual optimization would be time-consuming and complex. By incorporating constraints such as weather patterns, soil conditions, and crop types, GAs can evolve solutions that are robust across different scenarios and environmental conditions [43,44]. In crop planting schedules, GAs have also been successfully implemented to improve timing for planting and harvesting. The optimal schedule must account for various factors, such as weather conditions, pest management, soil health, and market demand for specific crops. Genetic algorithms can help optimize these schedules by generating solutions that balance the competing objectives of maximizing yield, reducing input costs, and maintaining soil health over time [7]. For example, one study showed that genetic algorithms could be used to optimize crop rotation plans that improve soil fertility while ensuring profitability for farmers [45,46]. Furthermore, in agricultural supply chain management, genetic algorithms have been applied to optimize logistics and distribution networks. These problems often involve complex trade-offs between transportation costs, storage costs, and product freshness, with solutions needed for multiple stakeholders, such as producers, distributors, and retailers. By applying GAs, agricultural supply chains can be optimized to reduce costs while improving efficiency and meeting market demand. One area of success has been in the optimization of cold chain logistics, where the timing of transportation and storage plays a crucial role in maintaining product quality [47].

1.4. Integrating Fuzzy Logic and Genetic Algorithms

The integration of fuzzy logic and genetic algorithms offers a powerful approach to agricultural management, combining the strengths of both methods as follows:

• Handling uncertainty: Fuzzy logic effectively manages the inherent variability and uncertainty within agricultural systems, providing a flexible framework for decision making.
• Optimization: Genetic algorithms identify efficient or near-optimal solutions for complex issues, such as resource distribution and planning, thereby improving overall system efficiency.
• Adaptability: This hybrid approach allows for dynamic adjustments to changing factors, such as weather conditions and market fluctuations. For instance, in irrigation management, fuzzy logic can evaluate water requirements based on factors like soil moisture and temperature [48]. Meanwhile, genetic algorithms can optimize irrigation schedules to reduce operational costs while improving crop yield quality.

The combination of these techniques ensures that water usage is optimized, preventing both over-irrigation and under-irrigation, which could lead to wastage or reduced crop performance. This has been demonstrated in various agricultural scenarios where precise water management plays a critical role in maximizing crop output [49,50]. In addition to irrigation, the integration of fuzzy logic and genetic algorithms can be applied to pest management. Fuzzy logic can be used to classify and assess pest threats based on various environmental factors, such as humidity, temperature, and other species [51]. Genetic algorithms can then be employed to create optimal pest control strategies, balancing the need for effective pest elimination with the goal of minimizing pesticide use and its associated environmental impact. By integrating both methods, farmers can make data-driven decisions that improve crop protection while reducing the ecological footprint of their practices [52]. Furthermore, the hybrid approach can enhance crop yield prediction models by incorporating both historical data and real-time environmental factors. Fuzzy logic can process ambiguous or incomplete information, such as varying soil quality or unpredictable weather patterns, while genetic algorithms can develop solutions that maximize yield predictions by adjusting for these uncertainties. This allows for more accurate forecasting, which is crucial for optimizing input usage such as fertilizers, water, and labor, ultimately leading to more sustainable and profitable farming practices [53,54].

In conclusion, integrating fuzzy logic and genetic algorithms into agricultural management offers a versatile, adaptive, and highly efficient approach to solving complex problems. As technology continues to advance, the hybridization of these techniques holds great promise in addressing the challenges of modern agriculture, from resource management to environmental sustainability. By combining the flexibility of fuzzy logic with the optimization power of genetic algorithms, agricultural systems can become more resilient, efficient, and responsive to changing conditions [55,56,57].

1.5. MATLAB Integration

MATLAB r2021b toolboxes provide significant advantages in implementing computational methods, making them essentials assets for agricultural optimization. The Fuzzy Logic Toolbox allows users to design and test fuzzy inference systems, offering a user-friendly framework for addressing uncertainties in agricultural systems. These uncertainties—such as fluctuating weather patterns, soil conditions, and market volatility—can profoundly influence agricultural productivity [58]. Meanwhile, the Global Optimization Toolbox supports the creation of customized genetic algorithms, making it ideal for tackling complex, multi-objective problems like crop planning and resource management [59].

Integrating fuzzy logic with genetic algorithms creates a robust hybrid approach for managing the trade-offs between cost, time, and quality (CTQ) that are characteristic of agricultural operations. Fuzzy logic’s capacity to model uncertainty, combined with the optimization capabilities of genetic algorithms, enables adaptive decision making. This facilitates precise resource allocation and effective scheduling within agricultural systems, which is particularly useful for operations requiring real-time adjustments, such as irrigation management, pest control, and crop rotation planning [60].

This methodology is versatile and can be applied across various agricultural contexts, ranging from small-scale farms to large industrial operations. By optimizing resource use and minimizing waste, the hybrid approach promotes both increased productivity and environmental sustainability. Tools like MATLAB r2021b simplify the process of applying these techniques, improving accessibility and scalability for practical use across diverse agricultural settings [61].

As computational techniques continue to evolve, their potential to transform modern agriculture becomes increasingly apparent. The adoption of these tools can enhance resilience, boost operational efficiency, and support sustainability efforts. These advancements play a crucial role in addressing the growing challenge of feeding a rising global population while maintaining ecological balance. The integration of cutting-edge technologies with agricultural expertise paves the way for a more sustainable, efficient, and innovative future in farming [1,5].

The following sections of the article are arranged in accordance with a detailed structure as follows: Section 2 outlines the problem definition and its modeling. Section 3 introduced and develops/defines the algorithm used. Section 4 describes the implementation of the mathematical model using the NSGA-II algorithm in a case study focused on CTQ management in modern agriculture. Given the inherent uncertainty, risk, and complexity in decision making for project managers, expert opinions are integrated using a fuzzy alpha-cut parameter. The model is evaluated for various fuzzy alpha-cut values, and the computational results are analyzed in Section 5. The discussion and conclusion are presented in Section 6. Finally, Section 7 offers limitations and future studies. By combining fuzzy logic, the Critical Path Method (CPM), and the genetic elite algorithm, this model effectively addresses the challenge of balancing time, cost, and quality in project management. Fuzzy logic accounts for the uncertainties in estimating these factors, while the genetic algorithm optimizes the execution of project activities, ensuring that the project plan is both efficient and of high quality.

2. Literature Review

The dynamic and often unpredictable nature of agricultural systems—shaped by fluctuating climate conditions, soil degradation, market demands, and resource limitations—necessitates the use of advanced decision-making tools to enhance both productivity and sustainability. The integration of fuzzy logic and genetic algorithms (GAs) offers a powerful framework for managing these complexities and uncertainties in agricultural optimization [35,62].

These advanced computational techniques enable more efficient resource management, better adaptability to environmental changes, and improved economic outcomes for farmers [63]. To truly understand the value of integrating fuzzy logic and genetic algorithms in agriculture, it is essential to explore how these technologies contribute to efficiency and sustainability in practical terms. Agriculture is inherently uncertain, influenced by fluctuating weather conditions, soil quality, pest outbreaks, and market dynamics. Traditional methods of managing crops, irrigation, and resource allocation often fail to keep up with these variables, resulting in inefficiencies that lead to economic losses. By leveraging fuzzy logic, farmers can make decisions based on a range of possibilities rather than rigid binary choices. This allows them to adapt quickly to changes, optimizing resource usage and improving crop yields in real-time, even under uncertain conditions.

2.1. Fuzzy Logic for Managing Uncertainty in Agriculture

Fuzzy logic, introduced by Zadeh in 1965, provides a mathematical approach to handling imprecise and uncertain data—conditions frequently encountered in agriculture. Unlike binary logic, which operates on clear-cut true or false values, fuzzy logic allows for degrees of membership, enabling more nuanced decision making [64,65]. For example, fuzzy models have been effectively used to optimize irrigation schedules under varying soil and climatic conditions [66,67,68]. The alpha-cut technique further refines fuzzy logic by considering both optimistic (low risk) and pessimistic (high risk) scenarios, making it applicable across diverse agricultural contexts [69,70,71].

In crop management, fuzzy logic enables the integration of multiple parameters—such as soil fertility, weather conditions, and crop maturity—thereby optimizing yield while minimizing resource use [72,73,74]. Studies focusing on staple crops like rice in Asia and wheat worldwide have demonstrated the effectiveness of fuzzy logic models in addressing regional challenges such as water scarcity and climate variability [75,76,77]. For instance, fuzzy logic models have been employed to predict crop growth and estimate yields, taking into account factors like soil moisture, nutrient availability, and pest populations [33,78]. These models provide real-time, actionable insights, that can significantly improve crop management strategies [79].

The role of fuzzy logic in irrigation management is critical. In regions where rainfall is unpredictable, managing water resources efficiently is a matter of both cost and survival for crops. Without advanced predictive models, farmers may over- or under-irrigate, leading to wasted water, lower yields, or even crop failure. On the other hand, genetic algorithms provide an optimization mechanism that fine-tunes decisions related to fertilizer application, crop rotation, and pest management. These models factor in a variety of objectives, such as maximizing yield, reducing costs, and minimizing environmental harm, which are often in conflict. The ability of genetic algorithms to provide an optimal balance across these competing factors is a significant advantage in ensuring long-term agricultural productivity and sustainability.

2.2. Genetic Algorithms for Multi-Objective Optimization

Genetic algorithms (GAs), inspired by natural selection, offer a computationally efficient means of solving complex, multi-objective problems [40,80]. In the context of agriculture, GAs have been used to optimize conflicting objectives, such as maximizing crop yield, minimizing costs, and ensuring environmental sustainability. These techniques enable dynamic responses to emerging agricultural challenges, such as extreme weather events, pest outbreaks, and shifting market demands [81,82,83]. For instance, GAs have been applied to identify optimal crop rotation strategies, irrigation schedules, and fertilizer application rates. This method has proven particularly effective for managing crops like barley in Europe and corn in the Americas, where input costs and market conditions can vary significantly [41,84,85]. Additionally, GAs facilitate the rapid convergence toward optimal solutions within large datasets, making them ideal for real-time decision making in agriculture [7,86,87]. GAs have also been integrated with other optimization techniques, such as simulated annealing and particle swarm optimization, to further enhance their performance in complex agricultural systems [88,89].

2.3. Case Studies and Model Validation

Agricultural decision making relies heavily on the availability and quality of data. In this study, historical agricultural datasets, sourced from organizations such as the USDA, FAOSTAT, and the Global Yield Gap Atlas, serve as the foundation for model calibration. One of the key challenges in agricultural data processing is the conversion of historical, often incomplete datasets into structured inputs for optimization models. To address this challenge, a systematic data preprocessing methodology is implemented. This involves data cleaning, normalization, and transformation into fuzzy numerical representations. For example, historical climate data, including rainfall variability and temperature fluctuations, are represented as triangular fuzzy numbers to better capture their inherent uncertainty. Additionally, soil composition data are categorized into fuzzy sets based on pH levels, organic matter content, and nutrient availability. The preprocessing framework also considers regional variations in crop growth cycles, accounting for factors such as seasonal planting schedules and soil degradation rates in different geographic locations. This ensures that the proposed model remains adaptable to diverse agricultural environments.

The integration of fuzzy logic and genetic algorithms (GAs) has been validated through various case studies on key crops, including rice, barley, wheat, and corn. These crops were selected for their global economic and strategic significance. Data from reputable sources such as the USDA, the Global Yield Gap Atlas, and FAOSTAT have provided valuable insights into regional agricultural challenges, including water scarcity in Asia, soil degradation in Europe, and climate volatility in the Americas [90,91,92]. These case studies have shown that the combination of fuzzy logic and GAs is effective in addressing fluctuating input costs, water availability, and pest resistance [93,94]. For instance, in rice cultivation, fuzzy-GA models were used to optimize water usage under uncertain rainfall conditions [29,95]. Similarly, for barley in Europe, the models addressed soil fertility and market variability, ensuring sustainable production [84,96]. Global studies on wheat have highlighted the ability of these models to balance yield with environmental sustainability, aligning with the United Nations Sustainable Development Goals (SDGs) [76,97,98]. In the Americas, fuzzy-GA models were employed to optimize water use and fertilizer application in corn production, ensuring both efficiency and the mitigation of the environmental impact [99,100,101].

These case studies demonstrate the adaptability of fuzzy-GA frameworks in real-world agricultural systems, validating their broader applicability [102,103]. The results provide strong evidence that integrating fuzzy logic with GAs can help farmers develop more resilient, resource-efficient farming practices that are adaptable to changing environmental and market conditions.

2.4. Alignment with Sustainability Goals

The proposed fuzzy-GA framework supports several global sustainability objectives, particularly SDG 2 (Zero Hunger), SDG 12 (Responsible Consumption and Production), SDG 13 (Climate Action), and SDG 15 (Life on Land) [104]. By optimizing resource efficiency and reducing environmental impact, fuzzy-GA models contribute to global efforts aimed at mitigating climate change and ensuring food security [9,105,106]. These models also promote precision agriculture, minimizing waste and reducing the carbon footprint of agricultural practices [107,108]. Furthermore, fuzzy-GA models enhance the efficiency of land and water use, aligning with the goals of sustainable intensification, which seeks to increase agricultural productivity while maintaining ecological integrity [4,109]. These models are particularly relevant in the context of climate change adaptation, offering strategies to cope with unpredictable weather patterns and mitigate the impacts of extreme events [110,111].

In conclusion, the integration of fuzzy logic and genetic algorithms offers a robust, flexible framework for tackling the challenges of modern agriculture. By addressing uncertainty, balancing competing objectives, and aligning with sustainability goals, this approach represents a significant advancement in agricultural optimization. These technologies are particularly valuable in dealing with the multifaceted problems that arise in the agricultural sector, where environmental, economic, and social factors are often at odds. Research has shown that fuzzy logic and genetic algorithms have proven successful in improving decision-making processes by enabling better resource management, reducing operational inefficiencies, and fostering increased adaptability to changing conditions [112,113]. Future research into machine learning, real-time data, and climate adaptation models promises to further enhance its applicability and impact [114,115,116]. These advancements will likely unlock even greater potential for optimizing agriculture and addressing global challenges like climate change, food security, and resource scarcity. Beyond the environmental and operational benefits, integrating these advanced computational methods also has direct economic implications. The economic impact of inefficiencies in resource use—such as water, fertilizers, and labor—can be significant. Without the predictive power of fuzzy logic and the optimization capabilities of genetic algorithms, farmers may struggle to achieve the best possible outcomes. For example, a lack of precise water management can lead to crop stress, reduced yields, and higher costs associated with water sourcing or irrigation infrastructure. A study conducted on rice farming in Asia revealed that inefficient water usage without optimization could lead to up to 30% loss in crop yield, thereby negatively affecting farmer income [117,118]. Similarly, failure to optimize fertilizer use results in excessive input costs and potential soil degradation, both of which impact profitability. Studies have demonstrated that by optimizing fertilizer application, farmers can reduce input costs by up to 15%, while also reducing environmental impacts such as nutrient leaching and soil erosion [119,120]. These economic benefits further emphasize the importance of these technological innovations in improving farm profitability and sustainability. The combination of fuzzy logic and genetic algorithms thus represents a step forward in precision agriculture, where decisions are more data-driven and tailored to real-time conditions. By reducing inefficiencies and improving the adaptability of agricultural practices, these tools contribute to a more resilient agricultural system. This is particularly crucial in the face of unpredictable climate patterns, such as droughts, floods, and other extreme weather events, which have been increasing in frequency and severity in recent years. Climate models suggest that crop yields in certain regions have already been affected by these events, with some studies indicating a 10–20% decrease in yields in areas heavily impacted by droughts and water shortages [49,121]. By utilizing fuzzy-GA models, farmers can make more informed decisions regarding irrigation, crop rotation, and pest management, ultimately improving their ability to mitigate these risks. In doing so, they help farmers better navigate the challenges posed by climate change, market fluctuations, and other uncertainties. In the long run, the widespread adoption of these technologies could lead to more sustainable farming practices that not only benefit the farmers economically but also help protect the environment and ensure food security for a growing global population. These technologies not only help mitigate these risks but can actively improve the profitability of farming operations by enhancing yield per unit of input and reducing waste. Research from the Global Yield Gap Atlas has demonstrated that the application of optimization models in crop management can increase overall yields by 10–20%, depending on the region and crop type [50,122]. Such improvements can have far-reaching effects on the global food supply, especially in areas where agriculture is the primary livelihood. The adoption of fuzzy logic and genetic algorithms can help ensure that agricultural practices are more resilient, cost-effective, and environmentally friendly, paving the way for a more sustainable future. Ongoing collaboration across disciplines, from agriculture to computer science, will be key in refining these technologies and scaling their implementation in agricultural systems worldwide. This will ensure that these solutions remain adaptable to the evolving needs of farmers and the global community, ensuring a more secure and sustainable agricultural future for generations to come.

3. Theoretical Background

3.1. Introduction to Fuzzy Logic

Fuzzy logic, introduced by Lotfi Zadeh in 1965, is a mathematical framework developed to manage uncertainty and imprecision in decision-making processes. Unlike traditional binary logic, which uses absolute true or false values, fuzzy logic allows reasoning with varying degrees of truth. This property makes it especially useful for addressing real-world problems where ambiguity and partial truths are inherent [123].

3.1.1. Fuzzy Sets and Membership Functions

A fuzzy set is defined by a membership function that assigns a value between 0 and 1 to each element, representing the degree to which an element belongs to the set. This degree indicates the level of membership an element has within the fuzzy set [31]. In agriculture, fuzzy sets can model variables such as “high soil moisture” or “low temperature”, effectively capturing the inherent uncertainty [124]. A commonly used membership function is the sigmoid function, which adjusts the steepness and central point to represent varying degrees of truth.

3.1.2. Fuzzy Rules and Inference Systems

Fuzzy inference systems (FIS) use “if–then” rules to map inputs to outputs. For example, an agricultural rule might state: “If soil moisture is low and temperature is high, then increase irrigation”. The FIS process typically involves the following steps [125]:

• Fuzzification: Converting precise input values into fuzzy sets.
• Rule evaluation: Applying fuzzy rules to determine the corresponding outputs.
• Aggregation: Combining multiple output fuzzy sets into a single set.
• Defuzzification: Converting the aggregated fuzzy set back into a precise value.

3.1.3. Fuzzy Logic Applications in Agriculture

Fuzzy logic has been widely applied in agriculture for optimizing irrigation, managing pests, predicting crop yields, and allocating resources. For example, a fuzzy system can determine water requirements for crops based on factors such as soil moisture levels and weather forecasts. The fuzzy logic system formulas used in these applications are outlined in

Table 1. Fuzzy logic system formulas.

Fuzzy Logic System Formulas:
Membership Function for a Fuzzy Set:	$A$ sigmoid membership function defines the degree of membership $\left(\mu A\right(x)\backslash mu\_A(x\left)\mu A\right(x\left)\right)$ of a variable $x$ in a fuzzy set $A$:
	${\mu }_A={\displaystyle \frac{1}{1+e^{-\alpha (X-C)}}}$
	where $\mu A\left(x\right)\backslash mu\_A\left(x\right)\mu A\left(x\right)$: Membership degree of $x$ in fuzzy set $A$. α: Sharpness parameter controlling the steepness of the curve. c: Center of the membership function where $\mu A\left(x\right)=0.5.$
Fuzzy Rules:	Rules in fuzzy systems are written as follows:
	$If X is A and Y is B,then Z is C.$
	An example in irrigation scheduling is as follows: If soil moisture is low and temperature is high, then irrigation need is high. Defuzzification Formula (Centroid Method) The crisp output $z$ from a fuzzy set $C$ is given by the following:
	$z={\displaystyle \frac{\int z\in c {\mu }_{c\left(z\right)d_z}}{\int z\in c^{{\mu c}^{\left(z\right)dz}}}}$
	where $z$: The output variable. $\mu C\left(z\right)$: Membership function of the fuzzy set $C$.

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3.2. Introduction to Genetic Algorithms

Genetic algorithms (GAs), introduced by John Holland in the 1970s, are optimization techniques inspired by the principles of natural selection. They are especially useful for solving complex problems where traditional methods may be less effective [80].

3.2.1. Working Principles of Genetic Algorithms

GAs mimic the process of natural evolution and involve the following steps [126]:

• Initialization: Generate an initial population of candidate solutions.
• Selection: Choose solutions based on their fitness, which reflects how well they perform relative to the problem’s objectives.
• Crossover: Combine selected solutions to produce offspring with traits from both parents.
• Mutation: Introduce random changes to some solutions, ensuring diversity in the population.
• Evaluation: Assess the fitness of each solution using a fitness function.
• Termination: The process ends when a predefined stopping condition is met, such as reaching a certain number of generations or achieving a satisfactory solution.

3.2.2. Fitness Function

The fitness function evaluates the quality of a solution based on how well it meets the specified objectives. In agricultural optimization, for example, the fitness function might aim to balance cost, time, and quality by assigning different weights to these factors [127].

3.2.3. GAs Applications in Agriculture

GAs have been successfully applied to optimize various agricultural tasks, such as planting schedules, irrigation systems, and supply chain management. For instance, they can be used to determine the most effective combination of fertilizers and pesticides to maximize crop yield while minimizing costs.

3.2.4. Combining Fuzzy Logic and Genetic Algorithms

The integration of fuzzy logic and GAs combines the strengths of both methods. While fuzzy logic is effective at handling imprecision and uncertainty, GAs excel at optimizing solutions. This hybrid approach is especially powerful for multi-objective problems, such as balancing cost, time, and quality in agricultural operations [40]. The formulas used in genetic algorithms are outlined in

Table 2. Genetic algorithm formulas.

Genetic Algorithm Formulas:
Fitness Function for Optimization	The fitness function evaluates a solution’s quality, considering the cost $\left(C\right)$, time $\left(T\right)$, and quality $\left(Q\right)$, as follows:
	$f\left(x\right)=w_c·c+W_T·T-W_Q·Q$
	where $wC,wT,wQ$: Weights assigned to cost, time, and quality based on priorities. $C,T,Q$: Values of cost, time, and quality for the solution $x$.
Selection Probability in Roulette Wheel Selection	The probability of selecting a solution $i$ based on its fitness $f_i$ is expressed as follows:
	$P_i={\displaystyle \frac{f_i}{\sum _{j=1}^n{f}_j}}$
	where $n$ is the total number of solutions.
Crossover Operation	For two parent solutions $P_1=\left(X_1,X_2,\dots ,X_n\right)$ and ${ P}_2=(y_1,y_2,\dots ,y_n)$, the offspring $O_1$ and $O_2$ are generated by single-point crossover at position $k$, as follows:
	$O_1=(X_1,X_2,\dots ,X_k,y_k+1,\dots ,y_n)$ $O_2={(y}_1,y_2,\dots ,y_k,x_k+1\dots ,x_n$)
Mutation Operation	For a gene $x_i$ in a solution, mutation introduces a small random change, expressed as follows:
	$x_i^{\prime }=x_i+{∆}_x$
	where ${ ∆}_x$ is a random value sampled from a predefined range.

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3.2.5. Hybrid Optimization Model

• Fuzzy logic component: This component defines the problem parameters and associates linguistic variables with fuzzy sets. For example, it can represent concepts such as “low cost” or “high quality”, using membership functions that capture degrees of truth.
• Genetic algorithm component: The genetic algorithm optimizes the parameters of the fuzzy system or directly addresses the problem by considering fuzzy objectives, providing a means to fine-tune decision making.
• Integration: The genetic algorithm evolves the fuzzy rules or membership functions to enhance decision making. For instance, it can adjust parameters like the sharpness (α) or the centers (c) of membership functions to improve outcomes [128].

The formulas used in the hybrid optimization model are detailed in

Table 3. Hybrid optimization model formulas.

Hybrid Optimization Model:
Objective Function Combining Fuzzy Logic and GA	$\min (w_c·cost\left(x\right)+w_T·Time \left(x\right)-w_Q·Qvality\left(x\right))$
	subject to constraints derived from fuzzy rules, e.g.,
	${\mu }_{Low cost}\left(c\right)·{\mu }_{High Quality\left(Q\right)}>Threshold$

.

3.3. Problem Definition and Modeling

3.3.1. Problem Definition and Modeling

The problem is optimizing time, cost, and quality. A project was studied as a case study. This project has n activities $(i=1,\dots ,n)$, where each activity has m execution methods $\left(modes\right) (j=1,\dots ,m)$ and each of the execution methods of the activities has an execution time as a triangular fuzzy number $(t=t_1,t_2,t_3)$, an execution cost as a triangular fuzzy number $(c=c_1,c_2,c_3)$, and an execution quality, ij as a triangular fuzzy number $(Q=q_1,q_2,q_3)$, where $V_{ij}$ defines the choice of the $j$-th method for $i$ performing the i-th activity and is represented by the following formula [81]:

$$v_{ij}=\left[(t_{ij},c_{ij},q_{ij})\right]$$

This study aims to optimize the trade-off between time, cost, and quality in project implementation within modern agriculture by integrating fuzzy logic and genetic algorithms. The objective is to identify the most effective methods for carrying out project activities, considering their time, cost, and quality, and to determine Pareto optimal solutions [129]. Each activity involves various implementation methods, each with distinct time, cost, and quality attributes. To address uncertainty, input data—such as time, cost, and quality—are represented as triangular fuzzy numbers. Additionally, the relative importance of each factor and activity is weighted to support decision making. This approach takes into account the interdependencies between activities and the risks associated with estimating these parameters [130].

3.3.2. Symbols and Variables of the Proposed Model

Before presenting the mathematical model, the symbols, parameters, and variables used in the model are defined and explained below.

$i$: Activity number in the activity network $\left(i=1,\dots ,n\right)$.

$J$: Number of implementation method for each activity $\left(j=1,\dots ,m\right)$.

K: Number of iterations of the algorithm until convergence is reached

($k=1,\dots ,Maximum Number of Iterations$).

${{\rm T}}_i^j$: The fuzzy duration of performing activity $i$ on the critical path with the execution method $j$, such that the following holds:

$$i=(1,\dots ,n I i ϵ critical path).$$

$DC:$ Fuzzy indirect cost of executing the i-th activity with the j-th execution method.

${IC}_j^i$: Fuzzy total cost of executing the i-th activity with the j-th execution method.

$C_i^j:$ Fuzzy quality of execution of the i-th activity with the j-th execution method.

$Q_i^j$: Fuzzy duration of the entire project.

$T$: Fuzzy duration of the entire project.

$C$: Fuzzy cost of the entire project.

$Q$: Fuzzy quality of the entire project.

$U:$ Fuzzy utility rate.

$w_{ti}:$ Relative weight percentage of the importance of the i-th activity compared to other activities.

$w_t:$ Weight percentage of the importance of the time criterion in the project.

$w_c$: Weight percentage of the importance of the cost criterion in the project.

$w_q$: Weight percentage of the importance of the quality criterion in the project.

$\alpha$: The level of risk tolerance in the experts’ opinion in estimating the fuzzy time, cost, and quality values for project activities. If the project manager fully trusts the experts’ opinions in estimating the existing uncertainty, its value is zero in real conditions. The more alpha approaches one, the more certain the conditions are, and the project manager ignores most of the experts’ opinions.

$x_j^i$: If the i-th activity is performed with the j-th method, its value is one, and otherwise, its value is zero [80,131,132,133].

3.3.3. Mathematical Model of the Problem

The optimization problem involving time, cost, and quality is formulated as a three-objective zero-one linear programming model [40,134], as presented below.

$$\begin{array}{c}{min}_T=\sum _i(T_i^j\times X_i^j)\\ \left(i=1,\dots ,{\displaystyle \frac{n}{i}}\in critical path\right),(j=1,\dots ,m)\end{array}$$

(1)

$${min}_c={\sum }_i^n\left({Dc}_i^j\times x_i^j+{Ic}_i^j\times x_i^j\right)={\sum }_i^n=1\left(C_i^j\times x_i^j\left)\right(i=1,\dots ,n),(j=1,\dots ,m\right)$$

(2)

$$\begin{array}{c}{max}_Q={\displaystyle \sum _i^n}=1(w_{ti}\times Q_i^j\times x_i^j)\\ \left(i=1,\dots ,n\right),(j=1,\dots ,m)\end{array}$$

(3)

$$Fuzzy Start Time Activity\left(i\right)+{\sum }_{j=1}^m(T_{\mathrm{İ}}^J\times x_i^j)\le Fuzzy Start Time Activity\left(i+1\right)(\mathrm{İ}=1,\dots ,n)$$

(4)

$$Fuzzy Start Time Activity\left(i\right)\ge 0(i=1,\dots ,n)$$

(5)

$$x_i^j=\left\{\mathrm{0,1}\right\}(i=1,\dots ,n){\sum }_j^m=1(x_i^j)=1$$

(6)

$${\sum }_j^m=1(x_i^j)=1,(i=1,\dots ,n)$$

(7)

$$w_q,w_c,w_t\le 1,=w_q,w_c,w_{t}1$$

(8)

$${\sum }_{i=1}^n\left({wt}_i\right)=1,0\le \alpha \le 1(i=1,\dots ,n)$$

(9)

$$0\le \alpha \le 1$$

(10)

Finally, after solving the problem and obtaining the set of Pareto optimal solutions using the genetic algorithm, the utility function in Equation (11) is applied to determine the final solution.

$$U=w_t\left(-T\right)+w_c\left(-c\right)+w_{q}Q$$

(11)

The optimization problem involving time, cost, and quality is formulated as a three-objective zero-one linear programming model, which allows for a sophisticated trade-off between project objectives. With a clear focus on agricultural project implementation, the optimization model will not only minimize project time and cost but also maximize the quality of the activities involved. Given the complex, interconnected nature of activities in agricultural projects, each activity’s execution method is chosen in a way that optimizes the entire project’s efficiency, ensuring a balance between costs, time, and quality. In real-world agricultural projects, the challenges extend beyond just managing these variables—external factors such as environmental conditions, market shifts, and regulatory constraints also impact decision making and execution. This makes the consideration of fuzzy logic even more relevant, as it allows for a more adaptable model that accommodates these uncertainties. The integration of fuzzy triangular numbers, which reflect expert estimates on time, cost, and quality, enhances the model’s robustness in real-world situations where data are often imprecise and estimates are based on subjective judgment rather than precise figures. Furthermore, as we move toward integrating genetic algorithms in this process, it is crucial to acknowledge that agricultural project management requires both short-term and long-term strategies. In this context, genetic algorithms do not only provide solutions for current optimization but also ensure the sustainability of those solutions over multiple iterations. The algorithm’s ability to evolve and adapt over time aligns with the cyclical nature of agricultural projects, where new variables and challenges may arise during execution.

The objective functions (1), (2), and (3) aim to balance the trade-off between time, cost, and quality, with the core challenge being to minimize time and cost while maximizing quality. The inclusion of risk tolerance (α) in relation (10) plays a crucial role in reflecting the project manager’s approach to uncertainty. If the manager is risk-averse (lower α), the solution will prioritize more conservative, reliable estimates for time and cost. Conversely, a higher α signifies a greater willingness to accept higher risks in exchange for potentially better project quality or cost-saving opportunities.

Additionally, relations (6) and (8) ensure that the relative importance of both the criteria and activities are accounted for in the optimization process. By assigning weights that sum to one, the model allows flexibility in prioritizing specific aspects of the project—such as focusing on cost reduction, in certain scenarios or emphasizing quality enhancement or minimizing time delays in others. The evaluation of each proposed solution through fuzzy logic, combined with genetic algorithms, facilitates an iterative decision-making process that continually refines the solutions, ensuring that the final set of Pareto optimal solutions reflects a pragmatic, well-balanced approach to time, cost, and quality management in agriculture. By applying such a comprehensive methodology, the model addresses various aspects of uncertainty while optimizing project outcomes. The flexibility provided by the risk tolerance parameter (α) further enhances the model’s capacity to adjust its decisions based on the project manager’s preference, ensuring that the final solution fits within the broader organizational strategy and risk appetite. In agricultural projects, where environmental and market volatility is a significant concern, this model provides a solid framework for navigating the complexities of execution while adhering to strategic goals such as cost-effectiveness, timely delivery, and high-quality outputs.

The model will provide the optimal allocation of resources, scheduling, and management strategies for the agricultural project. By utilizing fuzzy logic to represent uncertainties and genetic algorithms to optimize decision making, the model offers a set of recommendations that balance cost, time, and quality while allowing for flexibility in responding to varying levels of uncertainty.

In conclusion, the use of triangular fuzzy numbers in this model allows for an intuitive representation of uncertainty in the decision-making process, as illustrated in Figure 1. Triangular fuzzy numbers are particularly useful for capturing the subjective estimates provided by experts or stakeholders, such as possible ranges for cost, time, or quality. This representation helps the model handle vagueness in input data, which is a common challenge in agricultural projects due to unpredictable environmental and market conditions. By incorporating such fuzzy numbers, the model becomes more adaptable to real-world scenarios where precise values may not always be available, thereby improving the robustness and reliability of its recommendations [135].

4. Proposed Algorithm for Solving the Problem

In the task of optimizing the balance between time, cost, and quality of project activities, each activity has multiple execution methods. As a result, the total set of activities for the project consists of several possible execution methods for each activity. The proposed model aims to identify the optimal execution method for each activity, with the goal of minimizing the total time and cost of the project while maximizing the total quality of its execution.

In this research, the balancing of time, cost, and quality will be achieved using fuzzy logic, the Critical Path Method (CPM), and the Elite Genetic Algorithm. The steps involved in this process are illustrated in Flowchart (Figure 2), and the following sections of the article will provide a more detailed explanation.

4.1. Determining the Initial Solution Set to Start the Solution Process

Initially, from among the $m^n$ possible execution methods, the size of the population size for each generation is determined, a solution or chromosome is randomly selected as the initial solution set to begin the optimization process $(k=0)$. These solution sets must, of course, satisfy constraints (4) to (9).

$$X=(k=0)=\{X1 j (k=0),X2 j (k=0),X3 j (k=0),\dots ,Xn j (k=0\left)\right\}$$

(12)

4.2. Evaluation of the Suitability of the Solution Set Based on Objective Functions

For each solution set, its suitability must be evaluated in terms of the objective functions. First, by combining the Critical Path Method (CPM) and fuzzy logic, and utilizing the fuzzy project completion time results, the project’s timeline will be determined. Next, using the fuzzy weighted sum method, the fuzzy cost and quality of the project will also be calculated.

4.3. Determining the Pareto Solution Set of the Problem

This step aims to identify the optimal combination of implementation methods for the project activities. By comparing and combining different methods, it selects the best ones that align with the objectives of the proposed model. The set of solutions generated in this process is referred to as the Pareto solution set. Once the Pareto solution set for the current population (parent population) is determined and ranked (1), it is removed from the current population and transferred to the solution archive.

4.4. Determining the Fitness Function and Calculating the Probability of Selecting Each of the Parent Chromosomes

Based on the ranking performed in the previous step, the fitness function [127] is used to calculate the probability of selecting each of the parent chromosomes $\left(p\right)$ to produce the offspring. Then, from the remaining answers in the current set, the best answers (non-dominated answers) [136] related to the objectives are once again selected and assigned a rank of (2). Then, they are removed from the remaining population, and this process continues until all members of the population have their own Pareto rank.

$${1.3}^{(Rank\max -Rank p)}$$

(13)

$$P_p=f_p/\sum F_p$$

(14)

In the above relations, $f_p$ is a function of the fitness of parent $p$, and $p_p$ is the probability of choosing parent $p$ to produce offspring.

4.5. Checking the Convergence Condition of the Algorithm

The convergence condition of the algorithm is met when the Pareto solution set of each generation is nearly identical to that of the previous generation and the difference in the fitness function values between two consecutive iterations is negligible. Once these conditions are satisfied, the algorithm terminates. Figure 3 illustrates the network of activities involved in an agricultural project management process using the Critical Path Method (CPM). It outlines the sequence of tasks, beginning with the Preliminary Study for data collection and feasibility assessment, followed by Basic Engineering and Detail Engineering, where foundational and in-depth planning occurs. Before implementation, the Pre-Qualification (PRQ) stages (1 to 6) assess and evaluate various suitable solutions. The Construction (CONST) stages (1 to 6) represent the actual physical implementation of agricultural systems, such as planting or infrastructure installation. After construction, the project moves into the Test and Inspection phase to ensure quality, followed by Pre-Commissioning and Commissioning, where the systems are finalized and fully operational. This structured sequence captures the project’s lifecycle, emphasizing the management of cost, time, and quality throughout its various stages.

4.6. Generation of a New Generation

After selecting the parent strings, the selection operator and roulette wheel selection are used to create the next generation of strings. Then, the offspring for the new generation are also generated using crossover and mutation operators.

4.7. Transferring Archive Responses to the New Generation

In accordance with the principle of elitism in the algorithm, the set of Pareto solutions [129], with the first rank of each generation is preserved and transferred to the new generation [137].

4.8. Determining the Overall Optimal Solution Set for the Problem

The utility level for all Pareto solutions to the problem must be determined from the convergence of the solution, using the utility function defined in Equation (11). The solution with the highest utility then represents the overall optimal solution for balancing the time, cost, and quality of project activities.

5. Data Analysis

To evaluate the performance of the proposed genetic algorithm (GA), a case study was conducted where fuzzy alpha slicing was applied to estimate values for the cost, time, and quality. This technique helps quantify the uncertainty in expert evaluations, providing a clearer understanding of the risks associated with project activities. For instance, Haque and Hasin (2012) used NSGA-II to optimize irrigation scheduling in water-scarce regions, balancing water usage efficiency and crop yield, which highlighted the algorithm’s effectiveness in supporting sustainable agriculture practices [138]. Similarly, Luan et al. (2024) utilized NSGA-II for optimizing manufacturing processes by minimizing production costs and time while maximizing product quality [139]. Additionally, Zhang et al. (2022) demonstrated the application of NSGA-II in water resource management, specifically optimizing reservoir operations to balance flood control, water supply, and energy production [140]. These studies underscore the versatility and efficacy of the NSGA-II algorithm in optimizing complex, multi-objective problems across various sectors, including agriculture, manufacturing, and water management.

The project considered a set of different values for the fuzzy parameter $\alpha (\alpha =0,0.2,0.4,0.5,0.7,0.9,1)$ to evaluate the impact of varying risk levels on the optimization process. The results for the different α values enabled a thorough analysis of how the genetic algorithm (GA) performed under various levels of fuzziness and uncertainty. By adjusting the fuzzy parameter α, the study was able to evaluate the algorithm’s robustness and adaptability in handling real-world agricultural conditions, confirming its effectiveness in addressing dynamic and uncertain environments. The performance evaluation was conducted using MATLAB r2021b’s GA toolbox [58], which provided a comprehensive platform for coding and solving the optimization problem using a genetic algorithm approach. The toolbox streamlined the implementation process, enabling the efficient testing and refinement of the algorithm, ensuring that it could effectively manage the complexity and unpredictability inherent in agricultural systems.

Data Collection for Agricultural Projects (from 2003 to 2025):

To further validate the approach, we gathered relevant data for agricultural optimization from various sources as follows:

• Feed Grains Database by the USDA Economic Research Service [141]: This database provides comprehensive statistics on feed grains such as corn and barley, which are essential for understanding agricultural economics across various regions.
• Global Yield Gap Atlas [142]: This source offers yield gap data for crops such as wheat, barley, rice, and corn across different global regions, facilitating a comprehensive analysis of agricultural productivity and highlighting areas where optimization can be achieved.
• World Bank Commodity Price Data [143]: Historical monthly prices for key commodities such as rice, barley, maize (corn), and wheat are crucial for understanding market fluctuations, which play a significant role in optimizing cost and quality in agricultural projects.
• Enterprise budgets by The Ohio State University [144]: This dataset provides comprehensive production budgets for crops such as corn, soybeans, and wheat, offering essential information for evaluating the costs associated with agricultural production.

5.1. Sample Problem and Algorithm Parameter Setting

This study presents a detailed agricultural optimization problem involving 18 agricultural activities, each with seven potential execution methods. These methods represent a variety of farming techniques, crop varieties, and environmental conditions, all aimed at optimizing the balance between cost, time, and quality in agricultural projects. The methods cover a spectrum of scenarios, from pessimistic to optimistic estimates for time and cost, as well as varying quality outcomes, providing a comprehensive view of possible agricultural production futures.

For instance, in rice cultivation in Asia, each execution method considers factors such as planting techniques, irrigation methods, and climate variability. The impact of these factors on time, cost, and quality is evaluated using three-point estimation for time and cost (pessimistic, probable, and optimistic) and a five-point scale for quality (very low, low, medium, high, very high). This approach ensures that the model accounts for uncertainties and real-world complexities, such as fluctuating weather patterns and economic constraints. Similar methods are applied to barley production in Europe, wheat farming globally, and corn farming in the Americas, with each region’s unique agricultural conditions and production techniques considered.

The weighted percentages for time, cost, and quality are determined through consultations with agricultural experts, using techniques like the Delphi method [145]. In this study, the weights assigned to time, cost, and quality are 0.34, 0.34, and 0.32, respectively, reflecting the relative importance of each factor in agricultural optimization. This weighting system facilitates a balanced approach to resource allocation across diverse agricultural practices. Additionally, the relative importance of each activity is calculated based on expert input and presented in

Table 4. Time, cost, and fuzzy quality values as well as the weighted percentage of importance of the activities of the presented example problem.

NO	Activity	Method	Activity Time			Activity Cost			Activity Quality			${\mathit{w}}_{\mathit{i}\mathit{j}}$
			${\mathit{T}}_1$	${\mathit{T}}_2$	${\mathit{T}}_3$	${\mathit{C}}_1$	${\mathit{C}}_2$	${\mathit{C}}_3$	${\mathit{Q}}_1$	${\mathit{Q}}_2$	${\mathit{Q}}_3$
1	Preliminary Study	1	14	15	16	150,907,500	167,675,000	176,500,000	0.2	0.4	0.5	0.002
		2	14	15	16	135,816,750	150,907,500	158,850,000	0.3	0.5	0.7
		3	13	14	15	158,850,000	176,500,000	185,325,000	0.2	0.4	0.5
		4	13	14	15	150,907,500	167,675,000	176,500,000	0.7	0.8	1
		5	13	14	15	135,816,750	150,907,500	158,850,000	0.5	0.7	0.9
		6	12	13	14	158,850,000	176,500,000	185,325,000	0.3	0.5	0.7
		7	12	13	14	150,907,500	167,675,000	176,500,000	0.5	0.7	0.9
2	Basic Engineering	1	54	60	63	754,537,500	838,375,000	882,500,000	0.2	0.4	0.5	0.012
		2	54	60	63	679,083,750	754,537,500	794,250,000	0.3	0.5	0.7
		3	51	57	60	794,250,000	882,500,000	926,625,000	0.3	0.5	0.7
		4	51	57	60	754,537,500	838,375,000	882,500,000	0.3	0.5	0.7
		5	51	57	60	679,083,750	754,537,500	794,250,000	0.5	0.7	0.9
		6	46	51	54	794,250,000	882,500,000	926,625,000	0.5	0.7	0.9
		7	46	51	54	754,537,500	838,375,000	882,500,000	0.5	0.7	0.9
3	Detail Engineering	1	81	90	95	1,810,890,000	2,012,100,000	2,118,000,000	0.2	0.4	0.5	0.027
		2	81	90	95	1,629,801,000	1,810,890,000	1,906,200,000	0.3	0.5	0.7
		3	77	86	90	1,906,200,000	2,118,000,000	2,223,900,000	0.2	0.4	0.5
		4	77	86	90	1,810,890,000	2,012,100,000	2,118,000,000	0.7	0.8	1
		5	77	86	90	1,629,801,000	1,810,890,000	1,906,200,000	0.5	0.7	0.9
		6	69	77	81	1,906,200,000	2,118,000,000	2,223,900,000	0.3	0.5	0.7
		7	69	77	81	1,810,890,000	2,012,100,000	2,118,000,000	0.5	0.7	0.9
4	PRQ. Eng.	1	41	45	47	301,815,000	335,350,000	353,000,000	0.3	0.5	0.7	0.004
		2	41	45	47	271,633,500	301,815,000	317,700,000	0.5	0.7	0.9
		3	38	43	45	317,700,000	353,000,000	370,650,000	0.3	0.5	0.7
		4	38	43	45	301,815,000	335,350,000	353,000,000	0.7	0.8	1
		5	38	43	45	271,633,500	301,815,000	317,700,000	0.3	0.5	0.7
		6	35	38	41	317,700,000	353,000,000	370,650,000	0.2	0.4	0.5
		7	35	38	41	301,815,000	335,350,000	353,000,000	0.3	0.5	0.7
5	PRQ. 1	1	41	45	47	804,768,750	894,187,500	941,250,000	0.3	0.5	0.7	0.008
		2	41	45	47	724,291,875	804,768,750	847,125,000	0.3	0.5	0.7
		3	38	43	45	847,125,000	941,250,000	988,312,500	0.2	0.4	0.5
		4	38	43	45	804,768,750	894,187,500	941,250,000	0.7	0.8	1
		5	38	43	45	724,291,875	804,768,750	847,125,000	0.5	0.7	0.9
		6	35	38	41	847,125,000	941,250,000	988,312,500	0.2	0.4	0.5
		7	35	38	41	804,768,750	894,187,500	941,250,000	0.5	0.7	0.9
6	PRQ. 2	1	122	135	142	26,020,856,250	28,912,062,500	30,433,750,000	0.3	0.5	0.7	0.272
		2	122	135	142	23,418,770,625	26,020,856,250	27,390,375,000	0.5	0.7	0.9
		3	115	128	135	27,390,375,000	30,433,750,000	31,955,437,500	0.3	0.5	0.7
		4	115	128	135	26,020,856,250	28,912,062,500	30,433,750,000	0.3	0.5	0.7
		5	115	128	135	23,418,770,625	26,020,856,250	27,390,375,000	0.7	0.8	1
		6	104	115	122	27,390,375,000	30,433,750,000	31,955,437,500	0.5	0.7	0.9
		7	104	115	122	26,020,856,250	28,912,062,500	30,433,750,000	0.7	0.8	1
7	PRQ. 3	1	90	100	105	11,266,762,500	12,518,625,000	13,177,500,000	0.3	0.5	0.7	0.118
		2	90	100	105	10,140,086,250	11,266,762,500	11,859,750,000	0.5	0.7	0.9
		3	86	95	100	11,859,750,000	13,177,500,000	13,836,375,000	0.3	0.5	0.7
		4	86	95	100	11,266,762,500	12,518,625,000	13,177,500,000	0.5	0.7	0.9
		5	86	95	100	10,140,086,250	11,266,762,500	11,859,750,000	0.3	0.5	0.7
		6	77	86	90	11,859,750,000	13,177,500,000	13,836,375,000	0.3	0.5	0.7
		7	77	86	90	11,266,762,500	12,518,625,000	13,177,500,000	0.3	0.5	0.7
8	PRQ. 4	1	108	120	126	7,511,175,000	8,345,750,000	8,785,000,000	0.2	0.4	0.5	0.079
		2	108	120	126	6,760,057,500	7,511,175,000	7,906,500,000	0.5	0.7	0.9
		3	103	114	120	7,906,500,000	8,785,000,000	9,224,250,000	0.2	0.4	0.5
		4	103	114	120	7,511,175,000	8,345,750,000	8,785,000,000	0.7	0.8	1
		5	103	114	120	6,760,057,500	7,511,175,000	7,906,500,000	0.3	0.5	0.7
		6	92	103	108	7,906,500,000	8,785,000,000	9,224,250,000	0.5	0.7	0.9
		7	92	103	108	7,511,175,000	8,345,750,000	8,785,000,000	0.3	0.5	0.7
9	PRQ. 5	1	108	120	126	7,511,175,000	8,345,750,000	8,785,000,000	0.2	0.4	0.5	0.73
		2	108	120	126	6,760,057,500	7,511,175,000	7,906,500,000	0.5	0.7	0.9
		3	103	114	120	7,906,500,000	8,785,000,000	9,224,250,000	0.2	0.4	0.5
		4	103	114	120	7,511,175,000	8,345,750,000	8,785,000,000	0.7	0.8	1
		5	103	114	120	6,760,057,500	7,511,175,000	7,906,500,000	0.3	0.5	0.7
		6	92	103	108	7,906,500,000	8,785,000,000	9,224,250,000	0.5	0.7	0.9
		7	92	103	108	7,511,175,000	8,345,750,000	8,785,000,000	0.3	0.5	0.7
10	PRQ. 6	1	135	150	158	6,974,662,500	7,749,625,000	8,157,500,000	0.2	0.4	0.5	0.01
		2	135	150	158	6,277,196,250	6,974,662,500	7,341,750,000	0.3	0.5	0.7
		3	128	143	150	7,341,750,000	8,157,500,000	8,565,375,000	0.3	0.5	0.7
		4	128	143	150	6,974,662,500	7,749,625,000	8,157,500,000	0.3	0.5	0.7
		5	128	143	150	6,277,196,250	6,974,662,500	7,341,750,000	0.5	0.7	0.9
		6	115	128	135	7,341,750,000	8,157,500,000	8,565,375,000	0.5	0.7	0.9
		7	115	128	135	6,974,662,500	7,749,625,000	8,157,500,000	0.5	0.7	0.9
11	CONST. 1	1	54	60	63	1,073,025,000	1,192,250,000	1,255,000,000	0.3	0.5	0.7	0.075
		2	54	60	63	965,722,500	1,073,025,000	1,129,500,000	0.5	0.7	0.9
		3	51	57	60	1,129,500,000	1,255,000,000	1,317,750,000	0.3	0.5	0.7
		4	51	57	60	1,073,025,000	1,192,250,000	1,255,000,000	0.7	0.8	1
		5	51	57	60	965,722,500	1,073,025,000	1,129,500,000	0.5	0.7	0.9
		6	46	51	54	1,129,500,000	1,255,000,000	1,317,750,000	0.2	0.4	0.5
		7	46	51	54	1,073,025,000	1,192,250,000	1,255,000,000	0.5	0.7	0.9
12	CONST. 2	1	135	150	158	6,728,508,000	7,476,120,000	7,869,600,000	0.2	0.4	0.5	0.209
		2	135	150	158	6,055,657,200	6,728,508,000	7,082,640,000	0.3	0.5	0.7
		3	128	143	150	7,082,640,000	7,869,600,000	8,263,080,000	0.2	0.4	0.5
		4	128	143	150	6,728,508,000	7,476,120,000	7,869,600,000	0.7	0.8	1
		5	128	143	150	6,055,657,200	6,728,508,000	7,082,640,000	0.5	0.7	0.9
		6	115	128	135	7,082,640,000	7,869,600,000	8,263,080,000	0.3	0.5	0.7
		7	115	128	135	6,728,508,000	7,476,120,000	7,869,600,000	0.5	0.7	0.9
13	CONST. 3	1	162	180	189	19,811,718,000	22,013,020,000	23,171,600,000	0.2	0.4	0.5	0.031
		2	162	180	189	17,830,546,200	19,811,718,000	20,854,440,000	0.3	0.5	0.7
		3	154	171	180	20,854,440,000	23,171,600,000	24,330,180,000	0.2	0.4	0.5
		4	154	171	180	19,811,718,000	22,013,020,000	23,171,600,000	0.7	0.8	1
		5	154	171	180	17,830,546,200	19,811,718,000	20,854,440,000	0.5	0.7	0.9
		6	139	154	162	20,854,440,000	23,171,600,000	24,330,180,000	0.3	0.5	0.7
		7	139	154	162	19,811,718,000	22,013,020,000	23,171,600,000	0.5	0.7	0.9
14	CONST. 4	1	108	120	126	3,738,060,000	4,153,400,000	4,372,000,000	0.2	0.4	0.5	0.016
		2	108	120	126	3,364,254,000	3,738,060,000	3,934,800,000	0.5	0.7	0.9
		3	103	114	120	3,934,800,000	4,372,000,000	4,590,600,000	0.2	0.4	0.5
		4	103	114	120	3,738,060,000	4,153,400,000	4,372,000,000	0.7	0.8	1
		5	103	114	120	3,364,254,000	3,738,060,000	3,934,800,000	0.3	0.5	0.7
		6	92	103	108	3,934,800,000	4,372,000,000	4,590,600,000	0.5	0.7	0.9
		7	92	103	108	3,738,060,000	4,153,400,000	4,372,000,000	0.3	0.5	0.7
15	CONST. 5	1	68	75	79	1,644,746,400	1,827,496,000	1,923,680,000	0.3	0.5	0.7	0.018
		2	68	75	79	1,480,271,760	1,644,746,400	1,731,312,000	0.5	0.7	0.9
		3	64	71	75	1,731,312,000	1,923,680,000	2,019,864,000	0.3	0.5	0.7
		4	64	71	75	1,644,746,400	1,827,496,000	1,923,680,000	0.3	0.5	0.7
		5	64	71	75	1,480,271,760	1,644,746,400	1,731,312,000	0.7	0.8	1
		6	58	64	68	1,731,312,000	1,923,680,000	2,019,864,000	0.5	0.7	0.9
		7	58	64	68	1,644,746,400	1,827,496,000	1,923,680,000	0.7	0.8	1
16	CONST. 6	1	68	75	79	1,682,127,000	1,869,030,000	1,967,400,000	0.3	0.5	0.7	0.016
		2	68	75	79	1,513,914,300	1,682,127,000	1,770,660,000	0.5	0.7	0.9
		3	64	71	75	1,770,660,000	1,967,400,000	2,065,770,000	0.3	0.5	0.7
		4	64	71	75	1,682,127,000	1,869,030,000	1,967,400,000	0.7	0.8	1
		5	64	71	75	1,513,914,300	1,682,127,000	1,770,660,000	0.3	0.5	0.7
		6	58	64	68	1,770,660,000	1,967,400,000	2,065,770,000	0.2	0.4	0.5
		7	58	64	68	1,682,127,000	1,869,030,000	1,967,400,000	0.3	0.5	0.7
17	Test and Inspection	1	68	75	79	1,532,604,600	1,702,894,000	1,792,520,000	0.3	0.5	0.7	0.014
		2	68	75	79	1,379,344,140	1,532,604,600	1,613,268,000	0.3	0.5	0.7
		3	64	71	75	1,613,268,000	1,792,520,000	1,882,146,000	0.2	0.4	0.5
		4	64	71	75	1,532,604,600	1,702,894,000	1,792,520,000	0.7	0.8	1
		5	64	71	75	1,379,344,140	1,532,604,600	1,613,268,000	0.5	0.7	0.9
		6	58	64	68	1,613,268,000	1,792,520,000	1,882,146,000	0.2	0.4	0.5
		7	58	64	68	1,532,604,600	1,702,894,000	1,792,520,000	0.5	0.7	0.9
18	Pre-Commissioning and Commissioning	1	14	15	16	1,270,940,400	1,412,156,000	1,486,480,000	0.3	0.5	0.7	0.016
		2	14	15	16	1,143,846,360	1,270,940,400	1,337,832,000	0.5	0.7	0.9
		3	13	14	15	1,337,832,000	1,486,480,000	1,560,804,000	0.3	0.5	0.7
		4	13	14	15	1,270,940,400	1,412,156,000	1,486,480,000	0.5	0.7	0.9
		5	13	14	15	1,143,846,360	1,270,940,400	1,337,832,000	0.3	0.5	0.7
		6	12	13	14	1,337,832,000	1,486,480,000	1,560,804,000	0.3	0.5	0.7
		7	12	13	14	1,270,940,400	1,412,156,000	1,486,480,000	0.3	0.5	0.7

Algorithm is also considered to be Between 60 and 65. The probability of crossover and mutation during the execution stages of the algorithm is also given in Table 5.

, highlighting how different activities contribute to the overall success of the project.

The Genetic Algorithm (GA) is used to identify the optimal combination of execution methods for a project, taking into account the complex interdependencies between various activities. In configuring the GA, selecting an appropriate population size for each generation is critical. Larger population sizes provide a broader search space, thereby increasing the likelihood of finding a near-optimal solution. However, this also results in increased computational time, which can diminish the efficiency of the algorithm. Consequently, this study recommends using a population size of five or nine methods per activity, corresponding to approximately 100 individuals per generation. The algorithm’s execution is constrained by a maximum iteration limit of 90, a balance that facilitates both exploration and convergence towards an optimal solution. The algorithm’s performance is also dependent on the crossover and mutation probabilities, as detailed in

Table 5. Parameters of the proposed genetic algorithm.

Parameters	Values
Population Size (pop size)	100
Maximum Total Number of Iterations	60–65
Crossover Probability	0.80
Mutation Probability	0.42

. These parameters regulate the exploration of new solutions and the refinement of existing ones.

To validate the performance of the genetic algorithm (GA), agricultural data from 2003 to 2025 is utilized, incorporating key performance indicators (KPIs) for various crop types across multiple regions. This comprehensive dataset includes historical data for crops such as rice, barley, wheat, and corn, providing a detailed examination of how yield, cost, and time have evolved over time. The study investigates the influence of factors such as climate change, technological advancements, and market trends on agricultural productivity, costs, and quality.

This historical data are essential for understanding regional differences in farming practices and for applying the GA to real-world agricultural scenarios. The primary objective of the GA is to optimize the trade-offs between time, cost, and quality, thereby improving the efficiency of agricultural production. By modeling and analyzing these trade-offs, the GA helps forecast the future of agriculture, taking into account the growing impact of climate change and global market fluctuations. The GA’s ability to identify the most effective execution methods for each activity, while accounting for the specific conditions and constraints of different crops and regions, further enhances its practical applicability.

Additionally, the integration of fuzzy logic into the GA improves its ability to handle uncertainty in expert assessments and estimates. For instance, fuzzy alpha slicing can be applied to expert evaluations concerning time, cost, and quality, enabling the algorithm to more effectively manage the inherent uncertainties and risks in agricultural contexts. This enhances the adaptability and realism of the solutions generated by the algorithm, addressing the unpredictable nature of factors such as weather, market fluctuations, and labor availability.

Overall, the integration of genetic algorithms and fuzzy logic forms a powerful framework for optimizing agricultural production. By combining historical data, expert insights, and computational models, the GA facilitates more informed decision making for farmers, policymakers, and agricultural managers. The insights generated through this approach have the potential to significantly enhance agricultural productivity, mitigate risks, and promote sustainable growth in global food production. Through a detailed analysis of execution methods and their corresponding outcomes, the GA provides a comprehensive tool for optimizing agricultural practices, addressing the dynamic challenges posed by environmental, economic, and technological changes. To illustrate this, consider the following example from agricultural optimization. Table 4 presents a case study where various activities within an agricultural process were analyzed based on time, cost, fuzzy quality values, and the weighted importance of each activity. The table provides insights into how genetic algorithms and fuzzy logic can be applied to assess and optimize each activity in terms of resource usage and quality. In the table, the activities are evaluated not only based on their time and cost but also using fuzzy quality values that account for uncertainties and imprecision in the data. The weighted percentages of importance are used to prioritize activities based on their significance to the overall optimization process. The implementation of such advanced computational techniques in agriculture is expected to offer not only increased efficiency in resource management but also a reduction in environmental impacts. By simulating various agricultural practices and assessing their outcomes through fuzzy logic and the GA, farmers and stakeholders can make data-driven decisions that optimize resource utilization and minimize waste. These systems can also be integrated with smart farming technologies, such as sensors and IoT devices, to create more responsive and automated solutions for optimizing irrigation, pest control, and crop selection. As a result, the combination of fuzzy logic, genetic algorithms, and other AI-driven technologies presents a promising direction for achieving sustainable agricultural practices that can meet the growing demands of the global population while maintaining ecological balance.

5.2. Analysis of the Output Results and Figures

The optimization of time, cost, and quality in project management has long been a challenge, particularly when these factors are subject to uncertainty. In the context of the proposed model, these three factors are treated as fuzzy numbers, representing their inherent uncertainty. To facilitate the identification and comparison of Pareto optimal solutions, the surface center fuzzification method is employed, converting fuzzy values into precise figures for easier analysis [146]. The model is solved using the NSG II algorithm at different cutoff values (α), resulting in various Pareto solutions, each corresponding to different trade-offs between cost, quality, and time. The appropriate sample size must be determined in the analysis [147].

Table 5 illustrates the outcomes for various α values, where the relationship between these factors evolves with changing cutoff values. For instance, at α = 1, the results are more optimistic, favoring time efficiency, probable cost, and average quality, aligning with the expectations set under certainty conditions. As the conditions shift toward greater uncertainty (α = 0), the solutions tend to reflect probable time, probable cost, and reduced quality. These findings are crucial in understanding how different levels of certainty impact project outcomes.

This model’s applicability extends beyond project management theory into real-world agricultural practices. By analyzing agricultural systems such as rice cultivation in Asia, barley production in Europe, and wheat and corn farming across the Americas, the model can be adapted to account for fluctuations in time, cost, and quality. Key performance indicators (KPIs), including cost savings, production efficiency, and crop quality, will be assessed through case studies, demonstrating how the model can enhance decision making in the agricultural sector under varying conditions.

As mentioned before, the values of time, cost, and quality are fuzzy numbers and are the outputs of the model. To more easily determine the Pareto solutions of the problem and compare them with each other, the surface center fuzzification method is used to transform these values into precise figures [146]. Table 5 shows that the proposed model is solved using the $NSG II algorithm$ for different cutoffs $\alpha ,$ resulting in various Pareto solutions. For each cutoff value α, a different cost and quality are obtained to complete the project at a given time. If we examine

Table 6. Some Pareto solutions of the presented example problem for different cuts $\alpha$.

Activity Mode	Time (T1)	Cost (C1)	Quality (Q1)	Activity Mode	Fuzzy Time	Fuzzy Cost	Fuzzy Quality	Activity Mode	Average Time (α)	Average Cost (α)	Average Quality (α)
1	610	94,631,573,925	0.300	1	636	90,794,810,925	0.365	1	666.333	103,444,281,225	0.489
2	676	105,146,193,250	0.500	2	705	100,883,123,250	0.558	2	694.333	99,272,256,392	0.548
3	713	110,555,076,500	0.665	3	742	106,138,835,000	0.721	3	703.667	100,200,218,825	0.630
4	613	96,127,607,830	0.313	4	680	95,773,481,415	0.265	4	700.400	103,868,416,294	0.447
5	681	104,486,530,250	0.472	5	718	111,895,035,500	0.612	5	670.667	104,694,498,768	0.447
6	648.8	93,806,526,628	0.331	6	704	101,963,615,900	0.525	6	703.400	101,357,095,000	0.511
7	661	93,192,569,780	0.356	7	717	101,296,271,500	0.726	7	713.533	100,724,663,609	0.532

for the selected methods for the activities, at $\alpha =1$, the analysis of the results in Table 5 shows that the answers lean towards optimistic time, probable cost, and average quality, reflecting the project contract clauses under certainty conditions, which are also expected by the project manager. However, as certainty conditions shift towards $\alpha =0$, the answers from the algorithm tend towards probable time, probable cost, and lower quality. In modern agriculture, this approach can be applied to various crops and practices, such as rice cultivation in Asia, barley production in Europe, wheat farming globally, and corn farming in the Americas, and all of these are influenced by fluctuations in time, cost, and quality. To assess the effectiveness of the model in these agricultural contexts, key performance indicators $\left(KPIs\right)$ such as cost savings, production efficiency, and crop quality will be evaluated through case studies of real-world agricultural practices, offering insights into how these variables can be managed under different conditions.

The Pareto solutions of the problem, obtained using the center-of-surface defuzzification method, provided definitive values for decision making. Table 6 highlights how the proposed model, solved using the $NSG II$ algorithm for different cuts α\alphaα, produced diverse Pareto solutions. For instance, at $\alpha =1\backslash alpha=1\alpha =1$, the solutions tend towards optimistic time, probable cost, and average quality, reflecting contractual expectations under conditions of certainty. As $\alpha \backslash alpha\alpha$ decreases toward zero, the solutions shift towards probable time, probable cost, and lower quality, reflecting the influence of expert opinions under conditions of uncertainty and project risks. This shift demonstrates how uncertainties and risks can act as both threats and opportunities. Under uncertain conditions, incorporating expert opinions might deteriorate project metrics, while focusing on opportunities could improve them. This flexibility, enabled by the alpha-cut technique, helps the project manager weigh priorities like time, cost, and quality to select solutions with the highest utility, as guided by Equation (11). For example, at $\alpha =0.4\backslash alpha=0.4\alpha =0.4,$ one Pareto optimal solution with a determined utility value is shown in

Table 7. Set of overall optimal solutions to the problem for $\alpha =0.4$.

Description	Values
Optimal         Solution	(2,2,6,1,7,5,7,1,2,5,2,6,1,1,2,2,7,1) ${\mathrm{X}}_{\mathrm{G}}=\{{\mathrm{X}}_1^{\mathrm{G}},\dots ,{\mathrm{X}}_{\mathrm{n}}^{\mathrm{G}}\}$
Optimal         Fuzzy Project	(643.6, 698,741.2) Duration (${\mathrm{T}}^{\left(\mathrm{F}\right)})$
Optimal          Fuzzy Project	(93.739.101.852,101.890.328.100,108.305.011.980) Cost (${\mathrm{C}}^{\left(\mathrm{F}\right)})$
Optimal          Fuzzy Project	(0.365, 0.525, 0.739) Quality (${\mathrm{Q}}^{\left(\mathrm{F}\right)})$
Optimal          Project	694.267 $\mathrm{D}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(\mathrm{T}\right)$
Optimal          Project	$\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\left(\mathrm{C}\right)$ 101311480648
Optimal          Project	0.543
Quality (Q)
$│Solution Utility\left(U\right) │$	344.459 × 10

.

In modern agriculture, this approach has the potential to revolutionize crop management by effectively balancing uncertainties such as climate risks and economic constraints. Analyzing crop cultivation trends—such as rice in Asia, barley in Europe, wheat globally, and corn in the Americas—from 2003 to 2025 highlights patterns influenced by both opportunities (e.g., technological advancements) and threats (e.g., climate change). The use of comprehensive datasets, including the USDA ERS Feed Grains Database, the Global Yield Gap Atlas, World Bank Commodity Price Data, and enterprise budgets from The Ohio State University, greatly enhances the precision of these analyses. By viewing uncertainty as an opportunity rather than a risk, modern agriculture can achieve improved yields and greater sustainability, offering a strategic roadmap with a promising future. This framework for validation and analysis provides decision makers with the tools to optimize agricultural outcomes, similar to how a project manager selects optimal solutions in industrial projects.

As shown in Table 7, the optimal solution for the presented sample problem involves the strategic selection of methods for project activities, tailored to different conditions. For example, the first, second, ninth, eleventh, fifteenth, and sixteenth activities are carried out using the second method, which is characterized by pessimistic time, optimistic cost, and medium quality. The third and twelfth activities employ the sixth method, focusing on optimistic time, pessimistic cost, and medium quality. The fourth, eighth, thirteenth, fourteenth, and eighteenth activities are executed using the first method, which involves pessimistic time, probable cost, and low quality. In contrast, the fifth, seventh, and seventeenth activities are performed using the seventh method, emphasizing optimistic time, probable cost, and high quality. Finally, the sixth and tenth activities are executed using the fifth method, resulting in probable time, optimistic cost, and high quality. According to the contract documents, the final project time and cost are set at 720 time units and 111,500,000,000 cost units, respectively. Model validation reveals that the defuzzified time and cost values for all solutions are below these thresholds, thereby confirming the reliability of the model within the context of fuzzy multi-objective optimization.

The alpha-cut technique enables the project manager to adjust risk levels based on expert opinions. At α = 0\alpha = 0α = 0, higher uncertainty is reflected, whereas α = 1\alpha = 1α = 1 moves toward certainty, yielding definite values for time, cost, and quality. By incorporating the opinions of experts, the algorithm flexibly addresses risks and uncertainties, either as threats or opportunities. The NSG II algorithm further enhances computational efficiency, solving the problem involving 18 activities and seven execution methods per activity in under 10 min. This rapid convergence makes the model ideal for large-scale projects, enabling optimal execution methods and balancing objectives effectively. Applying this framework to modern agriculture introduces transformative potential for optimizing crop cultivation under uncertainty. From 2003 to 2025, data collection has provided insights into rice cultivation in Asia, barley in Europe, wheat farming globally, and corn in the Americas. Utilizing resources such as the USDA ERS Feed Grains Database, the Global Yield Gap Atlas, and World Bank Commodity Price Data enhances the ability to analyze costs, yields, and risks. The model’s alpha-cut approach offers a valuable tool for agricultural managers to balance uncertainties such as climate variability, economic constraints, and fluctuating input costs. By framing risks as opportunities, this approach enables the implementation of sustainable practices that can enhance productivity and foster a more resilient food system. Similarly to how time, cost, and quality are balanced in industrial projects, this methodology provides a strategic framework for the future of agriculture. By integrating expert insights with optimization techniques, it addresses both present challenges and emerging opportunities, guiding agricultural systems toward greater efficiency and sustainability.

As shown in Figure 4, the genetic algorithm is applied to multi-objective optimization, where it efficiently handles the trade-offs between multiple conflicting objectives. This figure illustrates the percentage distribution of solutions generated by the algorithm, demonstrating how the genetic algorithm explores the solution space by simulating processes such as selection, crossover, and mutation. The representation allows for an understanding of how the algorithm converges toward optimal solutions while maintaining a diverse set of potential outcomes. It highlights the algorithm’s effectiveness in balancing the various objectives, ensuring that no single objective is overly prioritized at the expense of the others, as seen below:

The description of Figure 4 is as follows: The genetic algorithm (GA) aims to optimize cost, time, and quality in agricultural decision making. The implementation involves initializing a population of potential solutions, applying selection, crossover, and mutation to evolve better solutions over multiple generations. The parameters defined include a population size of 100; a mutation probability of 0.42; and a crossover probability of 0.80, iterated for 60–65 generations. The fitness function evaluates multi-objective optimization, and the results are visualized as convergence curves, illustrating cost reduction over generations. It initializes a random population, evaluates fitness using a sum-of-squares function, applies selection (roulette wheel), crossover, and mutation, and tracks the best cost per generation. The output includes a convergence curve showing cost reduction across 65 generations. The X-axis denotes the number of generations (iterations), while the Y-axis represents the cost function value. At the beginning of the optimization, the cost is high due to the randomly initialized population. However, as the algorithm evolves through selection, crossover, and mutation, the cost function rapidly declines, achieving near-optimal solutions within the first 20–30 generations. This demonstrates the efficiency of the genetic algorithm in quickly identifying high-quality solutions within a limited number of iterations. The smooth decay curve in the plot signifies a well-tuned parameter selection, where an 80% crossover probability and a 42% mutation rate contribute to a balanced exploration–exploitation mechanism. The asymptotic behavior towards the later generations indicates that the algorithm has reached a near-optimal solution, stabilizing around a minimal cost value. This convergence pattern reinforces the robustness of the proposed fuzzy-genetic optimization framework in solving multi-objective agricultural planning problems, making it a valuable tool for decision makers in precision agriculture and sustainable resource management.

As illustrated in Figure 5, the 3D Pareto front visualization provides a clear depiction of the trade-offs between cost, time, and quality. This graphical representation allows for a deeper understanding of how these three critical factors interact and influence one another in decision-making processes. By visualizing the Pareto front in three dimensions, it becomes easier to identify optimal solutions that balance these variables effectively, highlighting the areas where improvements in one aspect may lead to compromises in the others. This analysis is crucial for evaluating the performance of different strategies and making informed decisions in complex systems, as described below.

The description of Figure 5 is as follows: The 3D Pareto diagram represents an optimized decision-making model for balancing time, cost, and quality in agricultural project management. It shows different possible solutions, each offering a unique combination of these three factors. The goal is to help decision makers understand how adjusting one factor—such as reducing cost—might impact the others, like increasing project time or decreasing quality. Each solution is represented as a point in the diagram, with values carefully calculated using fuzzy logic and genetic algorithms, which are mathematical techniques that help optimize uncertain and complex situations. Instead of a single “best” answer, the diagram provides a range of optimal solutions, allowing users to choose based on their priorities. The Pareto optimal solutions in this study illustrate the trade-offs between cost, time, and quality in agricultural project management. For example, the first solution (α = 1) achieves a time of 666.33 days, a cost of 103.44 billion, and a quality score of 0.489. In contrast, another optimized solution achieves a slightly lower cost of 99.27 billion but requires 694.33 days and a moderate quality of 0.548. This pattern demonstrates how prioritizing cost savings can increase project duration while marginally improving product quality. The data make it evident that no single “best” solution exists, but rather a set of efficient choices is provided, each with unique advantages. In agricultural planning, a farmer or organization may want to minimize costs while ensuring a high level of product quality. However, reducing costs too much might result in longer production times or lower quality outputs. This diagram makes these trade-offs visible by linking different solutions with a red line, showing how small adjustments in one factor affect the others. Additionally, a color gradient is used to indicate quality levels, making it easier to compare different options. Even without seeing the diagram, one can imagine it as a map of the best possible choices, where the most balanced solutions are highlighted, guiding decision makers toward an optimal plan that suits their needs. The significance of this research lies in its ability to assist precision agricultural and sustainable resource management. By applying fuzzy-genetic optimization, the model accounts for uncertainties such as weather conditions, soil quality, and market fluctuations—factors that traditional planning models struggle to address. A closer look at the higher-cost solutions shows an inverse relationship between cost and time efficiency. The most expensive solution, at 104.69 billion, completes the project in 670.67 days, yet delivers a slightly lower quality score of 0.447. Meanwhile, one of the most time-efficient options (703.40 days, 101.36 billion, 0.511 quality) suggests that moderate cost adjustments can enhance overall project balance. The color gradient in the diagram visually reinforces this relationship—higher-quality solutions appear at higher cost levels, proving that maintaining superior quality often demands increased financial investment. Ultimately, this multi-objective optimization approach offers decision makers the flexibility to prioritize objectives based on the available resources and goals. If cost minimization is the priority, solutions near 99–101 billion offer reasonable trade-offs. However, if time efficiency matters most, options within 670–700 days provide a practical balance. This research proves that genetic algorithms and fuzzy logic can successfully handle real-world agricultural uncertainty, providing quantifiable insights for sustainable decision making. This allows policymakers, farm managers, and agribusinesses to make informed and data-driven choices without being overwhelmed by the complexity of multiple conflicting objectives. The diagram serves as a powerful tool, not just for visualizing these trade-offs but for empowering smarter agricultural decisions, leading to higher efficiency, reduced waste, and better resource utilization in food production systems.

For a detailed analysis of Figure 6 (fuzzy multi-objective optimization with genetic algorithm), the author of the article has designed two figure models and provides the following explanations:

The description of Figure 6 is as follows: The first diagram (a) presents a 3D visualization of the cost–time–quality trade-off in project scheduling. The X-axis represents project duration (T), the Y-axis denotes the project cost (C), and the Z-axis signifies project quality (Q). The red markers indicate different optimal solutions that balance cost, time, and quality, demonstrating the complexity of multi-objective decision making. As project duration increases, cost variations fluctuate significantly, and a clear inverse relationship emerges between cost and quality—indicating that improving quality often results in higher costs. The second diagram (b) offers a 2D perspective on the relationship between project duration and cost, with quality as a color gradient to highlight its influence. The first diagram (a) presents a 3D visualization of the cost–time–quality trade-off in project scheduling. The X-axis represents project duration (T), the Y-axis denotes project cost (C), and the Z-axis signifies project quality (Q). The red markers indicate different optimal solutions that balance cost, time, and quality, demonstrating the complexity of multi-objective decision making. As project duration increases, cost variations fluctuate significantly, and a clear inverse relationship emerges between cost and quality, indicating that improving quality often results in higher costs. The second diagram (b) offers a 2D perspective on the relationship between project duration and cost, with quality represented as a color gradient to highlight its influence. The darker points represent lower-quality outcomes, while the brighter points indicate higher quality. This visualization emphasizes that while minimizing duration may reduce costs, it also risks sacrificing quality. Decision makers can leverage this insight to determine the most efficient project configurations based on their priorities—whether these are cost savings, rapid completion, or enhanced quality. Together, these visualizations provide a data-driven approach to optimizing project management. The trade-offs in an agricultural optimization problem using a fuzzy multi-objective approach with a genetic algorithm become visible. Our study plots fuzzy project duration, cost, and quality for different uncertainty levels (α) to show how these factors change under varying conditions. The genetic algorithm optimizes resource allocation for agricultural projects by balancing cost, time, and quality. The results guide decision making under uncertainty, ensuring sustainability and efficiency. The plotted graphs provide insights into how uncertainties affect agricultural outcomes, supporting strategic planning for resilient farming practices. The multi-objective analysis highlights trade-offs inherent in real-world scenarios, emphasizing the importance of fuzzy logic-based decision making to balance competing project constraints. By integrating these insights, project managers can make informed decisions that align with corporate objectives while ensuring sustainable and high-performance project execution.

6. Discussion and Conclusions

This study underscores the significant potential of integrating fuzzy logic and genetic algorithms to address the complex trade-offs between cost, time, and quality in modern agriculture. The agricultural sector faces mounting pressures due to unpredictable climate patterns, economic constraints, and the growing demand for sustainable practices. These challenges are further exacerbated by the inherent uncertainties in agricultural processes, such as fluctuating yields, variable input costs, and inconsistent product quality. By incorporating a fuzzy multi-objective optimization framework, this research effectively tackles these uncertainties, providing a more flexible and resilient decision-making model for managing agricultural resources.

The fusion of fuzzy logic and genetic algorithms presents a powerful tool for navigating the complexities inherent in agricultural optimization. The fuzzy logic component addresses the uncertainty and variability characteristic of agricultural systems, facilitating more informed decision making through its alpha-cut technique. This adaptability, with the capacity to transition between pessimistic and optimistic scenarios, ensures the model remains applicable across a range of environmental and economic contexts. Meanwhile, the computational efficiency of the genetic algorithm enables the model to manage large-scale agricultural systems, offering rapid and effective solutions, even when confronted with vast datasets and multifaceted challenges.

The case study, which includes crops from diverse global regions—such as rice in Asia, barley in Europe, wheat worldwide, and corn in the Americas—demonstrates the versatility of the proposed model. By utilizing comprehensive datasets, including those from the USDA and the Global Yield Gap Atlas, the study illustrates how the model effectively balances the competing objectives of cost, time, and quality, while managing the associated risks and opportunities.

The model’s ability to prioritize risk mitigation under uncertain conditions (with α = 0) and emphasize efficiency and sustainability under more certain conditions (with α = 1) makes it a valuable tool for agricultural managers. The model effectively accounts for the volatile nature of agriculture, offering practical solutions that can be applied in real-world contexts. Additionally, the rapid convergence of the genetic algorithm ensures that even complex optimization problems are resolved efficiently, making the model both scalable and computationally efficient. This research highlights the transformative potential of combining fuzzy logic with genetic algorithms to optimize agricultural decision making. It provides a pathway toward more sustainable, resilient, and productive agricultural practices that can help address the growing challenges of global food security.

As agricultural systems continue to evolve in response to environmental pressures and technological advancements, this approach represents a crucial step toward achieving a balanced and efficient future for global agriculture. The integration of fuzzy logic and genetic algorithms to manage the cost–time–quality trade-off offers a promising solution to the multifaceted challenges faced by the agricultural industry. However, as the agricultural landscape shifts due to emerging technologies, environmental changes, and evolving economic conditions, more research is needed. Future studies could incorporate machine learning techniques, climate adaptation models, sustainability considerations, and real-time data to further enhance the effectiveness of these optimization frameworks, ultimately driving more sustainable and efficient agricultural practices on a global scale.

This study on the integration of fuzzy logic and genetic algorithms (GAs) for agricultural optimization presents a significant contribution to the field, combining well-established computational techniques in a novel way. While similar studies have explored fuzzy logic and GAs in agriculture, this study offers unique insights for managing uncertainties and optimizing the cost–time–quality trade-offs across various agricultural scenarios. Here, we provide an overview of the similarities and unique aspects of our research compared to previous works as follows:

Li et al. (2023) and Soni et al. (2019) applied fuzzy-GA models for optimizing water use efficiency under uncertain rainfall conditions, a similar approach to this study’s focus on irrigation management in rice cultivation under fluctuating environmental conditions [95,148,149].

Zhao et al. (2024) and Saraswat et al. (2023) used fuzzy-GA techniques to address soil fertility and market variability in barley production. This aligns with our study’application of fuzzy-GA models to ensure sustainable production under varying conditions, particularly in Europe for crops like barley [150,151].

Gong et al. (2023) demonstrated the use of GAs for optimizing conflicting objectives like maximizing crop yield while minimizing costs and maintaining environmental sustainability. Similarly, this study addresses multiple objectives such as crop yield, resource efficiency, and environmental impact, making the approach comparable to these studies in terms of balancing trade-offs [152].

Gao et al. (2023) also highlighted the use of GAs in solving complex, multi-objective agricultural problems, which resonates with our focus on dynamic optimization in response to environmental changes and market demands [153].

Sachithra and Subhashini (2023) and Mondejar et al. (2021) used optimization techniques to explore the balance between agricultural productivity and environmental sustainability, aligning with our integration of fuzzy-GA models to optimize global crops like wheat and rice, in line with the United Nations Sustainable Development Goals (SDGs) [154,155].

The integration of alpha-cut techniques in the proposed model allows for adjustments between optimistic and pessimistic scenarios based on varying risk levels, offering a more nuanced approach compared to previous studies. The ability to adapt under conditions of uncertainty enhances the flexibility and applicability of the framework, particularly in the context of unpredictable agricultural environments. While prior research has largely focused on optimizing individual factors such as yield, water usage, or cost reduction, the current study introduces a comprehensive approach that effectively balances the trade-offs between cost, time, and quality. Multi-dimensional optimization, especially within the complexity of global agricultural systems, makes a significant contribution to the field. The extensive use of real-world data from diverse regions—including Southeast Asia for rice, Europe for barley, and the Americas for corn—drawn from reputable sources such as the USDA, Global Yield Gap Atlas, and FAOSTAT, further distinguishes our study. Region-specific validation not only provides depth but also enhances the generalizability of the model across various agricultural contexts.

Additionally, this study aligns with the United Nations Sustainable Development Goals (SDGs), particularly SDG 2 (Zero Hunger), SDG 12 (Responsible Consumption and Production), SDG 13 (Climate Action), and SDG 15 (Life on Land) [73]. By improving agricultural productivity and resource efficiency while minimizing environmental impacts, the study supports global efforts to achieve food security, promote sustainable practices, and mitigate the effects of climate change, contributing to a more sustainable agricultural future.

7. Limitations and Future Studies

7.1. Regional and Crop-Specific Optimization Models

While the present study provides a comprehensive global perspective, future research could delve deeper into regional and crop-specific optimization models. Different regions and crop types possess distinct requirements, constraints, and challenges. Developing tailored models for specific crops—such as rice, barley, wheat, and corn—and for specific agricultural regions—such as Southeast Asia for rice or Europe for barley—would yield more precise optimization solutions that take into account local conditions, farming practices, and market dynamics. Such region-specific models could further enhance the accuracy and applicability of optimization strategies.

7.2. Socioeconomic and Policy Analysis

The influence of socioeconomic factors and agricultural policies on farming practices is crucial for a holistic approach to optimization. Future research could expand the current framework by incorporating the social and political dimensions of agriculture. For instance, factors like labor availability, education levels, and access to technology could be integrated into the optimization model to better reflect the realities of various farming systems. Additionally, policy measures—such as subsidies for sustainable agricultural practices or penalties for excessive chemical fertilizer use—could be considered in the decision-making process to ensure alignment with government regulations and broader agricultural goals. This integration would enhance the model’s relevance and adaptability across different socio-political environments.

7.3. Optimization of Post-Harvest Operations

The agricultural value chain extends beyond crop cultivation to include post-harvest operations such as storage, transportation, and processing, all of which play a significant role in determining the overall cost and quality of agricultural products. Future research could explore the application of fuzzy logic and genetic algorithms in optimizing post-harvest activities, thereby minimizing waste, enhancing storage conditions, and reducing losses during transportation and processing. This would help address critical inefficiencies within the post-harvest phase, contributing to higher-quality outputs and more sustainable agricultural practices.