Unveiling the Potential of Metaheuristics in Transportation: A Path Towards Efficiency, Optimization, and Intelligent Management

Abstract

Importance: This bibliometric analysis of the application of metaheuristics in transportation and logistics examines over two decades of research (1999–present), aiming to uncover global trends, anticipate future directions, and highlight how interconnections between key factors facilitate the development of practical and sustainable solutions for the industry. Methodology: A quantitative approach is employed to analyze the evolution of the discipline by reviewing an extensive database of relevant research and key authors and utilizing advanced data processing tools. This analysis enables the assessment of advances in the optimization of metaheuristic models, with an impact on time and cost savings from an economically sustainable perspective. Results: The use of metaheuristics optimizes the efficiency and competitiveness of the transportation sector while promoting a positive economic impact on companies. The main areas of application are optimization and metaheuristic methods, cost and operational efficiency, planning and scheduling, logistics and transportation, supply chain and logistics networks, energy and sustainability, and demand and users. Additionally, genetic algorithms stand out as particularly important. Conclusions: This research provides a comprehensive and detailed view of the impact of metaheuristics on the transportation sector, highlighting their current and future trends (such as artificial intelligence) and their economic relevance.

1. Introduction

Historically, metaheuristics have proven remarkably effective in solving various complex combinatorial optimization problems across multiple practical application fields [1]. This bibliometric study aims to examine the evolution of research on metaheuristics in the transportation sector from 1999 to 2022, with a particular focus on their economic impact. This research is notable for being the first to comprehensively and at a large scale address the application of metaheuristics in transportation, considering their economic and financial impact on companies globally. The analysis focuses on 719 articles published over a 24-year period authored by 1897 researchers. This period was chosen because significant advancements in optimization problem solutions addressed by metaheuristics have occurred over the past two decades [2].

In the current context, the transportation and logistics sector faces increasingly complex challenges, which are being addressed through the implementation of metaheuristics and advanced algorithms. Among the main obstacles faced by the industry are the growing complexity of information systems, the globalization of supply chains, the need for real-time decision-making, the scalability of transportation networks at an international level, and the improvement of predictive capabilities to bring decisions closer to more realistic scenarios. The key lies in adapting to changing environments, such as market demand variability, while keeping specific goals of efficiency, sustainability, and profitability in sight.

Moreover, the current state of the literature often focuses on individual case studies or specific algorithmic approaches without offering a comprehensive perspective on the problems these solutions address. It also has the added value of broadening the scientific field by simultaneously focusing on a critical aspect for companies: the economic and financial impact of these intelligent systems. This study aims to fill that gap by examining not only the evolution and application trends of metaheuristics in transportation but also their economic implications.

Over the past two decades, as computational limitations have decreased, the international scientific community has refined and expanded the use of metaheuristic techniques. This research captures these changes and insights, adopting a multidisciplinary approach that highlights the virtues of metaheuristics to optimize the sector and showcase their solutions to complex problems. One of the central challenges in this new global technological revolution is integrating these advancements with the new opportunities offered by machine learning and deep learning artificial intelligence.

Currently, no bibliometric studies focus on this area, making it scientifically valuable to measure the evolution and address the significance of the cost–benefit relationship these optimization techniques represent. Additionally, their predictive power enables improvements in companies’ financial performance through cost savings and better investment decisions [3,4,5,6,7]

The study highlights the following aspects:

• Algorithms and computation-based decision support: Hybrid algorithms, neural networks, cooperative intelligent transport systems, and swarm intelligence, among others.
• Transport: Applicability in maritime transport, impact on inventory management, economic effects of air transport, public transport, green transport and smart cities, multimodal transport, rail transport, electric vehicles, simultaneous collection and delivery systems, logistics optimization, vehicle routing problems, and urban traffic congestion, among others.
• Business: Pursuit of cost savings and improved viability, the key to business survival through efficiency, company benefits, supplier selection calculations, minimization of customer waiting times, the impact of metaheuristics on customer satisfaction, and business intelligence systems.
• Sustainability: From the perspectives of the economy, transport, and the environment.
• Future: flying taxis, drone delivery, and new transport solutions that promise to revolutionize the industry and improve mobility in cities.

The justification centers on its ability to solve complex economic problems in the sector, making transportation companies more efficient and competitive in an increasingly specialized and demanding market [8]. This efficiency improvement not only boosts competitiveness but also enhances the brand image of these companies in the market [9]. Environmental sustainability is a central concern in the transportation industry. The importance of addressing the Green Vehicle Routing Problem is emphasized, as this approach seeks to optimize fuel consumption and minimize the use of polluting energy sources, thereby reducing the sector’s environmental impact [10]. Additionally, public transportation efficiency is crucial; inefficient systems not only increase demand for private vehicles but also exacerbate traffic, road congestion, and, consequently, CO₂ emissions, significantly contributing to global warming [11,12].

This research is important because it highlights the determinants and trends in the application of metaheuristics in transportation, offering researchers and professionals new perspectives on how these tools can optimize the sector with significant effects on companies’ economies. Since the transportation sector is responsible for approximately 23% of global CO₂ emissions, effective implementation of metaheuristics could significantly reduce these emissions. Achieving a zero-carbon footprint could reduce global pollution by up to one-quarter, improving overall well-being and health, as well as operational efficiency and satisfaction in business operations [13]. Compared to internal combustion engine vehicles, electric vehicles are considered a cleaner mode of transportation that can reduce greenhouse gas emissions [14].

The findings of this research suggest that metaheuristics are crucial for process optimization, customer satisfaction, and profitability by improving asset utilization and reducing costs. Additionally, their role in environmental sustainability is significant, as they help reduce carbon dioxide emissions. Metaheuristic techniques have a wide range of applications across various areas of transportation. The ongoing evolution of this field and its global contribution to transportation are highlighted, along with the importance of sustainability, efficiency, decision-making, transportation service optimization, and their impact on the economy and finances of companies.

Green transportation is gaining increasing importance within the context of smart cities [15]. At the same time, artificial neural networks are improving operational efficiency by addressing complex issues in nanotechnology, energy system renewal, electric load forecasting, and ecological modeling [16]. As a result, allocation and rationing decisions significantly impact inventory management in supply chains for high-value or scarce products [17]. Neural networks rely on mathematical and computational methods to solve specific problems from an overall efficiency perspective. From an economic standpoint, efficiency involves minimizing waste in resource usage; in other words, efficiency requires the rational use of resources [18]. To achieve this, intelligent decision-support systems are employed, which have demonstrated concrete results in optimizing transport routes, with improvements of 25.64% compared to their absence [19]. Other optimization strategies focus on minimizing disruptions, thus reducing delivery times and providing more direct routes for product delivery [20]

The article highlights the forefront of a sector where automated driving technologies continue to grow, and the influence of autonomous vehicles on traffic networks is expected to increase [21]. This is where the crucial role of metaheuristics becomes evident. Furthermore, a new trend is emerging that involves the use of electric vehicles in conjunction with metaheuristic algorithms, such as the self-adaptive elephant herd optimization algorithm (SA-EHO), which optimizes both economic costs and emission levels [22]. Additionally, decision systems that are expected to expand will prioritize precision in solutions relative to optimal outcomes [23]. Moreover, with the anticipated rise of unmanned vehicles, fuzzy logic has also been integrated into optimization algorithms to solve multi-objective route planning problems [24]. This includes the development of autonomous vehicles and delivery drones [25]. Finally, metaheuristics also aim to address new forms of transportation through collective transportation systems, seeking to maximize group sizes and minimize total distance traveled [26].

Therefore, this study explores the application of metaheuristics in the transportation sector, examining their impact on optimization, safety, and economic efficiency. We analyze a variety of applications, their role in advancing new technologies, and their financial and economic implications. Additionally, the study investigates how these techniques contribute to environmental and economic sustainability, emphasizing their benefits for the transportation industry. Furthermore, the study offers a scientific perspective that includes a historical analysis of key factors in the development of more resilient and adaptive transportation systems. In this way, it aims to address the growing and changing demands for mobility and logistics in the 21st century, which directly impact the social, environmental, and economic development of other sectors.

2. Literature Review

Metaheuristics applied to the transportation sector have multiple applications for optimizing and solving complex problems in the most efficient way using calculations that help maximize company efficiency and can be extrapolated to the rest of the industry.

Glover [27], cited by Schweickardt and Miranda [28], was the first to use the term metaheuristic, which “derives from the combination of the word ‘heuriskein’ and the prefix ‘meta’, meaning ‘beyond’ or ‘at a higher level’”. However, as the results of this research show, it was from 1999 onwards that the term began to expand in the transportation sector, with the first research articles on the subject being published.

The information is categorized into various research strata to provide a comprehensive perspective differentiated by specific categories. The literature review follows this order: optimization problems, applications of metaheuristics in transportation, and efficiency and optimization models.

One of the most analyzed optimization problems is vehicle routing. This is particularly significant for vital industries such as the pharmaceutical sector, which is responsible for delivering medications to individuals with health conditions. Dual problems, such as the opening of distribution centers and the minimization of transport costs, are analyzed and solved [29]. This is done by focusing on finding the lowest-cost routes using available vehicles and considering constraints such as time and road length [30]. This becomes crucial for addressing depopulation, ensuring that remote populations have timely access to essential medications. From a business and marketing perspective, optimizing routes leads to improved economic returns, as higher customer satisfaction positively impacts long-term profitability [31]. In passenger transport, this issue is addressed using a mixed integer nonlinear programming problem (MINLP) to enhance trip efficiency by reducing waiting times and delays [32].

Some applications involve air transport, particularly during volcanic eruptions, where the goal is to maximize efficiency, time, and transport costs by using genetic algorithms to select airports that maximize the rescue of people [33]. Fuzzy target scheduling is used to manage the distribution of emergency relief materials [34]. The container relocation problem, also known as the block relocation problem, is an optimization challenge that involves finding an optimal sequence of operations to retrieve containers from a yard [35]. However, few studies have incorporated demand elasticity into the model, extending the classic fixed-charge multi-commodity network design problem by incorporating demand elasticity into travel costs, turning it into a profit-oriented problem using the gravity model [36]. Another application involves optimizing the simultaneous delivery and collection problem in the classic vehicle routing scenario, specifically in the healthcare sector, although applicable to other industries as well [37].

Other solutions offered by metaheuristics, this time focusing on maritime and/or multimodal container terminals, involve using reversible rail arrangements as an economical and practical way to improve service levels [38]. Economy, efficiency, and sustainability become the three fundamental pillars for transport companies aiming to become more competitive and committed to the green economy. Additionally, passenger waiting times at bus stops play a significant role in determining dwell and travel times for public transport scheduling [39]. This is an important consideration in public transport schedule design; reducing waiting times not only attracts more riders but also improves the companies’ economic performance. This indirectly reduces greenhouse gas emissions, as the more people use public transport, the fewer polluting vehicles are on the road, thereby reducing the carbon footprint. This also promotes economic efficiency and an eco-friendly approach to the use of fossil energy resources [40]. Inefficient utilization of existing parking resources is a major cause of parking difficulties, especially in metropolises [41].

Moreover, increased efficiency can bolster a company’s profit margins and enhance operating income per employee. This is why the transportation of goods can constitute a significant portion of their overall price [42]. Consequently, product prices may increase, as evidenced by the container crisis during the 2020 pandemic. Following the economic impact of the pandemic, a bottleneck occurred due to the continuous increase in demand for flights [43]. This is a clear example of how optimization becomes essential for the future stability of the sector, impacting areas such as tourism and national economies. The number of commercial flights is expected to reach 48.7 million, with 13.5 billion passenger-kilometers flown by 2030 [44]. For this reason, a metaheuristic problem known as the airport shuttle bus scheduling problem (ASBSP) is being studied to address the challenge of connecting city centers with airports [45]. It aims to identify a set of near-optimal routes and corresponding frequencies while minimizing both user and operator costs [46]. In connection with air transport and new sector technologies, one of the most discussed developments in recent years is the potential use of unmanned aerial vehicles (drones) to transport packages, food, medicines, and other goods [47].

Minimizing the distance traveled by demand-responsive vehicles is a common objective in cost functions [48]. However, other approaches, such as reducing lead time to maximize customer satisfaction, are also considered [49]. Therefore, each company must seek an optimal balance, as delayed shipments lead to delay costs for the logistics provider, impacting production timelines. Conversely, early shipments result in inventory maintenance and storage costs [50]. Additionally, factors such as space requirements, inventory storage costs, intensive labor, and order-picking tasks contribute significantly to the high cost of storing goods [51]. Algorithms within the mixed integer linear programming model are used to minimize the total cost of truck services [52]. This represents an advancement in reducing land transport costs.

Furthermore, in countries like Brazil, the probability of theft must be factored into costs, as a reduction in kilometers that increases the likelihood of theft can, in the medium and long term, result in costs exceeding the savings from reduced fuel consumption. Therefore, in areas with higher theft rates, the model must incorporate theft costs to generate routes that are not necessarily the shortest [53].

For the transportation of dangerous goods, two multi-objective evolutionary algorithms, Nondominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO), are implemented to address the issue [54]. When addressing the problem of diffuse fixed charges in transport, Electromagnetism-like Algorithms (EMs), Genetic Algorithms (GAs), and Simulated Annealing (SA) are utilized [55].

Financially, companies need to account for the time value of money and supplier profits [56]. This approach ensures more accurate calculations and considers the satisfaction of key stakeholders, thereby preventing unexpected outcomes in agreements with suppliers, which is crucial in the transport sector within the supply chain.

Economically speaking, allocating a large amount of assets to core activities can lead to profit losses. Conversely, a smaller allocation might result in unmet demand [57]. Moreover, some companies are exploring the option for logistics providers to selectively charge customers additional fees to guarantee a high level of service [58].

A study on the importance of metaheuristics in industry demonstrates that incorporating stochastic requests without prepositioning can improve average profits by 18.6%, whereas prepositioning can increase average profits by 23.8% and reduce average wait times by 74.7% [59]. Regarding environmental and economic sustainability, advancements in product packaging materials have enabled supply chain systems to adopt policies favoring reusable transport packaging [60]. Another area of focus involves models that incorporate battery exchange stations for electric vehicles [61]. These models aim to maximize utility and reduce delivery times while maintaining a commitment to environmental sustainability.

Supply chains are one of the main application segments. For this purpose, various accurate prediction models are employed using different deep learning techniques, such as convolutional neural networks, which minimize errors caused by noise in the sample, as seen with the improved Lion algorithm [62]. Moreover, predictive capabilities constantly aim to optimize supply chains.

One of the most widely used algorithms is the genetic algorithm. It is utilized to solve supplier selection and assignment problems with specific innovations, such as the modified savings algorithm for the VRP, which is trained with multiple collections, single delivery, and time windows [63]. These computational tools are also applied to routing problems to enhance and leverage economies of scale [64]. The impact on company economies is reflected in reduced waiting times and operating costs while addressing vehicle capacity constraints [65]. In addition to genetic algorithms, swarm intelligence systems have also become highly relevant in recent years for improving efficiency in transportation problems [66].

Among allocation problems, one key issue is related to charging stations, particularly for electric vehicles, where environmental concerns play a significant role. Unlike other types of vehicles, electric ones require optimal locations for recharging their batteries. This creates challenges, as transportation companies are less inclined to adopt environmentally friendly electric vehicles due to the added difficulties of refueling times, mileage range, and the lack of charging stations. Metaheuristics in this area promote applicable solutions to increase the percentage of sustainable vehicles used in transportation and logistics. Since energy costs are lower, specific algorithms such as Grey Wolf Optimization, using stochastic modeling, have improved the net gain of companies by optimizing charging station allocation problems in electric vehicle networks [67]. This positively impacts waiting times and energy consumption in transportation, with cases reporting a 69.9% reduction in waiting times and a 48.03% decrease in fuel consumption [68].

Additionally, the aim is to improve the net profits of transportation companies through the design and planning of railway networks that ensure profitability by solving allocation problems related to passenger demand and line frequency [69]. The same goal applies to other modes of transportation, such as buses, where advances in information systems using algorithms like Benders decomposition have been introduced [70]. These innovations address multifactorial problems, with a dual focus on customer satisfaction and the operational performance of the transportation company. The following

Table 1. Main applications of metaheuristics with economic implications.

References	Parent Topics	Categories	Journals
Hasani, A., et al. [20]	Risk of supply chain disruptions	Supply chain	Transportation Research Part E: Logistics and Transportation Review
Chen, L., et al. [58]	Transportation for premium customers	Supply chain	Transportation Research Part E: Logistics and Transportation Review
Akpinar, M. E. [31]	Long-term profitability	Supply chain	Logforum
Patel, M., et al. [62]	Traffic flow prediction with deep convolutional neural networks	Supply chain	Journal of Intelligent Transportation Systems
Yanik, S., et al. [63]	Supplier assignment with a hybrid approach	Supply chain	European Journal of Operational Research
Baals, J., Emde, S., et al. [50]	Just-in-Time approach to minimize upfront or late costs in supplier networks	Supply chain	European Journal of Operational Research
Ghaffarinasab, et al. [64]	Economies of scale	Supply chain	Computers & Operations Research
Laporte, G. [65]	Simultaneous pickup and delivery and its impact on customer satisfaction	Efficiency	Naval Research Logistics
Shamsaldin, A. S., et al. [66]	Swarm intelligence	Efficiency	Journal of Computational Design and Engineering
Posada, M., et al. [48]	Metrics for creating algorithms that improve business efficiency and performance	Efficiency and profitability	International Journal of Urban Sciences
Eydi, A., et al. [56]	Models that incorporate value for money over time and supplier profit	Efficiency and profitability	Asia-Pacific Journal of Operational Research
Tak, S., et al. [21]	Interconnected and automated vehicles	New transport technologies	Sustainability
Somakumar, R., et al. [22]	Emission cost optimization and economic analysis for microgrids	Sustainability	International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Shabbar, R., et al. [67]	Allocation of charging stations for electric vehicle network	Sustainability and efficiency	Sustainability
Ntakolia, C., et al. [43]	Optimization of air traffic flow with ant colonies and fuzzy logic	Air transport	Operational Research
Hammedi, W., et al. [68]	Optimization of waiting times in locks	Shipping	ACM Transactions on Intelligent Systems and Technology
Dozic, S., et al. [57]	Balance between fleet size and demand	Multimodal transport	Transportation Research Procedia
Canca, D., et al. [69]	Railways and profit maximization	Ground transportation	Transportation Research Part E: Logistics and Transportation Review
Repolho, H. M., et al. [53]	Costs of theft on dangerous routes	Ground transportation	Soft Computing
Hu, Q., et al. [70]	Bus tourism problem	Ground transportation	International Transactions in Operational Research

provides some examples of economic impacts in the field of metaheuristics in transportation.

3. Methodology

Bibliometric analysis is a tool used to classify and quantitatively evaluate bibliographic materials (such as publications, citations, authors, and institutions) within a scientific discipline [71]. Production and citation patterns illuminate methodologies across disciplines within both the specialized field of Library and Information Science (LIS) and the broader non-specialized professional fields (non-LIS) [72].

Therefore, with the ongoing scientific development and the corresponding increase in publications, it becomes necessary and almost unavoidable to objectively evaluate the outcomes of scientific research. Bibliometrics has thus become a very important evaluation system for this purpose [73]. Furthermore, in this specific case, there is no existing bibliometric analysis that examines the scientific production of metaheuristics focused on transportation in all its aspects on a large scale. As a result, it helps in quantitatively understanding a research topic, contributing to science by providing a broader perspective on a line of research that continues to grow annually.

The strength of bibliometrics lies in its foundation on historical quantitative data, which minimizes research bias. By analyzing existing data on a specific topic, interrelationships are identified, and the quantities and connections are systematically interpreted to draw conclusions that benefit the scientific community and professionals in the field. More specifically, as shown in Figure 1, we detail the phases of the bibliometric analysis. First, a topic that has a research niche and that is of interest is chosen to add value to the existing content. In this case, the chosen topic is the use of metaheuristics in the transport sector. Once the topic is selected, the chosen database, in this instance, Web of Science, is analyzed. To ensure greater consistency and comparability in the data, we have chosen to use indexed articles that present a wide diversity both in their temporal and geographical scope worldwide. In addition, these articles cover a broad thematic spectrum and come from a wide variety of sources. The terms ‘metaheuristic’ and ‘metaheuristics’ are both used, as they may appear in research studies in either form. This approach ensures unbiased keyword selection, thereby facilitating a comprehensive analysis of the topic. A total of 23,116 documents on metaheuristics exist in the history of the database. A new search dimension is added including the word “transportation” and 914 documents appear. This indicates that the transport field accounts for 3.95%, or nearly 1/25th, of the total research on metaheuristics worldwide, hence the relevance of this research.

However, due to the focus on business and economic effects of the article, the areas “Operations research in management sciences”, “Transportation”, “Computer Science”, “Business economics”, “Automation control systems” and “Energy fuels” are chosen within the research areas section. The remaining areas were discarded after reviewing their articles, as they did not have a direct relationship with the object of study. The main reason for this choice is that all the chosen ones address the main topics of efficiency and optimization, sustainability, types of transport, business, and applied computing with effects on business performance. After selection, the number of documents is reduced from 914 to 742. This number of articles allows us to answer the research question in a representative way to address bibliometric research.

The selected period begins with the introduction of the term ‘metaheuristics’ in related research in 1999 and extends to the end of 2022. In this way, the evolution of the theme in the last two decades can be measured. Consequently, this study would represent 3.20% of all metaheuristics research and, simultaneously, 100% of metaheuristics research within the transport sector. When downloading data from WOS, the relevance of the articles is verified, ensuring that no duplicates are included by checking both the title and DOI number. Furthermore, all indexed articles selected are part of the ‘Core Collection’, ensuring greater reliability and precision in the results.

The bibliometric tools used for the preparation of this research article are VOSviewer and Biblioshiny for interpretation and RStudio for data adaptation and processing. Bibliometric studies have become essential tools for evaluating scientific activity, providing an overview of the growth, size, and distribution of scientific literature within a given discipline [74]. These tools are well-established in the field of bibliometric review and rely on a big data analytics platform like RStudio, which processes structured data to produce standardized and wide-ranging visualizations in the scientific domain. The limitations of these tools lie primarily in the predefined scope of their functionalities; however, their combined use enhances their capabilities, providing a more enriched analysis.

Furthermore, bibliometric analysis evaluates aspects such as collaboration between countries and institutions, the impact of sources, citation levels of articles, the relevance of countries, growth rates, main keywords according to their co-occurrence, the evolution of publication numbers by year and journal, the most prolific and relevant authors, connections between authors over time, the number of publications by key authors per year, factor analysis of key keywords, and the level of impact.

Technological advances, alongside the emergence of more sophisticated software and hardware and the growing influence of artificial intelligence, have amplified interest in metaheuristics. This is evident in the volume of research conducted, as further analyzed in Figure 2, which demonstrates an upward trend in annual growth. The emergence of new algorithms, innovative transport organization methods, and the increasing complexity of optimizing transport routes—driven by factors such as globalization and digitalization—justify this heightened research interest.

Moreover, with the exponential growth and global proliferation of artificial intelligence, the approach and potential of metaheuristics across various sectors are being realized, having direct repercussions on the economies of businesses and consumers.

The representativeness and application of advanced statistical methods, such as co-occurrence analysis, neural networks, trend analysis, and correspondence analysis, among others, enhance the study’s replicability by the scientific community, encouraging debate and promoting growth in the transport sector by fostering a comprehensive perspective on applied metaheuristics. For a deeper understanding of the methods employed, it is important to note that co-occurrence analysis is a technique frequently applied in text mining [75]. Similarly, neural networks are employed to model and reorganize information to solve complex problems, as discussed throughout the article.

Three distinct phases can be observed in the graph referenced above. The first phase spans from 1999 to 2003, with the number of publications close to zero. In the second phase, from 2004 to 2013, the slope increases considerably, becoming steeper. During this period, the number of publications rises from 6 to 29, reflecting a consistent average growth rate. The third phase, from 2014 to 2022, is characterized by a significant surge in scientific publications, culminating in 80 publications in the final year of the study. This growth is due to several factors: the increasing complexity of transportation networks, computational advances in terms of hardware and software processing performance, the inclusion and expansion of the internet, and the need for companies to satisfy customers in terms of time and price. This, in turn, causes journals to experience upward growth over the years since they began publishing, as can be seen in several figures corresponding to the results. A more detailed exploration of the data will follow in the subsequent section. This information justifies the study as a retrospective analysis that serves as a foundation for prospectively understanding the evolution of the field, tracing its origins, and projecting its future trajectory. This approach allows for quantitative illustration, specification, and synthesis of the information, facilitating informed conclusions based on the data.

4. Results

4.1. General Analysis

4.1.1. Description

This quantitative analytical study explores the bibliometrics of metaheuristic applications in the transport sector, covering various aspects to provide a comprehensive understanding. The research focuses on several key areas. These include the most relevant sources and their publication volumes. It also highlights prominent authors in the field and tracks the temporal evolution of research output. The study examines leading organizations and universities involved in this area. It looks at the participation of different countries in both national and international collaborations. The analysis also identifies the most prevalent keywords, illustrated through a word cloud. Additionally, it explores the network of collaboration between countries and conducts a co-occurrence analysis based on clusters of related keywords.

4.1.2. Source Analysis

Figure 3 presents the twenty most important sources in this study, ranked by the number of publications. Leading the list, the journal ‘Transportation Science’ stands out with 49 articles, making it the most prolific. It is followed by ‘Transportation Research Part-E: Logistics and Transportation Review’ with 43 articles, and in third place, ‘Transportation Research Part C: Emerging Technologies’, which has a significantly lower count of 30 articles.

Journals can be categorized into various subgroups based on their primary focus, such as those concentrating on transport applications, those focused on supply management, others specializing in critical aspects of metaheuristics like algorithmic optimization, those emphasizing technology and energy, and finally, those that highlight the selection of optimal decisions. The multidisciplinary nature of these journals emphasizes the intersection of economics, engineering, and computing as applied to transport sciences, and both public and private sector businesses.

The journals with the highest cumulative publication counts up to 2022 are analyzed below. Specifically, Figure 4 highlights the six journals with the most activity in terms of the number of papers.

In first place is “Transportation Science”, which, within the sample analyzed, is the one that has been in publication for the longest period. Its first publication was in 2001, but it was in 2003 that the journal began to consistently focus on metaheuristics as applied to transport, continuing until 2022, making it the leading contributor to this research field in each year during this period.

In second place is the “Transportation Research Part-E Logistics and Transportation Review”, which began scoring four years later, in 2005. It is noteworthy for having the steepest growth in cumulative publication counts since 2014; therefore, it is expected to become the first in rankings in the coming years, despite starting with a 4-year disadvantage and having an annual production that is lower than that of the previous magazine until 2014.

The journals in the next four positions exhibit similar trends and share a lower cumulative value compared to the top-ranked journals, ranging between 38.77% and 51.02%.

4.1.3. Author Analysis

Subsequently, the information provided in Figure 5 and

Table 2. The most globally cited documents.

Authors	Title	Journal	Institution and Country	Total Citations	Year
Rokpe, S., et al. [76]	An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows	Transportation Science	Technical University of Denmark (Denmark)	1037	2006
Braysy, O., et al. [77]	Vehicle routing problem with time windows, Part I: Route construction and local search algorithms	Transportation Science	University of Jyväskylä (Finland) and École Polytechnique de Montréal (Canada)	624	2005
Laporte, G [78]	Fifty years of vehicle routing	Transportation Science	HEC Montréal (Canada)	504	2009
Schneider, M., et al. [79]	The electric vehicle-routing problem with time windows and recharging stations	Transportation Science	RWTH Aachen University (Germany)	496	2014
Braysy, O., et al. [80]	Vehicle routing problem with time windows, Part II: Metaheuristics	Transportation Science	University of Jyväskylä (Finland) and École Polytechnique de Montréal (Canada)	447	2005
Coelho, L.C., et al. [81]	Thirty years of inventory routing	Transportation Science	Université Laval (Canada) and HEC Montréal (Canada)	318	2014
Pisinger, D., et al. [82]	Large neighborhood search	International Series in Operations Research & Management Science	Technical University of Denmark (Denmark)	304	2010
Peng, P., et al. [83]	Reliable logistics networks design with facility disruptions	Transportation Research Part B: Methodological	City University of Hong Kong (People’s Republic of China)	250	2011
Keskin, M., et al. [84]	Partial recharge strategies for the electric vehicle routing problem with time windows	Transportation Research Part C: Emerging Technologies	Sabanci University (Turkey)	215	2016
Montoya, A., et al. [85]	The electric vehicle routing problem with nonlinear charging function	Transportation Research Part B: Methodological	Universidad EAFIT (Colombia) and Université d’Angers (France)	202	2017

is analyzed collectively to enrich the analysis. The most relevant authors are located in Denmark, Canada, and Finland, particularly those affiliated with the Technical University of Denmark, the University of Jyväskylä, and Polytechnique Montréal.

Among the most prolific authors, G. Laporte stands out, with 14 articles. His publication “Fifty years of vehicle routing” (2009) ranks third in the ranking of most citations, with 504. In second place is D. Tedorovic, with 13 publications. However, none of his works rank among the top 10 most cited articles. In third place, in terms of the number of articles published, is W. Dullaert with 12 articles. However, as in the previous case, none of his articles are among the top 10 most cited.

Another noteworthy author in terms of citation counts is O. Braysy, who holds the second and fifth positions with articles from 2005. Specifically, some of the titles of his scientific contributions are “Vehicle routing problem with time windows, Part I: Route construction and local search algorithms” and “Vehicle routing problem with time windows, Part II: Metaheuristics”. In this ‘Part II’, it’s notable that the focus is on metaheuristics, which is influential in solving transport problems. However, the most prominent in terms of citations is Rokpe, S., with 1037 citations for the article “An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows”.

Linking the authors with the journals, it is notable that ‘Transportation Science’ occupies the top six positions among the most cited articles, followed, in seventh place, by “International Series in Operations Research & Management Science”. In eighth and tenth places is “Transportation Research Part B: Methodological”, and in ninth position is its namesake, “Transportation Research Part C: Emerging Technologies”. These articles highlight a noticeable shift from metaheuristics to the study of electric vehicles.

Regarding production over time, Teodorovic, D. has the longest publication span, with works published from 2002 to 2022. Among the 10 experts with the most articles, this author has a span of 3 to 13 years between his first and last publications. Laporte, G. also stands out as the author with the most publications during this period and in a single year; specifically, 2014 was his most active year on the topic under investigation, with three articles.

As shown in Figure 6, the period from 2014 to 2022 represents the third phase of growth, as described earlier. Therefore, it is important to highlight the most prolific authors from the recent past, up until 2022, over a span of 9 years. Among them are Laporte, G. and Dullaert, W. as maximum exponents. In the last 3 years, Juan, A.A., Sorensen, K., and Coelho, L.C. have driven a change in the trend among emerging authors.

When analyzing the studies by year, 2014 stands out, with the highest number of publications (10) on transport metaheuristics from the 10 most relevant authors; this is followed by 2015 with eight. The recent change in trends has led to fewer publications by the 10 most prominent authors despite an overall increase in publications; specifically, there were four in 2020, four in 2021, and six in 2022. In Figure 6, the red lines represent the production interval years, and the blue circles indicate the volume of publications per year; the darker the blue, the higher the number.

4.1.4. Affiliation and Country Analysis

Based on the bibliometric analysis, in Figure 7, the five universities most committed to metaheuristics in the transport sector are the University of Belgrade, Delft University of Technology, and the University of Antwerp, with 32, 20, and 18 articles published, respectively. In fourth and fifth place are the University of Technology of Troyes and the University of Vienna, with 17 publications.

It is noteworthy that the vast majority of these organizations are in Europe, indicating that many of these countries are at the scientific forefront in this field. Among non-European universities, Beijing Jiaotong University stands out, with 14 articles. The number of articles per institution is relatively low over the 24-year period. This indicates a highly specialized field where no institution exceeds a 5% contribution rate; the highest rate is 4.45%, with 32 documents out of the active 719.

This could be pertinent for universities considering future collaborations in a field experiencing consistent annual growth. This is also relevant for those interested in transport, route and service optimization, innovation in sustainability, improving transport company efficiency, and developing new algorithms for transport optimization at all levels. This includes economic, environmental, and business aspects, as well as engineering and computational advancements in the sector.

Another key aspect is to analyze the number of citations by countries that receive the publications. For this, it is necessary to take into account that each territory has a different size, so each country presents a greater or lesser dimension; therefore, a greater capacity for influence to be larger can make a greater number of publications, but with fewer citations, be positioned above countries with more citations, but which have less territory and, therefore, fewer contributions. However, to demonstrate European dominance in the subject, despite the fact that they are smaller countries than the United States or China, it can be seen in Figure 8 that 7 of the 10 countries that appear are European. Denmark has 1823 citations, followed by Canada with 1503, the USA with 1335, Finland with 1287, and China with 1036.

Nine of the ten nationalities of the authors who participate in the most cited studies coincide with the most cited countries. This, added to the above, shows that the influence of the main experts in the research niche considerably affects the power of influence of the countries within the research branch, hinting at the dominance of certain scientists compared to the rest of the less cited authors; however, it can also have another interpretation, that is, it is not the author but the university that promotes this type of research, making the country specialize and create experts with international impact due to their specialization, as it appears in terms of the impact on the number of publications from the European institutions.

In addition, information from the map of collaborations between the 20 countries with the most publications in the period was extracted. The analysis was conducted using 20 nodes, and interrelationships were established using the Louvain clustering algorithm, with a repulsion force of 0.1. Figure 9 depicts this, with the central value representing the country contributing the most globally and the different clusters showing countries that have collaborated with it on research. In this figure, the links between countries in the same cluster are in color, while connections with countries in other clusters appear in gray. In this way, the information can be appreciated in greater detail.

Starting from China as the axis of the first cluster, the largest number of collaborations occurs with the United States. In addition, it collaborates with Germany and Iran. This group consists of China, the United States, Germany, Iran, Austria, and Turkey. In the second cluster, the largest connection is between the United Kingdom and Belgium. In addition, there are countries such as India, Egypt and Greece. The third cluster has as its central and most influential value the country of Italy, which collaborates to a greater extent with the Netherlands, being the most consistent connection, as well as China and the United States. The fourth cluster has France as the country with the most connections, which in turn highlights its high link with Tunisia and Spain. Other countries that are part of this fourth group are Canada, Brazil, and Mexico.

In terms of collaborations between countries in different clusters, the Netherlands stands out in its collaboration with the United Kingdom, Canada, and China. In turn, China collaborates with France and the United Kingdom, and finally, Canada collaborates with the United Kingdom.

4.1.5. Keyword Analysis

Figure 10 shows the frequency of the main keywords. Among them, “optimization” stands out first, followed by “algorithm”. These are the most prominent in terms of transport-oriented metaheuristics. Following the two most frequent terms, the next most common keywords are ‘model’, ‘genetic algorithm’, ‘search’, ‘tabu search’, ‘time windows’, ‘system’, ‘design’, and ‘vehicle-routing problem’, among others. The prominence of each term in the visualization reflects its importance in transport metaheuristics based on the analyzed publications. Thus, it is essential to provide a general description of the discussed topics and to understand the impact of each primary term on metaheuristics.

Currently, the transport sector faces one of the challenges that most concerns companies, which is the improvement and optimization of the efficiency and effectiveness of the services offered. To this end, metaheuristics enable the improvement of every process and aspect of distribution through optimization of transport planning. In some applied examples, metaheuristics enable the design of an improved prediction model on traffic flow using the optimized deep convolutional neural network [62]. Thus, transitioning to new models helps solve the routing problems of current and future vehicles. The vehicle routing problem deals with optimal route design and has constraints related to means of transport, routes, and customers [65]. For this, mathematics, statistics, and computer sciences are used to offer solutions that minimize the economic impact of companies.

Search algorithms are commonly employed for optimization tasks in transportation. These algorithms function by exploring viable options to identify optimal solutions. For instance, they are utilized for supplier allocation and optimization, encompassing a hybrid metaheuristic approach that uses a Genetic Algorithm for supplier selection and assignment and a modified savings algorithm for VRP trained with multiple collection windows, single delivery, and time [63]. Another method for developing optimal solution systems is the tabu search algorithm. In certain cases, an average improvement of 6.12% and 8.93% is achieved by using two heuristic methods called selective firefly algorithm (SFA) and genetic classification algorithm (RGA) [86]. The study employed stochastic optimization for a multi-level supply chain.

All the terms converge on a common objective: efficiency. This directly impacts cost reduction, increases income through business model optimization, and enhances the benefits achieved. Additionally, it can reduce emissions in certain cases. Some of the results of research studies analyzed conclude that the methodology resulted in a 24.8 percent reduction in distances traveled, representing an annual reduction of 32,716 kg in CO₂ emissions [87]. In addition, the Large Neighborhood Search (LNS) technique can be applied to improve transportation efficiency and reduce product delivery time.

These algorithms also address issues related to urban traffic congestion. Severe traffic congestion can lead to lost time, air pollution, increased fuel consumption, and energy waste [88]. Another significant consideration addressed in vehicle routing problems is that of efficient delivery with prediction systems to reduce the time in failed deliveries. Computational experiments indicate that significant use of customer-related presence data can result in savings of up to 40% in system-wide costs compared to traditional vehicle routing solutions [89]. Some of the algorithms used are simulated annealing (SA), tabu search (TS), and a hybrid algorithm (HA) [90]. For a more comprehensive perspective, the BAT algorithm, particle swarm optimization, artificial bee colony optimization, cuckoo search, firefly algorithm, and harmony search can be employed as powerful methods to solve many optimization problems [91]. Beyond these optimization techniques, heuristics and local search strategies also prove beneficial for transportation optimization tasks. Key aspects of performance improvement also include economies of scale, the economic management of the transport company, and the impact on demand of maximizing the performance of transport resources. An example is the center location and flat routing problem (HLRP), which is used to exploit economies of scale [64].

With this information in hand, we address the keywords, granting a broader perspective of the metaheuristics applied to transport from a real approach to extract relevant scientific knowledge related to each term.

Concerning transport and metaheuristics, and their direct and indirect economic implications, the keywords “metaheuristics”, “optimization”, “algorithm” “metaheuristic”, “tabu search”, “vehicle-routing problem”, “design”, “search”, “pickup”, “delivery”, “time windows”, “transportation”, “model”, “transport”, “demand”, “management” and “large neighborhood search” are analyzed in depth.

Through a co-occurrence analysis of the article keywords, 20 distinct clusters are formed, establishing relationships between the main words previously commented and adding, in addition, the terms that are related to the metaheuristic in transport. This additional information is depicted in Figure 11.

To conclude the general analysis, it is worth highlighting the importance of metaheuristics in all types of transport. The figure above is proof of the number of factors that influence its efficiency that need to be investigated.

Different applications of metaheuristics are used in transport such as maritime. The results show that both the efficiency of navigation and the utilization of passage facilities can be improved by using the methods [92]. Some of the keywords, such as “metaheuristics”, “optimization”, “model”, “ant colony” and “hybrid”, are related to the research addressed by scientists in the sample as they are terms that appear in studies, for example, emergency water transport is the reactive response for dealing with droughts [93]. Regarding other types of transport, such as inland maritime, related terms include those linked to the optimization of waiting times, which is also investigated in other forms of transport due to its significance. Delay affects shipping costs and can affect other parts of the transport chain, negatively impacting the growth of this mode of transport [68]. In addition, all keywords affect modal transport as a whole since all types of transport are included in it. Many transport systems are multimodal; that is, the infrastructure supports various modes of transport, such as trucks, railways, air, and maritime/river navigation [94].

The priority objective, as it appears in Figure 10, is the search for optimization; hence, it is the most used word since it represents the main state of affairs. In turn, economic sustainability gains strength through the use of algorithms using sustainable transport, such as electric vehicles. The Grey Wolf Optimization (GWO) algorithm is used to select the best charging station locations with the aim of maximizing net gain in both budget and routing constraints [67]. This gives strength to the arguments that the advance of metaheuristics implies maximization of benefits and increasing search for sustainability.

Finally, Figure 12 displays the specific keywords most directly associated with metaheuristics. Unlike the previous one, in which the terms are analyzed at the macro level, this one focuses on a specific segment of the analysis. This focus aims to analyze which keywords have the strongest linkages. In this case, metaheuristics are related to optimization, demand, public transport, colony algorithms, air traffic, terminal control area, variable neighborhood search, blocking, multiobjective optimization, scheduling, constraints, swarm intelligence, aircraft, air transport, a ride problem, berth allocation, city logistics, memetic algorithm, intermodal transportation, vehicle route problem, pickup, heuristics, and tabu search.

4.2. Lessons Learned

Based on the key terms extracted from the researched articles, the binary counting method is used, considering the presence or absence of a term in the documents. A minimum of 10 co-occurrences per term is required to identify strong relationships within the content. Out of 9919 terms, 227 meet this threshold and are then filtered to identify key terms that aid in understanding the behavior of metaheuristics in transportation within the research domain to extract patterns. For analysis, normalization is performed using the association strength method in relational databases. This association strength method has been recognized for decades in studies such as by Spence and Owens [95] and Jenkins et al. [96], who used association strength to create associative clustering, as in this case. From the 227 terms, the 109 with the highest heuristic significance in terms of solving transportation problems are selected, leading to the creation of five clusters.

Main Trends in the Applications of Metaheuristics in Transportation

In Figure 13, it can be observed how the main key terms with the greatest weights are ‘route’, ‘cost’, and ‘performance’. This is because the primary objective of metaheuristics is to solve possible route combinations within a journey, improving the performance of connections between transportation modes. This presents a complex problem that must be addressed through computational processes to reduce overall travel time and, consequently, the total cost of trips. These impacts make a significant difference in a company’s profitability, the reduction of pollution, and the well-being of businesses and consumers seeking quick responses to their needs. To extract the main implications and trends,

Table 3. ‘Route’ co-occurrences in five clusters.

Cluster Name	Terms	Details
Route and transportation basics. Cluster 1 (blue).	Transportation request, ride problem, user, trip, fleet, DARP, road, bus, passenger, demand, planning, timetable	This cluster covers the essential management of transportation routes, focusing on route planning and fleet coordination. It includes the analysis of transportation requests and the demands of both passengers and cargo. With terms like DARP and timetable, it reflects a need for detailed planning and synchronization to optimize resource use across different types of transportation. Additionally, it focuses on transportation demand, aligning services with the specific needs of passengers and users.
Metaheuristic and problem solving. Cluster 2 (green).	Metaheuristics, initial solutions, NP-hard problem, near-optimal solutions, scheduling problem, depot, total cost, operator, local search, distance, simulated annealing, vehicle routing problem, customer demand, capacitated vehicle routing, collection.	This group focuses on metaheuristic techniques to solve complex optimization problems, where methods are needed to obtain near-optimal solutions in computationally difficult (NP-hard) problems. Terms like simulated annealing and local search refer to specific approaches for exploring and optimizing routes in vehicle routing problems with constraints, such as capacitated vehicle routing. The solutions in this cluster are aimed at minimizing total costs and meeting specific customer demands through optimization strategies.
Operational and cost optimization. Cluster 3 (yellow).	Ant colony optimization, sales problem, loading, truck, variable neighborhood search, destination, operational cost.	In this cluster, the focus is on reducing operational costs within logistics by optimizing loading and distribution processes. The use of techniques such as ant colony optimization and variable neighborhood search highlights specific optimization methods applied in truck routing and sales problems. The terms aim to find efficient routes for trucks and other vehicles that meet delivery destinations while minimizing costs, which has direct applications in resource management and profit maximization in destination logistics.
Urban and electric logistics. Cluster 4 (purple).	Station, energy, large neighborhood search, time window, electric vehicle, urban area, delivery problem, task.	This cluster focuses again on logistics but is centered on urban areas and the unique challenges that cities present, such as congestion and time constraints. The inclusion of terms like electric vehicle and energy indicates an interest in sustainable solutions for freight transportation, which is especially relevant in urban environments where electric vehicles are more suitable, given that battery mileage and charging time pose challenges for long-distance optimization. Additionally, the use of time windows and specific tasks highlights the need for precise planning to optimize deliveries within a complex urban context.
Supply chain and efficiency models. Cluster 5 (red).	Container, genetic algorithm, value, network, way, cost, performance, efficiency, optimization model, location, decision, impact, optimization problem, routing, logistics, trade, supply chain, combinatorial optimization, risk.	This group encompasses the analysis and optimization of the entire supply chain, from the flow of goods to strategic decision-making. Terms like genetic algorithm and combinatorial optimization indicate an advanced approach in optimization methods to improve efficiency. Additionally, keywords like risk, impact, and location reflect strategic concerns, such as risk mitigation and location decision analysis, to optimize efficiency and reduce costs. This cluster integrates both logistics and global planning within complex supply networks.

is created to organize and group information into categories that share similar characteristics based on ‘route’ and ‘cost’, which is in line with the economic focus of this metaheuristics research.

The vast majority of key terms co-occurring with ‘route’ also coincide with those of ‘cost’. This is because the economic aspect is one of the primary reasons why metaheuristics promote business optimization. This highlights the importance of conducting a bibliometric analysis from this perspective to understand the impact of costs on optimization within the logistics and transportation sector.

Costs influence seven thematic groups, reorganizing the terms with a direct impact to detect research trends:

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Optimization and metaheuristic methods: This group encompasses methods and strategies to solve complex optimization problems in logistics and transportation. Among these are metaheuristics, simulated annealing, ant colony optimization, and genetic algorithms, which facilitate near-optimal solutions in high-complexity problems (NP-hard problems). It also includes approaches such as local search and large neighborhood search, which enable efficient exploration of the solution space, optimizing routes, and allocating resources effectively.

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Cost and operational efficiency: This group focuses on reducing costs and improving efficiency in logistics operations. Factors such as total cost and operational cost are fundamental, with the aim of optimizing the relationship between performance and efficiency to achieve more profitable logistics that meet objectives. Terms like impact and value highlight the importance of assessing and maximizing added value in the supply chain and at each stage of transportation.

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Planning and scheduling: This group includes terms such as scheduling problem, timetable, and time window, which are key for organizing workflow, avoiding delays, and meeting real-time demands. Depot and collection represent specific aspects in scheduling loading and unloading points, while decision and planning form the foundation of an information system based on rapid response.

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Logistics and transportation: This group includes the fundamental elements of transportation logistics, such as transportation requests and fleet, bus, and vehicle routing problems, which form the basis of route and fleet management. It encompasses specific issues like DARP (dial-a-ride problem), which is common in passenger transport, and capacitated vehicle routing, where vehicle capacity constraints must be considered. It also includes aspects such as urban areas and delivery problems, representing the challenges of transportation in densely populated areas.

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Supply chain and logistics networks: The supply chain manages the flow of goods from origin until the product reaches the end consumer. This group includes terms such as supply chain, network, trade, and location, which are fundamental to logistics network planning. Routing and container are essential for optimization at each stage of transportation and storage, while decision and way enable a comprehensive supply strategy. Risk management and efficiency in the supply chain are crucial to maintaining competitiveness and ensuring the continuous flow of products.

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Energy and sustainability: In the context of growing environmental concerns, energy and sustainability are key factors in transportation optimization. These aspects are of interest beyond economic sectors, such as for governments of countries striving for carbon neutrality. This group includes terms like energy and electric vehicles, which represent the shift towards more eco-friendly transportation options, especially in urban areas.

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Demand and users: This group focuses on demand and how to meet the expectations and needs of users. Customer demand and demand reflect the pressure the market places on logistics operations, driving the adaptation of services and resources to improve customer satisfaction. Understanding these demands enables the design of routes and schedules that are more aligned with the final customer’s needs, thereby enhancing service experience and efficiency.

On the other hand, co-occurrences of different problems solved by metaheuristic techniques are analyzed to gain a deeper understanding of what each technique is related to, using all the keywords associated with them:

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Allocation problem: In the ‘location problem’ in logistics, key terms appear that influence its solution. Finding optimal ‘locations’ for resource allocation within a ‘network’ of transportation is essential for efficient operations. Elements like ‘terminals’, ‘containers’, and ‘vessels’ are optimized to maximize ‘efficiency’ and ‘performance’ while minimizing ‘costs’. As an ‘NP-hard problem’, techniques such as ‘local search’ and ‘genetic algorithms’ are applied to explore solutions in ‘routes’ and ‘capacities’. Additionally, ‘scheduling’ and destination selection are crucial for ensuring the system operates both efficiently and profitably.

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Combinatorial optimization: In the ‘combinatorial optimization’ problem, key terms appear that impact its resolution. ‘Efficiency’ plays a critical role in achieving optimal resource use, while reducing ‘cost’ directly affects profitability in complex systems. Techniques such as ‘bee colony optimization’ and ‘genetic algorithm’ are applied to manage the ‘complexity’ of options within a ‘network’, enhancing decision-making processes in logistics and resource allocation.

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The dial-a-ride problem (DARP): In the ‘Dial-a-Ride Problem’ (‘DARP’), key terms appear that influence its resolution. ‘Transportation requests’ reflect the demand for transportation services from ‘users’ or ‘passengers’, directly impacting route planning and vehicle allocation across different ‘locations’. The ‘time window’ sets pickup and drop-off schedules, limiting flexibility and requiring precision in operations. The ‘cost’ associated with routes affects the budget and profitability of the service, while techniques like ‘variable neighborhood search’ help optimize ‘efficiency’ in ‘fleet’ management, ensuring effective service within time and distance constraints.

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Ant colony solutions: In ‘ant colony optimization’, key terms appear that influence its application and effectiveness. Following the ‘genetic algorithm’, it is the most commonly co-occurring technique for tackling complex problems. As an ‘NP-hard problem’ solver, ‘ant colony optimization’ is widely applied to challenges like the ‘vehicle routing problem’ and ‘salesman problem’, where ‘routing’ and ‘optimization’ are crucial. This technique enhances ‘performance’ and ‘efficiency’ by simulating natural ant behavior to find optimal paths within a ‘network’. Its frequent use alongside the ‘genetic algorithm’ further strengthens decision-making in logistics.

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Variable neighborhood search: In ‘variable neighborhood search’, key terms emerge that shape its application in logistics and transportation optimization. It is frequently used for solving the ‘vehicle routing problem’ and ‘scheduling problem’, where flexibility in exploring different solutions enhances outcomes. Techniques like ‘tabu search’ are often combined to improve ‘delivery’ and ‘routing’ efficiency. Factors such as ‘time window’, ‘location’, and ‘capacity’ play critical roles in meeting demands within a ‘network’ while balancing ‘cost’ and maximizing ‘performance’. Applications in the ‘ride problem’ allow for optimized planning, benefiting ‘passenger’ services and resource allocation.

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Transportation scheduling problems (TSP): In the ‘Traveling Salesman Problem’ (‘TSP’), key terms appear that significantly impact its resolution. In the ‘first stage’, ‘initial solutions’ are developed as a foundation for advanced techniques like ‘hybrid metaheuristics’, which combine methods such as ‘tabu search’ and ‘variable neighborhood search’ to refine solutions. Factors like ‘distance’, ‘time window’, and ‘timetable’ are crucial for coordinating ‘routing’ and ‘delivery’, optimizing the use of ‘truck’ and ‘bus’ to fulfill the demand of ‘passengers’ and cargo. Efficient ‘operator’ management and resource allocation are essential to balance ‘cost’ and ‘performance’, enhancing operational ‘ability’ in a complex logistics environment. ‘Genetic algorithms’ are among the most widely used techniques for solving this problem.

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Genetic algorithms: The ‘genetic algorithm’ is one of the most widely used methods in combinatorial optimization for solving complex ‘NP-hard problems’. This approach enables the identification of ‘feasible solutions’ by selecting and evolving optimal combinations within a ‘network’. Its ability to integrate with techniques such as ‘simulated annealing’, ‘tabu search’, and ‘ant colony optimization’ allows for a ‘hybrid metaheuristic’ approach that enhances performance.

The ‘genetic algorithm’ is applied in ‘route’ planning to minimize ‘cost’, optimize ‘distance’, and meet ‘demand’ in transportation systems involving ‘truck’, ‘bus’, and ‘station’. It is also used to manage ‘load’ and adjust ‘time windows’, increasing ‘efficiency’ in ‘delivery’ logistics and resource flow. ‘Users’ and ‘passengers’ benefit from improved planning that accounts for ‘value’ and adaptability in response to changes in demand and logistical ‘decisions’.

Diving deeper into the main algorithms presented as solutions in transportation metaheuristics, they are all outlined below in order of frequency of appearances in research articles. Firstly, there is the ‘genetic algorithm’, which is inspired by natural genetic evolution to promote transportation optimization. It is also related to problems such as time windows. The second most used is ‘simulated annealing’, related to combinatorial optimization and the search for local optima in routing. The third most frequently appearing is ‘ant colony optimization’, which is inspired by the behavior of ants that use pheromones to find optimal route solutions. It is widely employed in routing optimization, traveling salesman problems, and vehicle routing. These problems are also solved with ‘tabu search’. More specifically, in network optimization, the fifth algorithm is ‘particle swarm optimization’, which is again inspired by biological nature to solve transportation network problems. ‘Memetic algorithm’ combines genetic algorithms with local search and focuses on solving more complex problems with more refined solutions, taking advantage of both methods, such as last-mile problems. Next in order of utilization is ‘variable neighborhood search’, which seeks to approach the global optimal route solution by avoiding local optima, aiming for the general optimization of vehicle routing problems. Others inspired by nature are ‘bee colony optimization’ and ‘firefly algorithm’, which allow adaptation to dynamic changes in the transportation environment, such as variations in demand or route changes. The branch solutions are especially useful with algorithms for time window solutions and combinatorial optimization; both ‘branch & cut’ and ‘branch & price appear’. Both solve large-scale problems by generating columns that represent routes or schedules to choose solutions that generate resource efficiency and, consequently, reduce transportation costs. Other algorithms that appear, following the order of use in the scientific field, are the ‘water cycle algorithm’, ‘cuckoo search algorithm’, and ‘scatter search algorithm’. The effects of these algorithms are directly related to the objectives of Intelligent Transportation Systems (ITSs). Regarding ‘ITS’, they improve safety, promote more sustainable mobility, and offer greater comfort while minimizing environmental impact [97]. Concerning the economic aspect, they reduce costs, promote improvements in transportation networks, and foster greater resilience in all economic sectors, given the dependence of companies and people on the transportation sector.

5. Discussion

5.1. Innovation Factor

The essence of any research article is to provide new knowledge to the scientific community. This section covers two main aspects. The first analyzes the published literature through a bibliometric analysis focused on metaheuristics related to transport. The second details which aspects of the article represent advancements in science.

To date, only seven bibliometric analyses related to metaheuristics have been conducted. However, to date, no study has comprehensively analyzed metaheuristics with a deep focus on the transportation sector and a high volume of investigated articles. Furthermore, no articles addressing this topic from an economic perspective have been found, marking a significant advancement. The state of the research is presented below in

Table 4. State of the Research.

Authors	Object of Study	Article	Year
Ezugwu, A. E., et al. [98]	Global metaheuristics. Not specialized in the transport sector.	Automatic clustering algorithms: a systematic review and bibliometric analysis of relevant literature.	2020
Ezugwu, A. E., et al. [99]	Metaheuristics and their taxonomic classification. Not specialized in the transport sector.	Metaheuristics: A comprehensive overview and classification along with bibliometric analysis.	2021
Baghalzadeh, M., et al. [100]	Metaheuristics and the construction sector. Superficially related to the transport sector.	Internet of things (IoT), building information modeling (BIM), and digital twin (DT) in construction industry: A review, bibliometric, and network analysis.	2022
Ajibade, S. S. M., et al. [101]	Particle swarm optimization algorithms. Very focused aspect of metaheuristics.	Bibliometric survey on particle swarm optimization algorithms (2001–2021).	2022
Rabbouch, B., et al. [102]	Related to metaheuristics and transport. Although focused exclusively on transport route problems, it does not cover the subject in its entirety.	Parallel processing algorithms for the vehicle routing problem and its variants: A literature review with a look into the future.	2020
Deniz, N., et al. [103]	Heuristics and logistics. It extracts information from 40 papers analyzed, so its sample is small and may incur bias problems.	A bibliometric and social network analysis of data-driven heuristic methods for logistics problems.	2023
Kiani, R., et al. [104]	Metaheuristics and cross docking.	Cross-docking: A systematic literature review.	2020

.

Upon further examination of related bibliometric analyses, it is evident that this article offers a novel approach, enriching the scientific field by addressing factors and aspects that have not been previously analyzed. It allows for the extraction of a reliable overview and the establishment of an integrative perspective on metaheuristics in transportation, broadly from the economic and financial perspective of businesses. This provides reliability and substantial information for professionals and researchers.

Another innovation factor is the absence of any bibliometric analysis that offers an expanded view of the economic and business implications arising from optimization. For the most part, the articles try to demonstrate new metaheuristic methods that optimize aspects of transport. Consequently, highlighting this business perspective makes metaheuristics more appealing to companies in the sector that seek to enhance efficiency and optimize their operations.

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As the only bibliometric study focusing on metaheuristics in the transport sector, this research presents several significant implications and benefits:

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Innovation and advancement of knowledge. As a pioneer in its field, this study provides a comprehensive analysis and unique insight into how metaheuristics are being applied to transportation. This can boost future research and open up new avenues of study.

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Identification of trends and gaps in research. By providing an overview of the current state of research in this area, the study can help identify prevailing trends as well as research niches that could advance research in this field.

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Facilitate evidence-based decision-making. This study can provide decision-makers with valuable insights into which metaheuristic techniques and strategies have proven most effective in transportation, helping them make more informed and effective decisions.

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Contribution to transport optimization. By highlighting how metaheuristics are being applied in transport, this study can contribute to improving and optimizing transport systems, which in turn can lead to benefits in terms of efficiency, sustainability, and cost reduction.

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Orientation towards finance and economics. Optimization leads to savings in terms of time, resources, or raw materials. This is reflected in the economic aspect of businesses, making this perspective essential to unify both variables in a paper, bringing together two necessary disciplines for the prosperity of economic sectors.

5.2. General Discussion

The goal should be to organize the vast array of existing metaheuristics, clarify innovations in novel metaheuristics, and identify suitable approaches for solving specific optimization tasks [105]. This study solves this problem, focusing not only on the transport sector but also on the aspects that concern society and companies. The need highlighted by Baketarić et al. [106] regarding the underutilized potential of metaheuristics in advanced optimization techniques is addressed in this study. Additionally, we have identified open challenges, providing researchers with opportunities for further advancement in this domain. This statement about the relevance of the field of research addressed is consistent with the current purposes of regions seeking to promote more environmentally friendly and efficient transport sectors [107,108].

In the sole existing bibliometric study on transport and metaheuristics by Deniz and Özceylan [103], only 40 articles are analyzed. In contrast, our study encompasses 719 articles, offering an understanding 17.97 times more comprehensive. In its bibliometric analysis, new lines of research were provided, and it was stated that machine learning and deep learning methods are considered among the most promising; however, as of 2023, artificial intelligence is increasingly prominent in transport heuristic systems, reinforcing prior research and highlighting its potential to revolutionize the transport sector.

According to the search results, it is clear that artificial intelligence is gaining traction in heuristic systems for intelligent transportation. Therefore, it can be stated that artificial intelligence is an important tool for efficient transport planning and optimization [109,110,111].

In general terms, the journals that publish the most on applied metaheuristics through the implementation of automatic clustering algorithms, without differentiating by sector, are Pattern Recognition, IEEE Access, BMC Bioinformatics, and Expert Systems with Applications. However, they are not specified by sectors, so this study covers the need for information on metaheuristics in transport, with the journals with the most articles being Transportation Science, Transportation Research Part-E Logistics and Transportation Review, and Transportation Research Part C-Emerging Technologies.

Another trend involves solving and optimizing vehicle route problems using algorithms applicable to all types of transport [10,30,31,42,53,58,112]. To achieve this, they aim to improve existing and new approaches to addressing these problems, focusing on both economic objectives and emission reduction [22]. However, this study identifies situations where environmental and economic objectives conflict, such as in the case of eliminating high-theft routes, which, while reducing the risk of vehicle assaults, may result in higher pollution [53]. Therefore, there are territorial affectations and diverse problems to be solved depending on the type of transport and the security conditions in each country.

In turn, “Optimization” and “algorithm” are the most prevalent keywords in our study, indicating the centrality of the search in economic and environmental efficiency through mathematical and computational solutions. Authors such as Arreeras and Arimura [33] focus on defending and demonstrating how algorithms optimize transport companies. Arrondo et al. [113] discuss location choice problems, which relate closely to route issues covered in our article. Addressing these challenges often demands modeling that accurately mirrors reality. This can become intricate due to factors like the placement of collection and delivery points [13], vehicle capacity [94], delivery time windows [14,30], and traffic forecasts [62].

Economic issues emerge as a recurring theme, with prominent keywords such as demand, management, pricing, efficiency, minimization, customers, city logistics, packaging, pickup, sustainability, and costs. Thus, the findings align with those of various authors who state that transport costs can be a significant expense for companies, particularly those reliant on the shipment of goods or the provision of transport services [114,115,116]. On the other hand, in terms of metaheuristics applied to transport, excluding economic terms with which they are directly related, the following topics are of interest to researchers: optimization, public transport, colony algorithms, air traffic, terminal control area, variable neighborhood search, blocking, multiobjective optimization, scheduling, constraints, swarm intelligence, aircraft, air transport, a ride problem, berth allocation, City Logistics, Memetic Algorithm, Intermodal Transportation, Vehicle Route Problem, Pickup, and Tabu Search.

Metaheuristic techniques are applied through various approaches, including hybrid methods that enhance previous techniques for specific objectives. These techniques perform simulations and predictions through calculations, aiming to find the optimal solution. This approach allows for the quantification of differences between scenarios, both in monetary and environmental costs [117]. Many transport companies conduct viability assessments for management purposes, yet not all employ metaheuristic techniques. Self-imposed time windows can yield solutions that reduce costs by 15.74–21.43% compared to viability controls [112]. These techniques aim to reduce time and distance; however, in countries with high theft rates, reducing distance may increase the risk of merchandise loss. In such cases, the primary goal is cost reduction, indicating that the calculation objective varies based on specific conditions. The use of metaheuristics also reduces wait times, as exemplified by the design of alternative geometries that efficiently address traffic conflict issues [118]. The study reveals that metaheuristics have evolved into a decision support system for various types of transport, helping to identify the most efficient solutions and thereby enhancing organizational competitiveness. To survive in a competitive business, it is crucial to take care of customers and improve processes and products [119]. Thus, it becomes a crucial factor in reinforcing the survival of companies and organizations while promoting a sustainable economic approach.

Building on the points discussed, new multidisciplinary research avenues are established across various areas for scientists and professionals in the sector. Additional research areas include autonomous vehicles, emission-free transport, smart city connectivity, and the role of artificial intelligence in sustainable transport policies.

The main limitations of this study stem from the scarcity of bibliometric research on metaheuristics in the transportation sector and the complete absence of economic approaches in existing studies. Another limitation is the potential selection bias, as results may vary depending on the keywords used. In this case, we employed “metaheuristic” and “metaheuristics” as unifying keywords to encompass relevant techniques. Given the economic and optimization focus of the study, we decided to delve deeper into these aspects as well as the techniques themselves, which introduces a bias in the selection of information and key references from other authors; however, this bias also represents the distinctive value of our research. By choosing specific research areas, 23 documents that did not align with the defined areas were excluded, reducing the sample by 3%. This means that the articles were not fully represented, as areas not related to Operations Research in Management Sciences, Transportation, Computer Science, Business Economics, Automation Control Systems, and Energy Fuels were left out. Another limitation is the exclusive use of the terms “metaheuristic” and “metaheuristics”, which may exclude works that employ metaheuristic techniques without using this specific term. Although this strategy restricts the scope of the search, it was adopted to maintain coherence and reduce the complexity that would arise from including multiple specific algorithm names, each potentially having various denominations and popularity levels. Had we opted for a broader approach, we would have introduced other biases by favoring more well-known methods over less common ones, thus hindering comparability and uniformity. Consequently, the current limitation is a result of a methodological choice that, despite its restrictions, contributes to a unified and homogenized understanding under the term “metaheuristics”. Finally, the number of documents represents a limitation, as a larger sample would offer greater representativeness. However, we have focused exclusively on the transportation sector; hence, the findings are not generalizable to other economic sectors that represent the remaining 96% of metaheuristics research. This approach allows us to delve into the specific issues that metaheuristics address within the transportation field.

Finally, as the first to address the application of metaheuristics in transport from a bibliometric perspective, this study marks a milestone and illuminates unexplored terrain. It offers a new dimension of understanding, unravels emerging trends, reveals gaps in research, and highlights innovation, acting as a catalyst for future research.

The results of this study offer decision-makers valuable insights, enabling them to understand the most effective metaheuristic strategies in the transport sector and assisting in making informed and effective decisions. Moreover, our analysis highlights how metaheuristics contribute to transport optimization, potentially leading to more efficient, sustainable, and cost-effective transport systems.

6. Conclusions and Research Implications

This bibliometric study on the efficiency of the transport sector through metaheuristics covered a 24-year period, from the first publication in 1999 to 2022, to track its evolution. A sample of 719 articles was used, comprising 288 information sources and 1897 authors. This provides a comprehensive analysis of a large dataset spanning the field’s origins. The publication growth rate remains positive, averaging 20.99% over the analyzed years. This indicates that the application of metaheuristics to transport is a hot topic, gaining increasing interest each year for its impact on efficiency and competitiveness in companies.

Regarding their implications, metaheuristics prove to be a valuable tool for optimizing processes and enhancing customer satisfaction by delivering better service. It also enhances the productivity of assets in companies and public institutions while reducing costs by maximizing capital efficiency. Additionally, it positively impacts the environment by reducing carbon dioxide emissions through more efficient processes and solutions to complex problems. Over the last decades, metaheuristic approaches have emerged as promising alternatives to solve the problem of designing public transport route networks [120]. Thus, the interest extends beyond companies to the public sector, aiming to improve efficiency and productivity globally.

This study represents a novel contribution, as there are no previous bibliometric articles analyzing metaheuristics focused on the transport and logistics sector from an economic perspective. This allows for the inclusion of a new dimension of knowledge within the multidisciplinary field of metaheuristics. Cost reduction is a side effect of time reduction and optimization, which ultimately leads to the adoption of sustainable practices that promote the reduction of polluting gas emissions into the atmosphere. This study unifies various fields, such as economics, engineering, and sustainability, in a heterogeneous investigation that delves into process optimization over several decades from an international perspective.

The most significant terms, using the binary counting method to measure co-occurrences and highlight interrelations between concepts, provide an in-depth understanding of trends. The word groups with the strongest connections are more related to cost, routes, connections, and performance. Various groupings stand out. Five clusters of term groups are identified as follows: Route and transportation basics; metaheuristics and problem-solving; operational and cost optimization; urban and electric logistics; and supply chain and efficiency models.

Regardless of the clusters, all main keywords can be categorized into nine trend groups: optimization and metaheuristic methods; cost and operational efficiency; planning and scheduling; logistics and transportation; supply chain and logistics networks; energy and sustainability; demand and users. It is noteworthy that the study delves into the allocation problem (among other transportation scheduling problems), the dial-a-ride problem (DARP), and variable neighborhood search. For these, solutions such as genetic algorithms, ant colony solutions, and the concept of time windows stand out as key methods for improving optimization.

The main algorithms in order of the number of appearances are genetic algorithm, simulated annealing, ant colony optimization, tabu search, particle swarm optimization, memetic algorithm, variable neighborhood search, bee colony optimization, firefly algorithm, branch and cut, branch and price, water cycle algorithm, cuckoo search algorithm, and scatter search algorithm.

This study addresses the challenge posed by Stegherr et al. [105] to organize existing metaheuristics by providing an in-depth analysis of their application in the transport sector. It also validates Baketarić et al.’s [106] claim regarding the untapped potential of metaheuristics, highlighting areas for future research. This research significantly expands on Deniz and Özceylan’s [103] work by including a corpus of articles 17.97 times larger, enabling a more comprehensive understanding of the topic. We emphasize the growing relevance of artificial intelligence in transport heuristic systems, which complements and enriches previous research on machine learning and deep learning.

Following the conceptual analysis of the articles, it is essential to explore other bibliometric aspects. The number of publications has increased year by year, with 2022 seeing the highest output, totaling 80 publications. Therefore, future projections suggest that scientific output will continue to grow, particularly with the increasing integration of artificial intelligence in business from 2023 onwards. The most prolific authors, in terms of the number of articles, are G. Laporte with 14 publications, D. Teodorovic with 13, and W. Dullaert with 12. Geographically, China leads in the number of publications. However, in terms of citation impact, European countries are the most prominent, representing 90% of the top 10 most cited articles. When focusing on citation count across all articles, Denmark, Canada, and the USA stand out. The most relevant universities in this field are the University of Belgrade, Delft University of Technology, and the University of Antwerp, with 32, 20, and 18 papers published, respectively. Keyword frequency analysis highlights ‘optimization’, ‘algorithm’, ‘model’, ‘tabu search’, ‘vehicle routing problem’, ‘design’, ‘system’, ‘genetic algorithm’, and ‘time windows’ as the most frequently used terms of greatest interest to researchers Additionally, 20 distinct clusters have been generated using co-occurrence connections, represented in a word map to provide perspective and visually depict the main terms by size and their interrelations. Furthermore, this study is the first to offer a global perspective on metaheuristics focused on transport, complemented by an economic approach to broaden the scope of its significance.

Suggested future research will focus on the advancement of metaheuristics in the transport sector, exploring new forms of optimization and assessing the impact of artificial intelligence on transport metaheuristics. It is also relevant to examine the role of transport in the context of increasing digitalization and product delivery in smart cities and towns, promoting the Sustainable Development Goals and the circular economy. After analyzing the past and present and looking toward the future, it is important to recognize the key role that transportation plays in advancing digitalization and the rise of digital twins in the metaverse. This progression would contribute to the development of smart cities equipped with a greater range of services and opportunities for inhabitants. Smart cities hold significant potential to be designed and implemented to address social problems and achieve more sustainable, equitable, and livable urban environments [121]. Furthermore, with the rapid emergence of artificial intelligence and the advancement of public knowledge in this field, a new paradigm is expected to emerge in the coming years, where metaheuristics will become increasingly integrated into businesses to enhance efficiency. Consequently, this topic is emerging as a major area of interest in organizational research.

Other future lines of research based on the results could examine how the advancement of metaheuristic techniques in transportation affects profitability beyond cost reduction. Additionally, the creation of new algorithms and the potential of quantum computers to optimize the complexity of transportation and logistics problems through machine learning and deep learning are promising avenues. Another future trend is the development of transportation neural networks to enable algorithms to self-adjust, not only for transportation itself but also in response to customer demand needs. This would allow for the optimization of times in advance by generating realistic demand forecasts that impact transport optimization before the journey takes place.

In conclusion, metaheuristics in transport are crucial for improving the competitiveness of companies and organizations. Companies that fail to adopt these techniques to enhance efficiency risk losing competitiveness in a market driven by technological innovation and business intelligence. At the societal level, metaheuristics help decongest traffic networks, improve consumer welfare, and reduce the carbon footprint. Companies that invest in the global transport system and focus on the entire value chain can enhance their competitiveness [122], which can be achieved through the application of metaheuristics to transport. Furthermore, the financial aspect is crucial for the survival and resilience of businesses in any region, as transportation directly impacts all economic sectors. Additionally, metaheuristics play a key role in advancing optimization and efficiency.