Search Results (13)

In recent years, numerous constrained multi-objective evolutionary algorithms (CMOEAs) have been proposed to tackle constrained multi-objective optimization problems (CMOPs). However, most of them still struggle to achieve a good balance among convergence, diversity, and feasibility. To address this issue, we develop an adaptive constraint-boundary learning-based two-stage dual-population evolutionary algorithm for CMOPs, referred to as CL-TDEA. The evolutionary process of CL-TDEA is divided into two stages. In the first stage, two populations cooperate weakly through environmental selection to enhance the exploration ability of CL-TDEA under constraints. In particular, the auxiliary population employs an adaptive constraint-boundary learning mechanism to learn the constraint boundary, which in turn enables the main population to more effectively explore the constrained search space and cross infeasible regions. In the second stage, the cooperation between the two populations drives the search toward the complete constrained Pareto front (CPF) through mating selection. Here, the auxiliary population provides additional guidance to the main population, helping it escape locally feasible but suboptimal regions by means of the proposed cascaded multi-criteria hierarchical ranking strategy. Extensive experiments on 54 test problems from four benchmark suites and three real-world applications demonstrate that the proposed CL-TDEA exhibits superior performance and stronger competitiveness compared with several state-of-the-art methods. Full article

Autonomous ship berthing requires advanced path planning to balance multiple objectives, such as minimizing berthing time, reducing energy consumption, and ensuring safety under dynamic environmental constraints. However, traditional planning and learning methods often suffer from inefficient search or sparse rewards in such constrained and high-dimensional settings. This study introduces a double deep Q-network (DDQN)-guided dual-population constrained multi-objective evolutionary algorithm (CMOEA) framework for autonomous ship berthing. By integrating deep reinforcement learning (DRL) with CMOEA, the framework employs DDQN to dynamically guide operator selection, enhancing search efficiency and solution diversity. The designed reward function optimizes thrust, time, and heading accuracy while accounting for vessel kinematics, water currents, and obstacles. Simulations on the CSAD vessel model demonstrate that this framework outperforms baseline algorithms such as evolutionary multitasking constrained multi-objective optimization (EMCMO), DQN, Q-learning, and non-dominated sorting genetic algorithm II (NSGA-II), achieving superior efficiency and stability while maintaining the required berthing angle. The framework also exhibits strong adaptability across varying environmental conditions, making it a promising solution for autonomous ship berthing in port environments. Full article

When addressing constrained multi-objective optimization problems (CMOPs), the key challenge lies in achieving a balance between the objective functions and the constraint conditions. However, existing evolutionary algorithms exhibit certain limitations when tackling CMOPs with complex feasible regions. To address this issue, this paper proposes a constrained multi-objective evolutionary algorithm based on a dual-population cooperative correlation (CMOEA-DCC). Under the CMOEA-DDC framework, the system maintains two independently evolving populations: the driving population and the conventional population. These two populations share information through a collaborative interaction mechanism, where the driving population focuses on objective optimization, while the conventional population balances both objectives and constraints. To further enhance the performance of the algorithm, a shift-based density estimation (SDE) method is introduced to maintain the diversity of solutions in the driving population, while a multi-criteria evaluation metric is adopted to improve the feasibility quality of solutions in the normal population. CMOEA-DDC was compared with seven representative constrained multi-objective evolutionary algorithms (CMOEAs) across various test problems and real-world application scenarios. Through an in-depth analysis of a series of experimental results, it can be concluded that CMOEA-DDC significantly outperforms the other competing algorithms in terms of performance. Full article

The effective resolution of constrained multi-objective optimization problems (CMOPs) requires a delicate balance between maximizing objectives and satisfying constraints. Previous studies have demonstrated that multi-swarm optimization models exhibit robust performance in CMOPs; however, their high computational resource demands can hinder convergence efficiency. This article proposes an environment selection model based on Bayes’ theorem, leveraging the advantages of dual populations. The model constructs prior knowledge using objective function values and constraint violation values, and then, it integrates this information to enhance selection processes. By dynamically adjusting the selection of the auxiliary population based on prior knowledge, the algorithm significantly improves its adaptability to various CMOPs. Additionally, a population size adjustment strategy is introduced to mitigate the computational burden of dual populations. By utilizing past prior knowledge to estimate the probability of function value changes, offspring allocation is dynamically adjusted, optimizing resource utilization. This adaptive adjustment prevents unnecessary computational waste during evolution, thereby enhancing both convergence and diversity. To validate the effectiveness of the proposed algorithm, comparative experiments were performed against seven constrained multi-objective optimization algorithms (CMOEAs) across three benchmark test sets and 12 real-world problems. The results show that the proposed algorithm outperforms the others in both convergence and diversity. Full article

This study addresses the realistic constrained multi-objective optimization problem of police patrols by constructing a mathematical model tailored to the actual operational context of police patrols in China. To solve this problem, a modified PPS-MOEA/D algorithm is proposed and its performance is systematically evaluated against several state-of-the-art Constrained Multi-Objective Evolutionary Algorithms (CMOEAs). The results demonstrate the superiority of the proposed approach in terms of the solution quality and computational efficiency. Furthermore, the optimal solution set is discussed and visualized on a map, providing decision makers with practical and actionable insights that align with real-world patrol requirements. This research not only advances the theoretical framework for police patrol optimization, but also offers a practical tool for enhancing the effectiveness and efficiency of law enforcement operations in urban environments. Full article

The solution to constrained multi-objective optimization problems (CMOPs) requires optimizing the objective functions while satisfying the constraint conditions. To effectively address CMOPs, algorithms must balance objectives and constraints. However, the limited adaptability of specific constraint-handling techniques (CHTs) has hindered the widespread applicability of constrained multi-objective evolutionary algorithms (CMOEAs). To overcome this limitation, this article proposes a population state-based CMOEA. First, a model is developed to identify population states based on the positions of the primary and auxiliary populations. Tailored environmental selection models are then designed for the auxiliary population according to different states, enabling them to guide the evolution of the main population more effectively. By dynamizing the CHTs, the proposed algorithm can adapt to a broader and more complex range of CMOPs. Additionally, state-specific optimal individual selection methods are introduced, allowing the auxiliary population to escape local optima and accelerate exploration. A simple yet effective resource allocation model is incorporated to address the potential computational resource waste associated with dual populations, enhancing the resource utilization. Comprehensive tests, including comparisons with seven state-of-the-art algorithms, were conducted on 47 benchmark functions and 12 real-world problems. The experimental results demonstrate that the proposed CMOEA outperforms existing CMOEAs in its convergence and diversity. Full article

In practical applications, constrained multi-objective optimization problems (CMOPs) often fail to achieve the desired results when dealing with CMOPs with different characteristics. Therefore, to address this drawback, we designed a constraint multi-objective evolutionary algorithm based on feedback tracking constraint relaxation, referred to as CMOEA-FTR. The entire search process of the algorithm is divided into two stages: In the first stage, the constraint boundaries are adaptively adjusted based on the feedback information from the population solutions, guiding the boundary solutions towards neighboring solutions and tracking high-quality solutions to obtain the complete feasible region, thereby promoting the population to approach the unconstrained Pareto front (UPF). The obtained feasible solutions are stored in an archive and continuously updated to promote the diversity and convergence of the population. In the second stage, the scaling of constraint boundaries is stopped, and a new dominance criterion is established to obtain high-quality parents, thereby achieving the complete constrained Pareto front (CPF). Additionally, we customized an elite mating pool selection, an archive updating strategy, and an elite environmental selection truncation mechanism to maintain a balance between diversity and convergence. To validate the performance of CMOEA-FTR, we conducted comparative experiments on 44 benchmark test problems and 16 real-world application cases. The statistical IGD and HV metrics indicate that CMOEA-FTR outperforms seven other CMOEAs. Full article

The core issue in handling constrained multi-objective optimization problems (CMOP) is how to maintain a balance between objectives and constraints. However, existing constrained multi-objective evolutionary algorithms (CMOEAs) often fail to achieve the desired performance when confronted with complex feasible regions. Building upon this theoretical foundation, a two-stage archive-based constrained multi-objective evolutionary algorithm (CMOEA-TA) based on genetic algorithms (GA) is proposed. In CMOEA-TA, First stage: The archive appropriately relaxes constraints based on the proportion of feasible solutions and constraint violations, compelling the population to explore more search space. Second stage: Sharing valuable information between the archive and the population, while embedding constraint dominance principles to enhance the feasibility of solutions. In addition an angle-based selection strategy was used to select more valuable solutions to increase the diversity of the population. To verify its effectiveness, CMOEA-TA was tested on 54 CMOPs in 4 benchmark suites and 7 state-of-the-art algorithms were compared. The experimental results show that it is far superior to seven competitors in inverse generation distance (IGD) and hypervolume (HV) metrics. Full article

Recently, optimization-based energy disaggregation (ED) algorithms have been gaining significance due to their capability to perform disaggregation with minimal information compared to the pattern-based ED algorithms, which demand large amounts of data for training. However, the performances of optimization-based ED algorithms depend on the problem formulation that includes an objective function(s) and/or constraints. In the literature, ED has been formulated as a constrained single-objective problem or an unconstrained multi-objective problem considering disaggregation error, sparsity of state switching, on/off switching, etc. In this work, the ED problem is formulated as a constrained multi-objective problem (CMOP), where the constraints related to the operational characteristics of the devices are included. In addition, the formulated CMOP is solved using a constrained multi-objective evolutionary algorithm (CMOEA). The performance of the proposed formulation is compared with those of three high-performing ED formulations in the literature based on the appliance-level and overall indicators. The results show that the proposed formulation improves both appliance-level and overall ED results. Full article

When solving complex constrained problems, how to efficiently utilize promising infeasible solutions is an essential issue because these promising infeasible solutions can significantly improve the diversity of algorithms. However, most existing constrained multi-objective evolutionary algorithms (CMOEAs) do not fully exploit these promising infeasible solutions. In order to solve this problem, a constrained multi-objective optimization evolutionary algorithm based on the dynamic constraint boundary method is proposed (CDCBM). The proposed algorithm continuously searches for promising infeasible solutions between UPF (the unconstrained Pareto front) and CPF (the constrained Pareto front) during the evolution process by the dynamically changing auxiliary population of the constraint boundary, which continuously provides supplementary evolutionary directions to the main population and improves the convergence and diversity of the main population. Extensive experiments on three well-known test suites and three real-world constrained multi-objective optimization problems demonstrate that CDCBM is more competitive than seven state-of-the-art CMOEAs. Full article

The performance of constrained multi-objective differential evolution algorithms (CMOEAs) is mainly determined by constraint handling techniques (CHTs) and their generation strategies. To realize the adaptive adjustment of CHTs and generation strategies, an adaptive constrained multi-objective differential evolution algorithm based on the state–action–reward–state–action (SARSA) approach (ACMODE) is introduced in the current study. In the proposed algorithm, the suitable CHT and the appropriate generation strategy can be automatically selected via a SARSA method. The performance of the proposed algorithm is compared with four other famous CMOEAs on five test suites. Experimental results show that the overall performance of the ACMODE is the best among all competitors, and the proposed algorithm is capable of selecting an appropriate CHT and a suitable generation strategy to solve a particular type of constrained multi-objective optimization problems. Full article

In the real-world, symmetry or asymmetry widely exists in various problems. Some of them can be formulated as constrained multi-objective optimization problems (CMOPs). During the past few years, handling CMOPs by evolutionary algorithms has become more popular. Lots of constrained multi-objective optimization evolutionary algorithms (CMOEAs) have been proposed. Whereas different CMOEAs may be more suitable for different CMOPs, it is difficult to choose the best one for a CMOP at hand. In this paper, we propose an ensemble framework of CMOEAs that aims to achieve better versatility on handling diverse CMOPs. In the proposed framework, the hypervolume indicator is used to evaluate the performance of CMOEAs, and a decreasing mechanism is devised to delete the poorly performed CMOEAs and to gradually determine the most suitable CMOEA. A new CMOEA, namely ECMOEA, is developed based on the framework and three state-of-the-art CMOEAs. Experimental results on five benchmarks with totally 52 instances demonstrate the effectiveness of our approach. In addition, the superiority of ECMOEA is verified through comparisons to seven state-of-the-art CMOEAs. Moreover, the effectiveness of ECMOEA on the real-world problems is also evaluated for eight instances. Full article

The Job Shop Scheduling Problem (JSSP) has enormous industrial applicability. This problem refers to a set of jobs that should be processed in a specific order using a set of machines. For the single-objective optimization JSSP problem, Simulated Annealing is among the best algorithms. However, in Multi-Objective JSSP (MOJSSP), these algorithms have barely been analyzed, and the Threshold Accepting Algorithm has not been published for this problem. It is worth mentioning that the researchers in this area have not reported studies with more than three objectives, and the number of metrics they used to measure their performance is less than two or three. In this paper, we present two MOJSSP metaheuristics based on Simulated Annealing: Chaotic Multi-Objective Simulated Annealing (CMOSA) and Chaotic Multi-Objective Threshold Accepting (CMOTA). We developed these algorithms to minimize three objective functions and compared them using the HV metric with the recently published algorithms, MOMARLA, MOPSO, CMOEA, and SPEA. The best algorithm is CMOSA (HV of 0.76), followed by MOMARLA and CMOTA (with HV of 0.68), and MOPSO (with HV of 0.54). In addition, we show a complexity comparison of these algorithms, showing that CMOSA, CMOTA, and MOMARLA have a similar complexity class, followed by MOPSO. Full article