Multiobjective-Based Constraint-Handling Technique for Evolutionary Constrained Multiobjective Optimization: A New Perspective

An evolutionary algorithm with directed weights for constrained multi-objective optimization

A dual-population algorithm based on alternative evolution and degeneration for solving constrained multi-objective optimization problems

Battery energy storage system for enhancing the electrolyzer capacity factor in small-scale WindtH2 system with a smoothing control strategy: Constrained multi-objective Pareto optimization and case study in Algeria

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

Generally, constraint-handling techniques are designed for evolutionary algorithms to solve Constrained Multiobjective Optimization Problems (CMOPs). Most Multiojective Particle Swarm Optimization (MOPSO) designs adopt these existing constraint-handling techniques to deal with CMOPs. In this chapter, the authors present a constrained MOPSO in which the information related to particles' infeasibility and feasibility status is utilized effectively to guide the particles to search for feasible solutions and to improve the quality of the optimal solution found. The updating of personal best archive is based on the particles' Pareto ranks and their constraint violations. The infeasible global best archive is adopted to store infeasible nondominated solutions. The acceleration constants are adjusted depending on the personal bests' and selected global bests' infeasibility and feasibility statuses. The personal bests' feasibility statuses are integrated to estimate the mutation rate in the mutation procedure. The simulation results indicate that the proposed constrained MOPSO is highly competitive in solving selected benchmark problems.

Solving constrained multi-objective optimization problems (CMOPs) is one of the most popular research topics in the multi-objective optimization community. Various approaches based on different algorithmic strategies have been proposed for benchmark CMOPs with different features and challenges. Although most of these algorithms employ one or more fixed strategies, determining the most suitable strategy is challenging and problem-dependent. This work presents a general multitasking framework comprising a main task for the original CMOP and an arbitrary number of auxiliary tasks based on different strategies for the auxiliary problems. Reinforcement learning techniques are utilized according to the population state to choose the most suitable auxiliary task during the evolutionary process. As instantiations, Q-Learning and Deep Q-Learning are successfully applied in the framework. Accordingly, two novel algorithms are developed to solve CMOPs. The results demonstrate the effectiveness of the proposed approaches on five benchmark CMOP test suites and real-world problems compared to 11 advanced methods.

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.

Highly constrained multiobjective optimization problems (HCMOPs) refer to constrained multiobjective optimization problems (CMOPs) with complex constraints and small feasible regions, which are commonly encountered in many real-world applications. Current constraint-handling techniques will face two difficulties when dealing with HCMOPs: 1) feasible solution is hard to be found and too much search effort is spent in locating the feasible region and 2) since the total feasible region of an HCMOP can consist of several disconnected subregions, the search process might be stuck in the comparatively larger feasible subregion, which does not contain the whole Pareto front (PF). To address these two issues, an evolutionary algorithm with constraint relaxation strategy based on differential evolution algorithm, that is, CRS-DE, is proposed in this article. In each generation, the CRS-DE relaxes the constraints by dividing the infeasible solutions into two subpopulations based on total constraint violation, that is, the ``semifeasible'' subpopulation (SF) and ``infeasible'' subpopulation (IF), respectively. The SF provides information on the promising regions of finding the feasible solution and is the driving force for convergence toward the PF, while the IF focuses on global exploration for new promising regions. Corresponding reproduction and selection strategies are devised for the SF, IF, and feasible subpopulations, which create a clear division of labor with cooperation to facilitate the search for feasible solutions. To leverage the influence of CRS and prevent the population from premature convergence, a mobility restriction mechanism is developed to restrict the individuals in the SF and IF from entering the feasible subpopulation and enhance the diversity of the whole population. Comprehensive experiments on a series of benchmark test problems and a real-world CMOP demonstrate the competitiveness of our method compared with other representative algorithms in terms of effectiveness and reliability in finding a set of well-distributed optimal solutions for HCMOPs.

Convergence, diversity and feasibility are three important issues when solving constrained multiobjective optimization problems (CMOPs). To deal with the balance among convergence, diversity and feasibility well, this article proposes a cooperative multiobjective evolutionary algorithm with propulsive population (CMOEA-PP) for solving CMOPs. CMOEA-PP has two populations, including propulsive population and normal population, and these two populations work cooperatively. Specifically, propulsive population focuses on convergence. Normal population gives priority to feasibility and is obligated to maintain diversity. To cross through the infeasible region and reach the Pareto front (PF), propulsive population does not consider constraints in the early stage and only considers constraints in the later stage. To further accelerate the speed of convergence, propulsive population only searches for corner solutions and center solutions, while normal population searches for the whole PF. As a result, propulsive population can cross through the infeasible region because of the lack of attention to feasibility. In addition, propulsive population also can guide and accelerate the convergence of the evolutionary process. Comprehensive experiment results on several sets of benchmark problems demonstrate that CMOEA-PP is better than existing state-of-the-art competitors.

In this paper, a new evolutionary algorithm (EA) to solve multi-objective constrained optimization problem (MCOP) is proposed. First, the rank of the individual and the scalar constraint violation of the individual are defined. Then, based on the rank and the scalar constraint violation of the individual, a new fitness function and a switch selection operator are presented. Accordingly, when the individuals are evaluated or ranked, it doesn't need to care about the feasibility of individuals, therefore it is a penalty-parameterless constraint-handling approach for multi-objective constrained optimization problem. Finally, the computer simulations demonstrate the effectiveness of the proposed algorithm.

Genetic algorithm based multi-objective reliability optimization in interval environment

The elements of the population of the artificial physics optimization (APO) algorithm are assigned mass, velocity, and displacement attributes. It is a new type of heuristic algorithm, but it still has defects such as low efficiency of non-dominated solution selection and unbalanced search capacity of global and local. This paper introduces the mechanism of improved fast non-dominant sorting and partition-guided individual evolution into the APO algorithm to overcome this imperfection. An improved multi-objective artificial physics optimization algorithm based on fast non-dominated sorting (IFNS-MOAPO) is proposed, which is the result of integrating numerous strategies into the APO algorithm. Firstly, an improved fast non-dominated sorting strategy is introduced. This strategy can increase the efficiency of selecting non-dominated solutions and decrease the running time of the algorithm. Secondly, the mechanism of individual evolution guided by partition is proposed. For individuals in infeasible and feasible domains, different mass functions and virtual force calculation rules are adopted to update the algorithm iteratively to boost the convergence performance. To verify the comprehensive performance of the IFNS-MOAPO algorithm, seven benchmark test problems are selected for simulation experiments and compared with five algorithms in terms of runtime duration, Pareto front plots, and metric values. The results show that the IFNS-MOAPO algorithm has good distribution and can converge to the true Pareto front quickly. It is a useful tool for solving constrained multi-objective optimization problems (CMOPs).

A staged diversity enhancement method for constrained multiobjective evolutionary optimization

Push and pull search embedded in an M2M framework for solving constrained multi-objective optimization problems

Constrained multiobjective optimization problems (CMOPs) widely exist in real-world applications, and they are challenging for conventional evolutionary algorithms (EAs) due to the existence of multiple constraints and objectives. When the number of objectives or decision variables is scaled up in CMOPs, the performance of EAs may degenerate dramatically and may fail to obtain any feasible solutions. To address this issue, we propose a paired offspring generation-based multiobjective EA for constrained large-scale optimization. The general idea is to emphasize the role of offspring generation in reproducing some promising feasible or useful infeasible offspring solutions. We first adopt a small set of reference vectors for constructing several subpopulations with a fixed number of neighborhood solutions. Then, a pairing strategy is adopted to determine some pairwise parent solutions for offspring generation. Consequently, the pairwise parent solutions, which could be infeasible, may guide the generation of well-converged solutions to cross the infeasible region(s) effectively. The proposed algorithm is evaluated on CMOPs with up to 1000 decision variables and ten objectives. Moreover, each component in the proposed algorithm is examined in terms of its effect on the overall algorithmic performance. Experimental results on a variety of existing and our tailored test problems demonstrate the effectiveness of the proposed algorithm in constrained large-scale multiobjective optimization.