When addressing constrained multiobjective optimization problems (CMOPs) via evolutionary algorithms, various constraints and multiple objectives need to be satisfied and optimized simultaneously, ...which causes difficulties for the solver. In this article, an evolutionary multitasking (EMT)-based constrained multiobjective optimization (EMCMO) framework is developed to solve CMOPs. In EMCMO, the optimization of a CMOP is transformed into two related tasks: one task is for the original CMOP, and the other task is only for the objectives by ignoring all constraints. The main purpose of the second task is to continuously provide useful knowledge of objectives to the first task, thus facilitating solving the CMOP. Specially, the genes carried by parent individuals or offspring individuals are dynamically regarded as useful knowledge due to the different complementarities of the two tasks. Moreover, the useful knowledge is found by the designed tentative method and transferred to improve the performance of the two tasks. To the best of our knowledge, this is the first attempt to use EMT to solve CMOPs. To verify the performance of EMCMO, an instance of EMCMO is obtained by employing a genetic algorithm as the optimizer. Comprehensive experiments are conducted on four benchmark test suites to verify the effectiveness of knowledge transfer. Furthermore, compared with other state-of-the-art constrained multiobjective optimization algorithms, EMCMO can produce better or at least comparable performance.
Constrained multi-objective optimization problems (CMOPs) contain the satisfaction of various constraints and optimization of multiple objectives simultaneously, thus they are extremely challenging. ...Although many constrained multi-objective evolutionary algorithms (CMOEAs) have been proposed, they ignore the information of each constraint, which might help utilize more various infeasible solutions to improve the search ability of the population. Therefore, this paper proposes a new dual-population CMOEA to solve CMOPs, in which a dynamic constraint processing mechanism and a dynamic resource allocating scheme are designed. To be specific, the proposed algorithm evolves two populations, which adopt different mechanisms to handle constraints respectively. The main population directly optimizes all constraints to find the feasible Pareto optimal solutions, which can improve the feasibility. The auxiliary population adopts a dynamic constraint processing mechanism, which gradually increases the number of constraints being processed, so as to fully utilize various infeasible solutions to help find feasible regions. Moreover, a new dynamic resource allocating scheme is proposed to reasonably allocate the limited computational resources to the two populations according to their performance feedback. Experimental results on three test suites and ten practical problems show that the proposed algorithm has a better or competitive performance compared with several state-of-the-art CMOEAs.
The key to solving constrained multiobjective optimization problems (CMOPs) lies in maintaining the feasibility, convergence, and diversity of the population. In recent years, various constraint ...handling techniques (CHTs) and strategies have been proposed to enhance the performance of constrained multiobjective evolutionary algorithms (CMOEAs). However, most of these algorithms face difficulties in dealing with problems that have large infeasible regions and discontinuous small feasible regions, as they have trouble crossing large infeasible regions while simultaneously maintaining the convergence and diversity of the population. To tackle this issue, this paper proposes a dual-population auxiliary coevolutionary algorithm with an enhanced operator, denoted as DAEAEO. Auxiliary population 1 employs an improved ϵ-constraint handling technique to provide high-quality feasible solutions for the main population. Auxiliary population 2 adopts the non-dominated sorting method to provide favorable objective information for the main population to help it cross the infeasible region. In addition, to further improve diversity, each population adopts an enhanced operator and a genetic operator to generate offspring, respectively. Finally, knowledge transfer between offspring is realized. Compared to six state-of-the-art CMOEAs on DASCMOPs, LIR-CMOPs, DOC test suites, and two real-world problems, the proposed DAEAEO achieved superior performance, especially for CMOPs with large infeasible regions and discontinuous small feasible regions.
•A constrained multiobjective coevolutionary algorithm is proposed, termed DAEAEO.•A dual-population auxiliary evolutionary strategy is proposed.•The use of knowledge transfer promotes information interaction among offspring.•An enhanced search operator is developed to balance convergence and diversity.•The effectiveness of DAEAEO is verified on test suites and two real-world problems.
During the search process, the characteristics of the feasible regions encountered by the population continually change in Constrained Multiobjective Optimization Problems (CMOPs). This variability ...poses a challenge for traditional evolutionary algorithms, which often struggle to adapt to the diverse problem characteristics of the encountered feasible regions. To overcome this limitation, we propose a Dual-Stage and Dual-Population Cooperative Evolutionary Algorithm (DDCEA) to address CMOPs characterized by diverse feasible regions. DDCEA employs a dual-stage mechanism to adapt the offspring generation strategy and establishes two distinct populations to evaluate offspring using constraint-sensitive and constraint-free strategies. Comparative analyses reveal that DDCEA surpasses chosen state-of-the-art CMOEAs in adapting to the changing feasible regions and then approximating the constrained Pareto fronts.
•Establishes dual stage and dual population cooperative mechanism.•Two populations collaborate using the method of weak cooperation.•Utilizes GA and DE operators to generate offspring in different search stages.•Applies two different evaluation strategies to select offspring.
In recent years, solving constrained multiobjective optimization problems (CMOPs) by introducing simple helper problems has become a popular concept. To date, no systematic study has investigated the ...conditions under which this concept operates. In this study, we presented a holistic overview of existing constrained multiobjective evolutionary algorithms (CMOEAs) to address three research questions: (1) Why do we introduce helper problems? (2) Which problems should be selected as helper problems? and (3) How do helper problems help? Based on these discussions, we developed a novel helper-problem-assisted CMOEA, where the original CMOP was solved by addressing a series of constraint-centric problems derived from the original problem, with their constraint boundaries shrinking gradually. At each stage, we also had an objective-centric problem that was used to help solve the constraint-centric problem. In the experiments, we investigated the performance of the proposed algorithm on 66 benchmark problems and 15 real-world applications. The experimental results showed that the proposed algorithm is highly competitive compared with eight state-of-the-art CMOEAs.
Over the past decade, incorporating information from the objective function into the constraint-handling process has garnered considerable attention in evolutionary algorithm research. Stemming from ...this, multiobjective optimization has emerged as a promising approach that simultaneously optimizes the objective function and constraints. However, the challenges associated with optimizing objective functions and satisfying constraints exhibit significant variability. Some constraints and/or objective functions can be exceptionally challenging, necessitating specific methods to identify the optimal solution within a limited feasible region. This study proposes an adaptive gradient descent-based repair method to enhance the search capability for both objective function optimization and constraint satisfaction. This method leverages objective function information to rectify infeasible solutions using gradient descent, thereby reducing the limitations of a purely constraint-based approach and automating the application of the repair method. Furthermore, an enhanced variant of the ɛ-constrained multiobjective differential evolution algorithm is developed for solving constrained optimization problems. The efficacy of the proposed approach is assessed using 57 benchmark test functions derived from real-world applications. Empirical results demonstrate that our approach is capable of locating high-quality solutions, outperforming several selected state-of-the-art algorithms.
•The information from objective function has been utilized to improve the standard gradient-based repair method.•An adaptive scheme is specifically designed to automate our proposed repair method for ɛ-constrained multiobjective optimization.•The proposed approach has been demonstrated by comparing it with several state-of-the-art algorithms on 57 benchmark test functions.
When solving constrained multiobjective optimization problems (CMOPs), the utilization of infeasible solutions significantly affects algorithm's performance because they not only maintain diversity ...but also provide promising search directions. In light of this situation, this article proposes a new multitasking-constrained multiobjective optimization (MTCMO) framework, in which a dynamic auxiliary task is created to assist in solving a complex CMOP (the main task) via the knowledge transfer. Moreover, the constraint boundary of the auxiliary task reduces dynamically, so that it keeps a high relatedness with the main task to continuously provide supplementary evolutionary directions. Furthermore, an improved <inline-formula> <tex-math notation="LaTeX">\epsilon </tex-math></inline-formula> method is designed for the auxiliary task to utilize diverse high-quality infeasible solutions for breaking through infeasible obstacles in the early stage and approaching the feasible boundary from infeasible regions in the later stage. Besides, a new test function with decision space constraints is designed, where one parameter can be adjusted to control the overlap degree between the constrained Pareto front and the unconstrained Pareto front. This function and the other two modified existing functions are used to analyze the characteristics of MTCMO. Finally, compared with 11 state-of-the-art peer methods, the superior or competitive performance of MTCMO is demonstrated on 54 benchmark functions and two real-world applications.
PDF
