Constrained Multi-objective Evolutionary Algorithms Based On Dynamic Selection Strategy

With the development of modern computer and mathematical theory,numerous complex optimization problems in science and engineering have been abstracted into Constrained Multi-objective Optimization Problems.The solution based on evolutionary algorithms simulates the natural evolution,selection,and variation process of biological systems.By employing the survival-of-the-fittest individual evaluation strategy,evolutionary algorithms greatly enhance their robustness in solving various constrained multi-objective optimization problems.However,the existing research still faces challenges in dealing with complex constrain ed multi-objective optimization problems,such as poor convergence of Pareto solution set and imbalanced search capability in the objective space,which limits their practical applications in engineering optimization.Therefore,the study of efficient constrained multi-objective evolutionary algorithms has important theoretical and practical significance.This article aims to improve the performance of evolutionary algorithms in solving various constrained multi-objective optimization problems by making improvements based on the foundation of evolutionary algorithms.This paper mainly includes the following three aspects.(1)A Pareto front estimation-based constrained multi-objective optimization algorithm is proposed.Firstly,a representative set of solutions is obtained by evaluating the distance between individuals in the population.This set is then used to estimate the shape and position of the Pareto front,which guides the evolution of the population.Secondly,the algorithm employs two different populations with different focuses to enhance the quality of the solution set.One population focuses on improving the convergence of the population,while the other focuses on increasing the diversity of the population.Finally,the dynamic fitness function values of solution individuals in both populations are sorted,and the better solution set is selected for environmental selection.Environmental selection calculates the adaptive penalty function of individuals in the population,repairs infeasible solutions,and ensures that the final soluti on that enters the next generation is feasible and meets the constraints.Experimental results demonstrate that the proposed algorithm significantly improves the convergence accuracy when solving constrained multi-objective problems.(2)A constrained multi-objective optimization algorithm based on the learning constraint boundary is proposed.Firstly,the degree of constraint violation is introduced as a new optimization objective in the existing constrained multi-objective problem,resulting in a new multi-objective optimization problem.Secondly,an enhanced co-evolutionary framework is developed for this newly formulated problem: the main population dynamically searches the objective space and repairs infeasible solutions using a dynamic weight function.In the auxiliary population,only individuals with objective function values that meet the learning constraint boundary are given priority to enter the next generation and approach the Pareto Front under its guidance.The learning constraint boundary absorbs information from infeasible solutions in the population and dynamically updates the feasible region within the constraint boundary based on the constraint violation degree values of the current population.The auxiliary population extracts information from infeasible solutions in the objective space through the interactive relationship within the co-evolutionary framework.It can also constrain and limit the offspring generated by the main population during the iteration process to increase environmental selection pressure.Experimental results demonstrate that incorporating the learning constraint boundary into the improved co-evolutionary framework effectively enhances the algorithm’s convergence accuracy and environmental selection pressure.(3)A dual operator preference-based constrained multi-objective evolutionary algorithm is proposed.Firstly,after completing the initialization,two different offspring are generated for the population using Differential Evolution and Genetic Algorithm search operators.Secondly,during the environmental selection,different selection strategies are employed to screen the two offspring.For the offspring generated by the Differential Evolution search operator,a dynamic fitness function value is used to continuously update the individual selection strategy.In the initial stage of evolution,the population prefers to retain individuals with better diversity.As the number of iterations increases,the population prefers to preserve individuals with better converg ence.The combination of the Differential Evolution search operator and the dynamic fitness function increases the randomness of individual,thereby reducing the possibility of the population falling into local optima.The offspring generated by the Genetic Algorithm search operator is evaluated using a static fitness function to assess individual performance,aiming to maintain the convergence stability of the current population and stably preserve better individuals for the next generation.Finally,better individuals from the two different offspring are extracted to supplement the parent population,improving the environmental selection scope of the population.Through experiments,the combination of multiple search operators and preference-based fitness function values in the proposed algorithm effectively enhances the overall performance in solving constrained multi-objective optimization problems.