Chaotic opposition initialization and average mutation update-based differential evolution

The diversity of individuals affects the quality of the solution sets and determines the distribution of the solution sets in solving multi-objective optimization problems. In order to expand the search direction of individuals, increase the diversity of the population and avoid individuals from gathering at the boundary during the mutation process, a chaotic opposition initialization and average mutation update-based differential evolution (COI-AMU_DE) is proposed. Firstly, in order to generate a uniformly distributed initial population, random numbers are subjected to tent chaotic map and opposition-based learning in the initialization process to generate uniformly distributed random numbers. Secondly, a mutation operator is processed to avoid individuals from gathering at the boundary to improve the diversity of population. In each iteration, the average mutation update of the individuals is carried out for legalization, and the weighted sum of the rankings based on the Pareto dominance and the constrained dominance principle (CDP) are calculated. Then the next generation of individuals is selected according to the weighted sum sorting, and the process is repeated until the end condition is satisfied to obtain the result sets. Finally, a total of 38 multi-objective optimization problems in three test suites are selected to evaluate the performance of the proposed algorithm, and it is compared with seven algorithms. The simulation results show that COI-AMU_DE has high comprehensive performance in solving constrained multi-objective optimization problems.