Evolutionary algorithm using feasibility-based grouping for numerical constrained optimization problems

Abstract

When Evolutionary algorithms are used for solving constraint optimization problems, how to deal with the relationship between the feasible and infeasible parents directly influences the quality of the final results. The ratio of feasible/infeasible parents in a population is first investigated. Through experimental studies on bench-mark and hypothetical problems, it is revealed that the solutions are very dependent on how the ratio of feasible I infeasible parents balanced. Also, this is dependent on the problem itself - what may be an optimal approach for one problem may not be optimal for another. The upper and lower bounds of the number of feasible parents are given out. To fully utilize the scope between the upper and lower bounds, an evolutionary algorithm using feasibility-based grouping is proposed. Feasible and infeasible individuals are divided into two groups: feasible group and infeasible group. The evaluation and ranking of these two groups are performed separately. Two parents selection methods: proportional parent selection strategy and parent selection strategy inspired by population ecology are proposed for parents production from the two groups. Objective function and bubble sort method are selected as the fitness function and ranking method for the feasible group. Three existing evolutionary algorithms, dynamic penalty method, annealing penalty method, and stochastic ranking method, are modified to evaluate and rank the infeasible group. The new method is tested using a (μ, λ)-ES on thirteen benchmark problems. The influence of (μ, λ) values on the results is also discussed.