Dual population approximate constrained Pareto front for constrained multiobjective optimization

Abstract

For constrained multiobjective optimization problems (CMOPs), the ultimate goal is to obtain a set of well-converged and well-distributed feasible solutions to approximate the constrained Pareto front (CPF). Various constraints may change the position and/or shape of the CPF. This poses great challenges to the approximation of the CPF. This is especially true when the CPF mainly lies on constraint boundaries (i.e., CPF and unconstrained PF have little or even no intersection). To tackle this issue, we propose a novel dual population algorithm for approximating the CPF from both sides of the constraint boundaries. Specifically, 𝑃 𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛1 uses the constrained-domination principle to approximate the CPF from the sides of feasible regions only; 𝑃 𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛2 adopts an improved 𝜖-constrained method to approximate the CPF from both the feasible as well as infeasible regions. Offspring generated by both populations are merged and combined with 𝑃 𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛1 and 𝑃 𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛2. In addition, some selected members of 𝑃 𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛1 and 𝑃 𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛2 are permitted to migrate to the combined populations to facilitate knowledge sharing. Systematic experiments carried out on three benchmark test suites and 10 real-world CMOPs show the proposed algorithm achieved superior or competitive performance, especially for CMOPs where the CPF is mainly located at constraint boundaries. Therefore, on the basis of dual population, approximating CPFs from both sides of feasible and infeasible regions contributes an alternative approach to solving CMOPs.