A Multi-objective Evolutionary Algorithm for Decision Support using Infeasible Information
Shinya Sekizaki, Ichiro Nishizaki, Tomohiro Hayashida · 2021
Multi-objective evolutionary algorithms (MOEAs) have been widely used for solving multi-objective optimization problems (MOPs). Although many previous works on MOEAs have focused on unconstrained MOPs (UMOPs), MOPs in the real world often have constraints, and in such cases, constrained MOPs (CMOPs) should be solved. In practical problems with severe constraints, keeping infeasible individuals with good objectives and small constraint violations in the population can improve the performance of MOEAs, and the convergence to the Pareto front can be improved by using the information on both feasible and infeasible individuals. When a small constraint violation greatly improves the objective values, information on infeasible solutions near the feasible region can be important for decision makers. In this paper, we propose an MOEA that can provide the decision maker with information on (1) the trade-offs relationship between the constraint violations and the objective value(s), and (2) the objective value(s) of feasible solutions that can be improved by allowing constraint violations. For maintaining the diversity of non-dominated solutions, the proposed MOEA divides the objective space into multiple subspaces and preserves individuals in each subspace. The population is divided into feasible and infeasible populations and different selection pressures are used in each population. The proposed MOEA is validated by the computational experiments using modified benchmark test problems with constraints.