On the use of the Total Constraint Violation as an Additional Objective in Evolutionary Multi-Objective Optimization

In real-world applications, multi-objective optimization problems (MOPs) usually have multiple constraints. To solve constrained MOPs (CMOPs), various constraint handling techniques (CHTs) were proposed in the field of evolutionary multi-objective optimization (EMO). A simple CHT with high applicability is to use the total constraint violation as an additional objective. The total constraint violation-based CHT transforms a constrained <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(m-1)$</tex>-objective MOP to an unconstrained m-objective MOP. This CHT was also used to create a real-world unconstrained multi-objective test suite called RE from real-world constrained problems. Recently, the RE test suite has been frequently used for evaluating EMO algorithms. Only when the additional objective value is zero (i.e., only when the total constraint violation is zero), solutions are feasible in the original constrained MOP. This means that feasible solutions of the original constrained MOP are located on the boundary of the Pareto front of the formulated unconstrained MOP. As a result, the final population of an EMO algorithm on the formulated unconstrained MOP includes many infeasible solutions of the original constrained MOP. This means that good solution sets for the unconstrained MOP are not always good solution sets for the original constrained MOP. In this paper, we propose an improved total constraint violation-based CHT. The core idea is to use not only positive constraint violations but also negative constraint violations. We apply the proposed CHT to real-world constrained MOPs. Experimental results show that the proposed modification improves the quality of feasible solutions obtained by the total constraint violation-based CHT.