Exploiting the marginal profits of constraints with evolutionary multi-objective optimization techniques

Many real-world search and optimization problems naturally involve constraint handling. Recently, quite a few heuristic methods were proposed to solve the nonlinear constrained optimization problems. However, the constraint-handling approaches in these methods have some drawbacks. In this paper, we gave a Multi-objective optimization problem based (MOP-based) formula for constrained single-objective optimization problems. We proposed a way to solve them by using multi-objective evolutionary algorithms (MOEAs). By simulation experiments, we find this approach for constraint handling not only can find the constrained optimally, but also can provide the decision maker (DM) with a group of trade-off solutions with slightly constraint violation and meanwhile with substantial gain in the objective function. This can enable the DM to have more freedom to choose his preferred solution and therefore exploit more profits in the margin of constraint violations, where the constraint violations are small or acceptable.