Solving Hard Multiobjective Optimization Problems Using epsilon-Constraint with Cultured Differential Evolution

In this paper, we propose the use of a mathematical programming technique called the e-constraint method, hybridized with an evolutionary single-objective optimizer: the cultured differential evolution. The e-constraint method uses the cultured differential evolution to produce one point of the Pareto front of a multiobjective optimization problem at each iteration. This approach is able to solve difficult multiobjective problems, relying on the efficiency of the single-objective optimizer, and on the fact that none of the two approaches (the mathematical programming technique or the evolutionary algorithm) are required to generate the entire Pareto front at once. The proposed approach is validated using several difficult multiobjective test problems, and our results are compared with respect to a multi-objective evolutionary algorithm representative of the state-of-the-art in the area: the NSGA-II.