Multi-objective Differential Evolution with Helper Functions for Constrained Optimization

Solving constrained optimization problems by multi-objective evolutionary algorithms has scored tremendous achievements in the last decade. Standard multi-objective schemes usually aim at minimizing the objective function and also the degree of constraint violation simultaneously. This paper proposes a new multi-objective method for solving constrained optimization problems. The new method keeps two standard objectives: the original objective function and the sum of degrees of constraint violation. But besides them, four more objectives are added. One is based on the feasible rule. The other three come from the penalty functions. This paper conducts an initial experimental study on thirteen benchmark functions. A simplified version of CMODE is applied to solving multi-objective optimization problems. Our initial experimental results confirm our expectation that adding more helper functions could be useful. The performance of SMODE with more helper functions (four or six) is better than that with only two helper functions.