Constrained Single- and Multiple-Objective Optimization with Differential Evolution

Most real-world optimization problems are single- or multiple-objective optimization problems with constraints. However, the most common approach adopted to deal with constrained search spaces is the use of penalty functions which require a careful and difficult tuning of the penalty factors. In this paper, we proposed a multi-objective optimization concept to handle constraints. Firstly, we redefine the problems by converting all the constraints into new objective functions. Thus, the problems with m objective functions and n constraints become unconstrained optimization problems with m+n objective functions. Then we could utilize all kinds of multi-objective evolutionary algorithms to optimize the redefined problems. In this work a recent multi-objective differential evolution (DEMO) was used for multi-objective optimization. In order to evaluate the ability of our method we chose eight famous constrained test functions, including four single-objective test functions (g06, g08, gll and Gearbox) and four multiple- objective test functions (CONSTR, SRN, TNK and KITA). Experimental results from eight constrained test functions show that the proposed method is capable of successfully optimizing constrained single- and multiple-objective problems.