Extension of Zoutendijk method for solving constrained multiobjective optimization problems

Abstract

This paper extends the use of Zoutendijk method for constrained multiobjective optimization problems. This extension is a nonparametric direction-based algorithm. More precisely, considering all objective functions and binding constraints, this algorithm proposes a convex quadratic subproblem for generating a convenient improving feasible direction. Then, by using some elementary computation, the step length corresponding to the current direction is obtained. Some useful theoretical results corresponding to the proposed method are demonstrated. Using some of these theoretical results and under some mild conditions, the convergence of the proposed method is proved. The Zoutendijk multiobjective optimization (ZMO) method is not a population-based method. However, in order to find an approximation of the nondominated frontier, we need to have an appropriate population of initial feasible solutions. To achieve this aim, in this paper a cutting plane-like procedure which can generate an appropriate population of feasible solutions over the feasible set is proposed.Finally, in order to show its superiority, the proposed method is implemented for some well-known test problems. By employing some performance assessment criteria, the obtained numerical results are compared with the NSGA II method for all test problems. To have a more convenient comparison, the results are depicted in some performance profiles. Moreover, the obtained nondominated frontiers of these methods are compared for some test problems. The numerical results confirm the high performance of the ZMO method.