The modified objective-constraint scalarization approach for multiobjective optimization problems

In this article, a novel scalarization methodology, called the modified objective-constraint technique, is proposed for determining efficient solutions a given multiobjective programming problem. The suggested scalarized problem extends some existing problems. It is shown that how adding slack variables to the constraints, can help us to find easily checked conditions concerning (weak, proper) Pareto optimality. By applying the suggested problem, we generate an almost even approximation of the efficient front. The performance and capability of the developed approach are demonstrated in test problems containing disconnected or nonconvex fronts and feasible points. In particular, we apply the suggested approach in an engineering design problem with two objective functions.

Automated summary

This article proposes a modified objective-constraint technique for solving multiobjective programming problems. By adding slack variables, easily checked conditions for Pareto optimality can be found. The suggested approach generates an almost even approximation of the efficient front.