On approximating weakly/properly efficient solutions in multi-objective programming
This paper deals with approximate solutions of general (that is, without any convexity assumption) multi-objective optimization problems (MOPs). In this text, by reviewing some standard scalarization techniques we are interested in finding the relationships between epsilon-(weakly, properly) efficient points of an MOP and epsilon-optimal solutions of the related scalarized problem. For this purpose, the relationships between epsilon is an element of R >= and epsilon is an element of R(>=)(m), for a single objective and multi-objective problems, respectively, are analyzed. In fact, necessary and/or sufficient conditions for approximating (weakly, properly) efficient points of a general MOP via approximate solutions of the scalarized problems are obtained. (C) 2011 Elsevier Ltd. All rights reserved.
approximate solution multi-objective optimization epsilon-proper efficiency scalarization method