Norm-Based Approximation in E-Convex Multi-objective, Programming

Abstract

This paper addresses the problem of capturing nondominated points on non-convex Pareto frontiers, which are encountered in \(E\)-convex multi-objective optimization problems. We define a nondecreasing map \(T\) which transfers a non-convex Pareto frontier to a convex Pareto frontier. An algorithm to find a piecewise linear approximation of the nondominated set of the convex Pareto frontier is applied. Finally, the inverse map of \(T\) is used to obtain the non-convex Pareto frontier.