Including Users Preferences in the Decision Making for Discrete Many Objective Optimization Problems

Abstract

In many applications one is faced with the problem that many objectives have to be optimized concurrently leading to a many objective optimization problem (MaOP). One important characteristic of discrete MaOPs is that its solution set, the so-called Pareto set, consists of too many elements to be efficiently computed. Thus, though specialized evolutionary algorithms are in principle capable of computing a set S of well spread candidate solutions along the Pareto set, it is not guaranteed that the decision maker of the underlying problem will find the "ideal" solution within S for his or her problem. We argue in this paper that it makes sense to perform akind of post processing for a selected solution s 2 S. More precisely, we will propose two different methods that allow to steer the search from s along the Paretoset into user specified directions. Numerical resultson instances of the vehicle routing problem with time windows will show the effectivity of the novel methods.