Robust multi-objective optimization in high dimensional spaces

Abstract

In most real world optimization problems several optimization goals have to be considered in parallel. For this reason, there has been a growing interest in Multi-Objective Optimization (MOO) in the past years. Several alternative approaches have been proposed to cope with the occurring problems, e.g. how to compare and rank the different elements. The available techniques produce very good results, but they have mainly been studied for problems of "low dimension", i.e. with less than 10 optimization objectives. In this paper we study MOO for high dimensional spaces. We first review existing techniques and discuss them in our context. The pros and cons are pointed out. A new relation called ε-Preferred is presented that extends existing approaches and clearly outperforms these for high dimensions. Experimental results are presented for a very complex industrial scheduling problem, i.e. a utilization planning problem for a hospital. This problem is also well known as nurse rostering, and in our application has more than 20 optimization targets. It is solved using an evolutionary approach. The new algorithms based on relation ε-Preferred do not only yield better results regarding quality, but also enhances the robustness significantly. © Springer-Verlag Berlin Heidelberg 2007.