Searching for knee regions in multi-objective optimization using mobile reference points

Abstract

Evolutionary algorithms have amply demonstrated their effectiveness and efficiency in approximating the Pareto front of different multi-objective optimization problems. Fewer attentions have been paid to search for the preferred parts of the Pareto front according to the decision maker preferences. Knee regions are special portions of the Pareto front containing solutions having the maximum marginal rates of return, i.e., solutions for which an improvement in one objective implies a severe degradation in at least another one. Such characteristic makes knee regions of particular interest in practical applications from the decision maker perspective. In this paper, we propose a new updating strategy for a reference points based multi-objective evolutionary algorithm which forces this latter to focus on knee regions. The proposed idea uses a set of mobile reference points guiding the search towards knee regions. The extent of the obtained regions could be controlled by the means of a user-defined parameter. The verification of the proposed approach is assessed on two- and three-objective knee-based test problems a priori and interactively. The obtained results are promising.