Comparative study of knee-based algorithms for many-objective optimization problems

Abstract

Nowadays, most real-world optimization problems consist of many and often conflicting objectives to be optimized simultaneously. Although, many current Multi-Objective optimization algorithms can efficiently solve problems with 3 or less objectives, their performance deteriorates proportionally with the increasing of the objectives number. Furthermore, in many situations the decision maker (DM) is not interested in all trade-off solutions obtained but rather interested in a single optimum solution or a small set of those trade-offs. Therefore, determining an optimum solution or a small set of trade-off solutions is a difficult task. However, an interesting method for finding such solutions is identifying solutions in the Knee region. Solutions in the Knee region can be considered the best obtained solution in the obtained trade-off set especially if there is no preference or equally important objectives. In this paper, a pruning strategy was used to find solutions in the Knee region of Pareto optimal fronts for some benchmark problems obtained by NSGA-II, MOEA/D-DE and a promising new Multi-Objective optimization algorithm NSGA-III. Lastly, those knee solutions found were compared and evaluated using a generational distance performance metric, computation time and a statistical one-way ANOVA test.