An angle dominance criterion for evolutionary many-objective optimization

Abstract It is known that Pareto dominance encounters difficulties in many-objective optimization. This strict criterion could make most individuals of a population incomparable in a high-dimensional space. A straightforward approach to tackle this issue is modify the Pareto dominance criterion. This is typically done by relaxing the dominance region. However, this modification is often associated with one or more parameters of determining the relaxation degree, and the performance of the corresponding algorithm could be sensitive to such parameters. In this paper, we propose a new dominance criterion, angle dominance, to deal with many-objective optimization problems. This angle dominance criterion can provide sufficient selection pressure towards the Pareto front and be exempt from the parameter tuning. In addition, an interesting property of the proposed dominance criterion, in contrast to existing dominance criteria, lies in its capability to reflect an individual’s extensity in the population. The angle dominance is integrated into NSGA-II (instead of Pareto dominance) and has demonstrated high competitiveness in many-objective optimization in comparison with a range of peer algorithms.