Multiobjective Test Problems with Degenerate Pareto Fronts

In multiobjective optimization, a set of scalable test problems with a variety of features allows researchers to investigate and evaluate abilities of different optimization algorithms, and thus can help them to design and develop more effective and efficient approaches. Existing, commonly-used test problem suites are mainly focused on the situations where all the objectives are conflicting with each other. However, in some many-objective optimization problems, there may be unexpected characteristics among objectives, e.g., redundancy. This leads to a degenerate problem. In this paper, we systematically study degenerate problems. We abstract three generic characteristics of degenerate problems, and on the basis of these characteristics we present a set of test problems, in order to support the investigation of multiobjective search algorithms on problems with redundant objectives. To assess the proposed test problems, ten representative multiobjective evolutionary algorithms are tested. The results indicate that none of the tested algorithms is able to effectively solve these proposed problems, calling for the need of developing new approaches to addressing degenerate multi-objective problems.