Challenging test problems for multi- and many-objective optimization

In spite of the extensive studies that have been conducted regarding the construction of multi-objective test problems, researchers have mainly focused their interests on designing complicated search spaces, disregarding, in many cases, the design of the Pareto optimal fronts of the problems. In this regard, the work related to scalable multi-objective test problems – i.e., problems that can be formulated for an arbitrary number of objectives – has been much less studied. This paper introduces a new set of continuous and box-constrained multi-objective test problems which are scalable in both the number of objectives and in the number of decision variables. Each test problem included in the proposed test suite has a peculiar Pareto front different from those observed in the existing scalable multi-objective test suites. In addition to different Pareto fronts, the proposed test suite introduces features related to the search space that place obstacles that complicate exploring Pareto optimal solutions. Such features can be easily switched on and off by the user to analyze specific mechanisms of multi-objective evolutionary algorithms (MOEAs). The components used in the proposed test suite can be used as a toolkit to construct new test instances not included in this set of problems. To illustrate the use and difficulties of the proposed test suite, some experiments are presented adopting three MOEAs using selection mechanisms based on Pareto optimality, decomposition, and a performance indicator (hypervolume).