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A Review of Features and Limitations of Existing Scalable Multiobjective Test Suites

Abstract:

In multiobjective optimization, a scalable test problem is one that can be formulated for an arbitrary number of objectives. Scalable test problems evaluate the conceptual foundations of the so-called many-objective evolutionary algorithms. As an important class of problems, scalable test problems should contemplate a wide variety of features allowing us to evaluate and judge specific components of many-objective evolutionary algorithms. This, in fact, should promote the development of new strategies and/or methods in the design of many-objective optimization approaches. For this reason, the study of features and difficulties of this class of problems, plays a salient role in the development of many-objective approaches. As a result, a number of multiobjective scalable test problems have been proposed in recent years. In this paper, we present a review of features and limitations of existing multiobjective test problems formulated in continuous and unconstrained search spaces. We examine some features observed in some test problems which have not been properly discussed before. Additionally, we summarize a list of features and recommendations that should be considered in the design of scalable multiobjective test instances. Then, we preset a review of the state-of-the-art scalable test suites, including their features and limitations according to the recommended guidelines discussed herein. Finally, some possible paths for future research in this area are briefly discussed.