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Review of coevolutionary developments of evolutionary multi-objective and many-objective algorithms and test problems

In the evolutionary multi-objective optimization (EMO) community, some well-known test problems have been frequently and repeatedly used to evaluate the performance of EMO algorithms. When a new EMO algorithm is proposed, its performance is evaluated on those test problems. Thus algorithm development can be viewed as being guided by test problems. A number of test problems have already been designed in the literature. Since the difficulty of designed test problems is usually evaluated by existing EMO algorithms through computational experiments, test problem design can be viewed as being guided by EMO algorithms. That is, EMO algorithms and test problems have been developed in a coevolutionary manner. The goal of this paper is to clearly illustrate such a coevolutionary development. We categorize EMO algorithms into four classes: non-elitist, elitist, many-objective, and combinatorial algorithms. In each category of EMO algorithms, we examine the relation between developed EMO algorithms and used test problems. Our examinations of test problems suggest the necessity of strong diversification mechanisms in many-objective EMO algorithms such as SMS-EMOA, MOEA/D and NSGA-III.