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The difficulty of solving a multi-objective optimization problem is impactedby the number of objectives to be optimized. The presence of many objectivestypically introduces a number of challenges that affect the choice/design ofoptimization algorithms. This paper investigates the drivers of thesechallenges from two angles: (i) the influence of the number of objectives onproblem characteristics and (ii) the practical behavior of commonly usedprocedures and algorithms for coping with many objectives. In addition toreviewing various drivers, the paper makes theoretical contributions byquantifying some drivers and/or verifying these drivers empirically by carryingout experiments on multi-objective NK landscapes and other typical benchmarks.We then make use of our theoretical and empirical findings to derive practicalrecommendations to support algorithm design. Finally, we discuss remainingtheoretical gaps and opportunities for future research in the area of multi-and many-objective optimization.

What if we Increase the Number of Objectives? Theoretical and Empirical Implications for Many-objective Optimization