What if we increase the number of objectives? Theoretical and empirical implications for many-objective combinatorial optimization. (September 2022) - Allmendinger, Richard; Jaszkiewicz, Andrzej; Liefooghe, Arnaud; Tammer, Christiane
Abstract: The difficulty of solving a multi-objective optimization problem is impacted by the number of objectives to be optimized. The presence of many objectives typically introduces a number of challenges that affect the choice/design of optimization algorithms. This paper investigates the drivers of these challenges from two angles: (i) the influence of the number of objectives on problem characteristics and (ii) the practical behavior of commonly used procedures and algorithms for coping with many objectives. In addition to reviewing various drivers, the paper makes theoretical contributions by quantifying some drivers and/or verifying these drivers empirically by carrying out experiments on multi-objective combinatorial optimization problems (multi-objective NK-landscapes). We then make use of our theoretical and empirical findings to derive practical recommendations to support algorithm design. Finally, we discuss remaining theoretical gaps and opportunities for future research in the area of multi- and many-objective optimization. Highlights: Investigated the impact of the number of objectives in an optimization problem. Theoretically quantified the impact. Empirically verified the impact using multi-objective NK landscapes. Derived practical recommendations to support algorithm design. Discussed theoretical gaps and opportunities for future research.