Pareto-based many-objective optimization using knee points
Justin Maltese, Beatrice M. Ombuki-Berman, Andries Petrus Engelbrecht · 2016
Many real-world optimization problems contain multiple (often conflicting) goals to be optimized simultaneously, commonly referred to as multi-objective problems (MOPs). Currently, there exists a plethora of Pareto optimizers designed to solve MOPs. Previous literature has demonstrated that the performance of these optimizers degrade for problems which possess more than three objectives, known as many-objective problems (MaOPs). The downfall of the traditional Pareto approach is that the dominance-based selection strategy loses effectiveness in distinguishing desirable solutions as the number of objectives grows larger, inhibiting convergence to the true Pareto front. One potential solution to this problem is to utilize the concept of knee points as a secondary metric for optimization. Two new knee-driven algorithms are proposed within this work, namely the knee point driven particle swarm optimization (KnPSO) and knee point driven differential evolution (KnDE) algorithm. Due to the nature of the knee point identification mechanism used, both of these algorithms have the benefit of naturally producing a diverse set of solutions without having to incorporate additional criterion. The existing knee-driven evolutionary algorithm (KnEA) along with the proposed approaches are compared against several non-knee variants. Experimental results on nine challenging MaOPs demonstrate that knee points are a viable option for improving the performance of Pareto-based approaches. The knee point driven algorithms are shown to produce significantly higher inverted generational distance and hypervolume metric values in comparison to their non-knee counterparts.