Performance Comparison of Multi-Objective Evolutionary Algorithms on Simple and Difficult Many-Objective Test Problems

Recently, a number of many-objective evolutionary algorithms have been proposed in the literature. Those algorithms are often evaluated using the frequently-used DTLZ and WFG test problems. One feature of those test problems is the use of the same distance function in all objectives in each problem. As a result, the distance from each solution to the Pareto front is minimized by optimizing the distance function. This means that the convergence improvement is a single-objective optimization independent of the number of objectives. This feature makes the DTLZ and WFG test problems easy. Recently, some difficult test problems have been proposed by removing this feature. In this paper, we examine the performance of many-objective evolutionary algorithms through computational experiments on a recently-proposed difficult test problem with no distance function. We show that totally different comparison results are obtained for the easy test problems with distance functions (i.e., DTLZ and WFG) and the difficult test problem with no distance function.