Regular Pareto Front Shape is not Realistic

Performance of evolutionary multi-objective and many-objective optimization algorithms is usually evaluated by computational experiments on a number of test problems. Thus, performance comparison results depend on the choice of test problems. For fair comparison, it is needed to use a wide variety of test problems with various characteristics. However, most of well-known and frequently-used scalable test problems have the same type of Pareto fronts called "regular" Pareto fronts: Their shape is triangular. In this paper, we discuss the reality of this type of Pareto fronts. First, we show that a triangular Pareto front has some unrealistic properties as the Pareto front of a real-world multi-objective problem. Next, we examine the shape of the Pareto fronts of some other multi-objective test problems with independently generated objectives (i.e., with objectives that are not derived from a pre-specified shape of Pareto fronts). It is shown that the Pareto fronts of those test problems are inverted triangular (i.e., not regular). Then, we demonstrate that the shape of Pareto fronts (i.e., triangular or inverted triangular) has large effects on the performance of decomposition-based and hypervolume-based algorithms. Finally, we show difficulties of hypervolume-based performance evaluation for many-objective problems with inverted triangular Pareto fronts.