Shape of Feasible Regions of Real-World Multi-Objective Problems

In the community of evolutionary multi-objective optimization (EMO), artificially designed test problems (e.g., DTLZ) are usually used to evaluate the performance of EMO algorithms. To analyze the performance of EMO algorithms on these test problems, researchers usually consider the features of the test problems such as the shape of the Pareto front, the number of objectives, and the number of decision variables. However, a few studies investigate the shape of the feasible region of the test and real-world problems. In this paper, we visualize the feasible regions of some real-world problems in their objective spaces. Our visualization results show that the feasible region shape of most real-world problems is similar to that of WFG and Minus-DTLZ test problems. These observations suggest the usefulness of WFG and Minus-DTLZ as test problems to evaluate EMO algorithms. Our observations are also consistent with reported performance comparison results on DTLZ, WFG, Minus-DTLZ, Minus-WFG and some real-world problem suites in the literature.