Partially Degenerate Multi-objective Test Problems

Pang，Lie Meng; Nan，Yang; Ishibuchi，Hisao

10.1007/978-3-031-27250-9_20

2023

0302-9743

1611-3349

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

13970 LNCS

277-290

Degenerate multi-objective test problems are included in test suites to evaluate EMO algorithms on a wide variety of test problems. However, it was pointed out in some studies that the frequently-used degenerate DTLZ5, DTLZ6 and WFG3 test problems do not have degenerate Pareto fronts. Their Pareto fronts are different from the originally intended degenerate shapes. Actually, they are partially degenerate test problems. Modified formulations of DTLZ5 and DTLZ6 were proposed to remove the non-degenerate parts of their Pareto fronts. However, the original formulations of DTLZ5, DTLZ6 and WFG3 continue to be used as degenerate test problems in many studies whereas they are not degenerate test problems. One issue in their use as degenerate test problems is that reference point sets for IGD calculation are sampled from the originally intended degenerate Pareto fronts whereas they are not the true Pareto fronts. Nevertheless, the original DTLZ5, DTLZ6 and WFG3 formulations are useful for performance evaluation of EMO algorithms since their Pareto front shapes are similar to some real-world problems and much more complicated than other test problems. That is, their use helps us to evaluate the performance of EMO algorithms on a wide variety of test problems including realistic and challenging test problems. In this paper, we clearly demonstrate the usefulness of the original DTLZ5, DTLZ6 and WFG3 formulations. Then, after pointing out the difficulty in their use in computational experiments, we explain how we can obtain reliable experimental results on those test problems.

Degenerate Pareto fronts Evolutionary multi-objective optimization IGD indicator Partially degenerate Pareto fronts Test problems

First ; Corresponding

English

2-s2.0-85151053519

Scopus

Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation,Department of Computer Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China

Pang，Lie Meng,Nan，Yang,Ishibuchi，Hisao. Partially Degenerate Multi-objective Test Problems[C],2023:277-290.