Hindrances for robust multi-objective test problems

• Five hindrances are employed to improve and propose challenging robust multi-objective test problems.
• 12 robust multi-objective test problems have been proposed.
• Five robust multi-objective algorithms have been compared on the proposed test functions.
• Deceptive robust multi-objective test functions are proposed for the first time.
• Biased robust multi-objective test functions are proposed for the first time.

Despite the significant number of benchmark problems for evolutionary multi-objective optimisation algorithms, there are few in the field of robust multi-objective optimisation. This paper investigates the characteristics of the existing robust multi-objective test problems and identifies the current gaps in the literature. It is observed that the majority of the current test problems suffer from simplicity, so five hindrances are introduced to resolve this issue: bias towards non-robust regions, deceptive global non-robust fronts, multiple non-robust fronts (multi-modal search space), non-improving (flat) search spaces, and different shapes for both robust and non-robust Pareto optimal fronts. A set of 12 test functions are proposed by the combination of hindrances as challenging test beds for robust multi-objective algorithms. The paper also considers the comparison of five robust multi-objective algorithms on the proposed test problems. The results show that the proposed test functions are able to provide very challenging test beds for effectively comparing robust multi-objective optimisation algorithms. Note that the source codes of the proposed test functions are publicly available at www.alimirjalili.com/RO.html.

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