Multi-objective L-shaped Test Functions
Angus Kenny, Tapabrata Ray, Hemant Kumar Singh · Proceedings of the Genetic and Evolutionary Computation Conference · 2025
Many real-world multi-objective optimization problems exhibit L-shaped Pareto fronts, characterized by steep trade-offs between objectives near their extreme values. This class of problems poses significant challenges for evolutionary algorithms in obtaining uniformly spread solutions across the Pareto front (PF). This paper introduces eight new test functions with L-shaped and reflected L-shaped PFs, intended to provide a valuable framework for benchmarking multi-objective optimization algorithms. The functions are based on modifications of the well-known DTLZ2 problem and a reciprocal function formulation, each formulated in standard and 'hard' variants. The 'hard' variants introduce modifications to the auxiliary functions, increasing problem difficulty by biasing the distribution of non-Pareto solutions away from the PF as the problem dimensionality increases. Numerical experiments are conducted using NSGA-II and MOEA/D algorithms, with performance evaluated using hypervolume and inverted generational distance metrics. The results demonstrate that the proposed test functions effectively challenge the algorithms, especially in their 'hard' variants, and outline the differences in algorithm performance based on the shape of the PF. These findings highlight the need for development of more robust multi-objective optimization techniques capable of handling such PF geometries.