An analysis of SAT constrained MNK-landscapes as benchmark problems for multi-objective evolutionary algorithms

Abstract

Benchmark problems have been fundamental in advancing our understanding of the dynamics and design of multi-objective evolutionary optimization algorithms. Within the binary domain, there is a lack of multi-objective benchmark problems that can help further research on constrained optimization. This paper presents highly configurable benchmark problems for constrained binary multi-objective optimization combining SAT Constraints, constructed from satisfiability clauses, and MNK-Landscapes. The benchmark problems are scalable in the number of equality and inequality constraints, feasibility-hardness, number of objectives, number of variables, and epistasis between variables. This paper studies how SAT Constraints affect the distribution of feasible solutions in objective and decision spaces and illustrates their impact on the performance and dynamics of multi-objective evolutionary algorithms when solving SAT Constrained MNK-Landscapes.