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Exploring the decision and objective space of SAT constrained multi-objective problems

Although most real-world problems include many constraints that limit the set of feasible solutions, there is significantly less study in constrained benchmark problems when compared to unconstrained ones. SAT constraints attempt to aid the study of constrained multi-objective optimization by allowing any number of equality and inequality constraints, with controllable feasibility ratio, to be added to state-of-the-art benchmark problems. This paper studies the features of SAT constraints by looking at some of their properties such as distribution, clustering and distance of feasible solutions in the decision and objective space when added to 0-1 multi-objective knapsack problems and multi-objective MNK-Landscapes.