A Generator for Scalable SAT Constrained Multi-Objective Optimization Benchmark Problems

Benchmark problems play a key role in the development of Multi-Objective Evolutionary Algorithms, as they help evaluate their performances and functionalities. Although there is a significant amount of research related to unconstrained optimization, there has been less focus in constrained optimization and their benchmark problems, which, in general, offer limited configurability for scalibility. This article proposes a method to generate equality and inequality constraints, based on Boolean satisfiability problems, that are scalable in the number of constraints, number of variables in the constraints and feasibility ratio of the search space. The constraints can be attached to any existing state-of-the-art binary benchmark problem scalable in the number of objectives and variables of the problem. In this paper, we analyze some properties of the generated constraints and features of the resulting problems when the constraints are attached to bi-objective Knapsack and MNK-landscape problems.