Improving Search Efficiency and Diversity of Solutions in Multiobjective Binary Optimization by Using Metaheuristics Plus Integer Linear Programming

Abstract

Metaheuristics for solving multiobjective problems can provide an approximation of the Pareto front in a short time, but can also have difficulties finding feasible solutions in constrained problems. Integer linear programming solvers, on the other hand, are good at finding feasible solutions, but they can require some time to find and guarantee the efficient solutions of the problem. In this work we combine these two ideas to propose a hybrid algorithm mixing an exploration heuristic for multiobjective optimization with integer linear programming to solve multiobjective problems with binary variables and linear constraints. The algorithm has been designed to provide an approximation of the Pareto front that is well-spread throughout the objective space. In order to check the performance, we compare it with three popular metaheuristics using two benchmarks of multiobjective binary constrained problems. The results show that the proposed approach provides better performance than the baseline algorithms in terms of number of the solutions, hypervolume, generational distance, inverted generational distance, and the additive epsilon indicator.