A Hyper-Matheuristic Methodology for Mixed Integer Linear Optimization Problems

Metaheuristics and exact methods are the most common tools used to solve Mixed Integer Linear Optimization Problems (MILPs). These problems are usually NP-hard problems, being intractable to obtain optimal solutions in reasonable time for large scale instances of the problem. In this work, we propose a MILP-based decomposition in which the main problem is divided in two hierarchical subproblems according to the complexity of the latter. In this paper, we investigate a decomposition separating the discrete and continuous variables, treating each subproblem with different optimization methods. A metaheuristic focuses on the discrete variable search space while the exact method takes into account the continuous variables. Hence, the metaheuristic uses an indirect representation which encode an incomplete solution for the problem, while the exact method is applied to decode the solution and generate a complete solution. The experimental results show that the solutions obtained applying the proposed MILP-based decomposition are better than those obtained solving the problem globally using a metaheuristic method. Moreover, a novel Hyper-Matheuristic scheme is introduced in which the best algorithm selection is found for a set of cooperative metaheuristics and exact optimization algorithms.