A new co-evolutionary decomposition-based algorithm for bi-level combinatorial optimization

Bi-Level Optimization Problems (BLOPs) are a class of challenging problems with two levels of optimization tasks. The main goal is to optimize the upper level problem which has another optimization problem as a constraint. The latter is called the lower level problem. In this way, the evaluation of each upper level solution requires finding an (near) optimal solution to the corresponding lower level problem, which is computationally very expensive. Many real world applications are bi-level by nature, ranging from logistics to software engineering. Further, proposed bi-level approaches have been restricted to solve linear BLOPs. This fact has attracted the evolutionary computation community to tackle such complex problems and many interesting works have recently been proposed. Unfortunately, most of these works are restricted to the continuous case. Motivated by this observation, we propose in this paper a new Co-evolutionary Decomposition Algorithm inspired from Chemical Reaction Optimization algorithm, called E-CODBA (Energy-based CODBA), to solve combinatorial bi-level problems. Our algorithm is based on our previous works within this research area. The main idea behind E-CODBA is to exploit co-evolution, decomposition, and energy laws to come up with good solution(s) within an acceptable execution time. The statistical analysis of the experimental results on the Bi-level Multi-Depot Vehicle Routing Problem (Bi-MDVRP) show the out-performance of our E-CODBA against four recently proposed works in terms of effectiveness and efficiency.