A Co-evolutionary Decomposition-based Chemical Reaction Algorithm for Bi-level Combinatorial Optimization Problems

Bi-level optimization problems (BOPs) 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. In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the upper level one. Such a requirement makes the optimization problem difficult to solve, and has kept the researchers busy towards devising methodologies, which can efficiently handle the problem. Recently, a new research field, called EBO (Evolutionary Bi-Level Optimization) has appeared thanks to the promising results obtained by the use of EAs (Evolutionary Algorithms) to solve such kind of problems. However, most of these promising results are restricted to the continuous case. The number of existing EBO works for the discrete (combinatorial case) bi-level problems is relatively small when compared to the field of evolutionary continuous BOP. Motivated by this observation, we have recently proposed a Co-evolutionary Decomposition-Based Algorithm (CODBA) to solve combinatorial bi-level problems. The recently proposed approach applies a Genetic Algorithm to handle BOPs. Besides, a new recently proposed meta-heuristic called CRO has been successfully applied to several practical NP-hard problems. To this end, we propose in this work a CODBA-CRO (CODBA with Chemical Reaction Optimization) to solve BOP. The experimental comparisons against other works within this research area on a variety of benchmark problems involving various difficulties show the effectiveness and the efficiency of our proposal.