An Improved Co-evolutionary Decomposition-based Algorithm for Bi-level Combinatorial Optimization

Abstract

Several real world problems have two levels of optimization instead of a single one. These problems are said to be bilevel and are so computationally expensive to solve since the evaluation of each upper level solution requires finding an optimal solution at the lower level. Most existing works in this direction have focused on continuous problems. Motivated by this observation, we propose in this paper an improved version of our recently proposed algorithm CODBA (CO-evolutionary Decomposition-Based Algorithm), called CODBA-II, to tackle bi-level combinatorial problems. Differently to CODBA, CODBA-II incorporates decomposition, parallelism, and co-evolution within both levels: (1) the upper level and (2) the lower one, with the aim to further cope with the high computational cost of the overall bi-level search process. The performance of CODBA-II is assessed on a set of instances of the MDVRP (Multi-Depot Vehicle Routing Problem) and is compared against three recently proposed bi-level algorithms. The statistical analysis of the obtained results shows the merits of CODBA-II from effectiveness viewpoint.

A co-evolutionary decomposition-based algorithm for the bi-level knapsack optimisation problem

“…Recently, a CODBA-II (Chaabani et al, 2015b) has been proposed that is shown to perform better than representative and prominent works in the bi-level combinatorial optimisation research area. This latter has demonstrated a good results on the well-known bi-MDVRP combinatorial problem.…”

“…• An improved CODBA-II (Chaabani et al, 2015b): Is an improved version of the CODBA method. It incorporates decomposition, multi-threading, and co-evolution within both levels (upper and lower) with the aim to further cope with the high computational cost of the over-all bi-level search process and to improve the quality of generated solutions.…”