A Hybrid Evolutionary Approach with Group-Based Solution Encoding for Solving the Constrained Bilevel Multi-Depot Vehicle Routing Problem

Hierarchical decision-making can be observed in different research areas where two optimization levels define a bilevel optimization problem. For instance, in a supply chain production and distribution problem, two decision-makers control these processes respectively, where one company is dedicated only to the distribution of the products, and the other is dedicated to the production of these products. This kind of problem is considered challenging. This work is then on the solution of the Bilevel Multi-Depot Vehicle Routing Problem (BiMDVRP), in which multiple depots need to deliver cargo to cover the demand of many retailers subject to the production plants to meet the demand of each depot optimally. A hybrid genetic algorithm to solve the aforementioned bilevel planning problem is proposed in this work. We use the available information on the problem to implement heuristic mechanisms to improve the results reported by state-of-the-art algorithms. We propose a representation based on groups for the feasible configuration of each depot, due to constraints related to a depot being satisfied. The experimental results show that group-based coding quickly obtains high-quality solutions for the set of instances used in our experimentation setup.