Solving capacitated vehicle routing problem using cooperative firefly algorithm

Abstract

The capacitated vehicle routing problem (CVRP) is a classical combinatorial optimization problem, which has received much attention due to its main challenges as distribution, logistics, and transportation. This proposed attempts to find the vehicle routes with minimizing traveling distance, in which the excellent solution delivers a set of customers in one visit by capacitated vehicle. For solving the CVRP problem, a cooperative hybrid firefly algorithm (CVRP-CHFA) is proposed in this paper with multiple firefly algorithm (FA) populations. Each FA is hybridized with two types of local search (i.e., Improved 2-opt as a local search and 2-h-opt as a mutation operator) and genetic operators. The proposed algorithms (FAs) communicate from time to time for exchanging some solutions (fireflies). The main aim of the hybridization and communication strategies is to maintain the diversity of populations to prevent the proposed algorithm from falling into local optima and overcome the drawbacks of a single swarm FA. The experiments are conducted on 108 instances from eight standard benchmarks. The results revealed that the proposed CVRP-CHFA got promising results compared to other well-known methods. Moreover, the proposed CVRP-CHFA significantly outperformed the recent three hybrid firefly algorithms.