A co-evolutionary genetic algorithm with knowledge transfer for multi-objective capacitated vehicle routing problems

Abstract

The capacitated vehicle routing problem (CVRP) aims to find the routes that minimize transportation costs. However, in real-world applications, the equitable workload is essential for the drivers and logistics companies. For assigning an appropriate load for each vehicle, this paper formulates the CVRP with workload balancing as a multi-objective optimization problem (MO-CVRP). The goal is to simultaneously minimize the total length of routes and the variance of loads assigned to each vehicle. Although several multi-objective evolutionary algorithms (MOEAs) have been proposed for the MO-CVRP, they often suffer from slow convergence speeds due to the complexity of the search space, which hinders the identification of clear search directions. To address this issue, the knowledge transfer method is introduced that can leverage search experiences from related problems to expedite the solution process of the current problem. Specifically, a co-evolutionary genetic algorithm with knowledge transfer is proposed, where a simplified version of the traveling salesman problem (TSP) by disregarding the vehicle capacity constraint is utilized to facilitate the quick solution of the original MO-CVRP. To enable information interaction between these two problems, the widely used denoising autoencoder is adopted to construct a transformation relation between solutions from the TSP to the MO-CVRP. Additionally, an adaptive migration strategy is proposed to adaptively select the migration methods and an improved split operator strategy is designed to ensure the feasibility of the solutions. The proposed algorithm is compared with four state-of-the-art MOEAs on MO-CVRP test sets with different scales. Experimental results show that the proposed algorithm exhibits faster convergence speed and achieves solutions with superior convergence.