Abstract
The multiobjective vehicle routing problem considering customer satisfaction (MVRPCS) involves the distribution of orders from several depots to a set of customers over a time window. This paper presents a self‐adaptive grid multi‐objective quantum evolutionary algorithm (MOQEA) for the MVRPCS, which takes into account customer satisfaction as well as travel costs. The degree of customer satisfaction is represented by proposing an improved fuzzy due‐time window, and the optimization problem is modeled as a mixed integer linear program. In the MOQEA, nondominated solution set is constructed by the Challenge Cup rules. Moreover, an adaptive grid is designed to achieve the diversity of solution sets; that is, the number of grids in each generation is not fixed but is automatically adjusted based on the distribution of the current generation of nondominated solution set. In the study, the MOQEA is evaluated by applying it to classical benchmark problems. Results of numerical simulation and comparison show that the established model is valid and the MOQEA is effective for MVRPCS.
Highlights
The vehicle routing problem VRP is one of the most important and widely studied combinatorial optimization problems, with many real-world applications in logistic distribution and transportation 1
In order to evaluate the performance of the algorithm, the proposed MOQEA is compared with the hybrid multiobjective evolutionary algorithm HMOEA developed in 34
In the HMOEA, feasible individuals are constructed as the initial population by using the pushforward insertion heuristic PFIH, and the GA is used to update these populations to obtain the new subpopulation and to improve the individuals of the subpopulation by the local search method of λ-interchange with variable probability, non-dominated solution set is constructed by using the Challenge Cup rule
Summary
The vehicle routing problem VRP is one of the most important and widely studied combinatorial optimization problems, with many real-world applications in logistic distribution and transportation 1. Since the VRP was firstly proposed by Dantzig and Ramser in 1959 2 , it has been focused in the field of operational research and combinatorial optimization 3–5. The aim of VRP is to find optimal routes for a fleet of vehicles serving a set of customers with known demands. A solution for this problem is to find out a set of minimum cost routes that are used to represent vehicles distribution and clients’ permutation. Current studies on VRP 6, 7 are mainly focused on the single objective problem and the objective is to optimize the number of vehicles dispatched and the travel distance, that is, reducing the service costs of the provider
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
