Applying hybrid meta-heuristics for capacitated vehicle routing problem Shih-Wei Lin a,b , Zne-Jung Lee b, * , Kuo-Ching Ying c , Chou-Yuan Lee d a Department of Information Management, Chang Gung University, No. 259, Wen-Hwa 1st Road, Tao-Yuan, Taiwan b Department of Information Management, Huafan University, No. 1, Huafan Road, Taipei, Taiwan c Department of Industrial Management and Management Information, Huafan University, No. 1, Huafan Road, Taipei, Taiwan d Department of Information Management, Lan Yang Institute of Technology, Taiwan Abstract The capacitated vehicle routing problem (CVRP) is one of the most important problems in the optimization of distribution networks. The objective of CVRP, known demands on the cost of originating and terminating at a delivery depot, is to determine the optimal set of routes for a set of vehicles to deliver customers. CVRP is known to be NP-hard problem, and then it is difficult to solve this problem directly when the problem size is large. In this paper, a hybrid algorithm of simulated annealing and tabu search is applied to solve CVRP. It takes the advantages of sim- ulated annealing and tabu search for solving CVRP. Simulation results are reported on classical fourteen instances and twenty large-scale benchmark instances. From simulation results, the proposed algorithm finds eight best solutions of classical fourteen instances. Addi- tionally, the solutions of the proposed algorithm have also admirable performance for twenty large-scale benchmark instances. It shows that the proposed algorithm is competitive with other existing algorithms for solving CVRP. Ó 2007 Published by Elsevier Ltd. Keywords: Capacitated vehicle routing problem; Hybrid algorithm; Simulated annealing; Tabu search 1. Introduction CVRP is a generic name given to a whole class of prob- lems in which a set of routes for a fleet of vehicles based at one or several depots must be determined for a number of geographically dispersed customers, and vehicles have the maximal loading capacity. The objective of CVRP is to minimize the total cost (i.e., a weighted function of the number of vehicles and the travel distance of vehicles) to serve a set of customers with known demands. The route must be designed in such a way that each customer is vis- ited once and by only one vehicle. CVRP is a well known combination problem which falls into the category of NP-Hard problem, since it concludes the bin packing prob- lem and the traveling salesperson problem as a special case (Laporte & Semet, 2001; Prins, 2004). CVRP can be solved by mathematical methods or heu- ristic approaches. The use of mathematical methods can obtain the optimal solutions. However, the required com- putational complexity will result in exponential time when the problem size is large (Lee, Lee, & Su, 2002; Lee, Su, & Lee, 2003). Heuristic approaches can be divided into the classical heuristic approaches and the meta-heuristic approaches. The classical heuristic approaches can find one feasible solution quickly, but this feasible solution may have a large disparity compared with the best solution. The meta-heuristic approaches can obtain near optimal solutions or even global optimal solutions. Therefore, meta-heuristic approaches such as simulated annealing (SA) and tabu search (TS) are usually employed to find the optimal solutions. Recently, many researchers have found that the employment of local search in optimization problems can improve the quality of problem solving (Lee & Lee, 2005; Lee et al., 2002; Lee et al., 2003; Xu & Kelly, 1996). A local search approach starts with an initial solu- tion and searches within neighborhoods for better solu- 0957-4174/$ - see front matter Ó 2007 Published by Elsevier Ltd. doi:10.1016/j.eswa.2007.11.060 * Corresponding author. Tel./fax: +886 2 26632102. E-mail address: johnlee@hfu.edu.tw (Z.-J. Lee). www.elsevier.com/locate/eswa Available online at www.sciencedirect.com Expert Systems with Applications 36 (2009) 1505–1512 Expert Systems with Applications