International Journal of Innovative Computing, Information and Control ICIC International c 2011 ISSN 1349-4198 Volume 7, Number 7, July 2011 pp. 1–10 COOPERATING MEMES FOR VEHICLE ROUTING PROBLEMS Xianshun Chen 1 , Yew Soon Ong 1 and Meng Hiot Lim 2 1 Nanyang Technological University School of Computer Engineering 50 Nanyang Avenue, Singapore 639798 chen0469@ntu.edu.sg; asysong@ntu.edu.sg 2 Nanyang Technological University School of Electrical and Electronic Engineering, 50 Nanyang Avenue, Singapore 639798 emhlim@ntu.edu.sg Received March 2010; revised September 2010 Abstract. To date, algorithms that are designed for solving different Vehicle Routing Problem (VRP) benchmarks usually incorporate domain driven biases of various forms. This makes an algorithm effective and efficient for some VRP benchmark sets but not necessarily on others. This paper presents a memetic algorithm for Capacitated Vehicle Routing Problems (CVRPs), which is specially designed for applying intense local search methods or memes. The main con- tribution of this work is a VRP domain-specific cooperating multi-strategy individual learning procedure. The MA finds high-quality solutions by using cooperating individual learning strate- gies or memes, each having different learning roles and search features. Experiments on several sets of VRP benchmarks of various problem characteristics showed that the algorithm are better or competitive when compared with a number of state-of-the-art memetic algorithms and meta- heuristics for CVRPs. Keywords: Memetic Algorithms, Cooperating Memes, Vehicle Routing Problems, Metaheuris- tics, Combinatorial Optimization 1. Introduction. The Vehicle Routing Problems (VRPs) represent the cornerstone of opti- mization for distribution networks. Being one of the most important practical problems of operation research, VRP is considered as one of the most difficult problems due to its complex combinatorial nature; it is the fusion of two NP-hard problems, namely the Traveling Salesman Problem (TSP) and the Bin Packing Problem (BPP). For VRP instances with few nodes, the branch and bound method is deemed to be effective and known to provide the best solution to date [4]. However, exact methods such as branch and bound are not viable for large-scale VRP. Classical VRP of medium scale dimension remains computationally intractable using the exact enumeration methods[38]. As a result, most researchers have turned to metaheuristics for solving real world VRPs. The drawback is that generic metaheuristics do not guarantee con- vergence to global optimum [43, 13]. Genetic algorithms [16, 40, 44], Simulated Annealing (SA) [7, 27, 1], Tabu Search (TS) [7, 11], Ant Colony Optimization [10], and constraint programming [35], represent some of the popular metaheuristics algorithms that have been developed for han- dling real-life VRPs, with reasonably high degree of success. Gendreau et al. [13] reported that Tabu Search (TS) with specialized mechanisms and data structures were among some of the most successful metaheuristic algorithms currently available for dealing with large-scale VRPs. Evolutionary algorithms (EAs) such as GAs have also shown very promising results in real- world VRPs such as Capacitated VRPs [44], VRPS with Time-varying Travel Times [16], VRP disruption management with Fuzzy Time Window [41] or the Request Changes of Customers [40], etc. Meanwhile, memetic algorithm (MA) represents one of the recent growing fields in evolution- ary algorithm (EA) research [2, 24] and has been studied quite extensively for VRPs [22, 21, 34]. 1