A hybrid GA–TS algorithm for open vehicle routing optimization of coal mines material Shiwei Yu a,b,⇑ , Chang Ding a , Kejun Zhu a a School of Economics and Management, China University of Geosciences, Hubei, Wuhan 430074, China b Center for Energy and Environmental Policy Research, Beijing Institute of Technology, Beijing 100181, China article info Keywords: Open vehicle routing problem Genetic algorithms Tabu search Hybrid Optimize Coal mine material abstract In the open vehicle routing problem (OVRP), the objective is to minimize the number of vehicles and the total distance (or time) traveled. This study primarily focuses on solving an open vehicle routing problem (OVRP) by applying a novel hybrid genetic algorithm and the Tabu search (GA–TS), which combines the GA’s parallel computing and global optimization with TS’s Tabu search skill and fast local search. Firstly, the proposed algorithm uses natural number coding according to the customer demands and the captiv- ity of the vehicle for globe optimization. Secondly, individuals of population do TS local search with a cer- tain degree of probability, namely, do the local routing optimization of all customer sites belong to one vehicle. The mechanism not only improves the ability of global optimization, but also ensures the speed of operation. The algorithm was used in Zhengzhou Coal Mine and power Supply Co., Ltd.’s transport vehicle routing optimization. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Open vehicle routing problem (OVRP) is a special vehicle rout- ing problem that differs from the well-known vehicle routing prob- lem (VRP) in that the vehicles do not necessarily return to their original locations after delivering goods to customers; if they do, they must visit the same customers in the reverse order (Dantzing & Ramser, 1959). For example, when coal mines material logistics and distribution companies have no dedicated distribution team, or the number of their own distribution vehicle is not enough to meet the material demands of the mining area, the company had to rent vehicles. Because the rental vehicles do not need to return to the depot after the completion of the task, the routing is open. The OVRP analyzes efficient routes with minimum total cost for a fleet of vehicles that serve some goods to a given number of cus- tomers. Each customer is visited exactly once by one vehicle, while vehicle activity is bounded by capacity constraints, duration con- straints and time constraints. The OVRP can be seen as a slight var- iant of the standard CVRP model by simply ignoring the return trip of the vehicles to the central depot. Therefore, the goal of the OVRP is to design a set of Hamiltonian paths (open routes) for satisfying customers’ demand. In terms of the OVRP objective, most research- ers assume that the cost for hiring an additional vehicle far sur- passes any travel cost savings achieved by this additional route (Fu, Eglese, & Li, 2006). The article of Schrage (1981) which classi- fies the features encountered in practical routing problems was the first to distinguish between closed trips traveled by private vehi- cles, and open trips assigned to common carrier vehicles. Bodin, Golden, Assad, and Ball (1983) propose the first solution approach for the OVRP. From the early 1980s to the late 1990s, the OVRP re- ceived very little attention in the operations research literature. However, recently OVRP has attracted more and more concern from practitioners and researchers. Since 2000, several researchers have used various heuristics and meta-heuristics to solve the OVRP with some success. Brandão (2004) and Fu, Eglese, and O Li (2005) carried out a Tabu search (TS) heuristic to solve the OVRP with con- straints on vehicle capacity and maximum route length. Tarantilis, Ioannou, Iranoudis, and Prastacos (2005) solved the OVRP by adopting the LBTA algorithm which proposed the solution of the multi-depot OVRP (Tarantilis & Kiranoudis, 2002). In Pisinger and Ropke (2007) presented an adaptive large neighborhood search heuristic to solve an OVRP. Li, Golden, and Wasil (2007) proposed a record-to-record travel heuristic and a deterministic variant of simulated annealing to solve the OVRP. Cao and Lai (2010) consid- ered the open vehicle routing problem with fuzzy demands. Zachariadis and Kiranoudis (2010) proposed a local search meta- heuristic whose moves are statically encoded into static move descriptor entities to explore the wide neighborhoods. This paper presents a hybrid adaptive genetic algorithm and Tabu search (GA–TS) for solving OVRP, The algorithm combines the GA’s parallel computing and global optimization with TS’s Tabu 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.02.108 ⇑ Corresponding author at: School of Economics and Management, China University of Geosciences, Hubei, Wuhan 430074, China. Tel.: +86 02767883206; fax: +86 02767883201. E-mail address: ysw81993@sina.com (S. Yu). Expert Systems with Applications 38 (2011) 10568–10573 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa