An iterated local search platform for transportation logistics

Transcription

1 An iterated local search platform for transportation logistics Takwa Tlili 1, and Saoussen Krichen 1 1 LARODEC, Institut Supérieur de Gestion Tunis, Université de Tunis, Tunisia. Abstract. Recent technological advances in optimization and transportation have enabled the development of efficient tools that support the decision making process of logistic managers. The aim of this paper is to present a decision support system (DSS) that integrates an Iterated Local Search (ILS) for solving the Vehicle Routing Problem (VRP). Its clear design allows an efficient exploration of the solution by the decision maker. The computational experiments show that the ILS is very competitive in comparison to state-of-the art algorithms. Keywords: Iterated local search; Decision Support System; Vehicle routing problem. 1 Introduction The efficient transportation management holds significant value due to its high impact on customer satisfaction by reducing delivery costs. Bearing in mind that logistic problems are generally modeled as VRPs, such a formulation contributes directly to minimize costs of all such processes (Alabas-Uslu and dengiz, 2011). Routing problems have drawn the attention of many researchers due to the increasing concerns on economic and environmental problems. The VRP seeks the tours of minimum cost such that the vehicles start their trips from a central depot and turn back after serving all vertices in the network. Numerous variations of the classical VRP have been introduced by modifying or adding additional attributes on solutions construction. The asymmetric VRP (AVRP) is concerned with finding a solution in which the distance between each pair of nodes in the two directions is not the same (Almoustafa et al., 2013). The Open VRP (OVRP) is the variant where the vehicles are not required to come back to the depot after completing their services (Li et al., 2012, Erbao et al., 2014 and Marinakis & Marinaki, 2014). The Multi-Depot VRP (MDVRP) is a generalization of the problem where more than one depot may be considered (Tu et al., 2014). More recently, other VRP variants have been evoked such as Split Delivery VRP (Archetti et al., 2014), rollon rolloff VRP (Wy & Kim, 2013) and Multi-Trip VRP (Cattaruzza et al., 2014). To cup with the routing variants, a variety of exact approaches have been devoted but optimal solutions are only limited to small-scaled instances. Given the fact that the VRP is NP-hard (Lenstra and Kan,

2 2 Takwa Tlili 1, and Saoussen Krichen ), several approximate algorithms have been proposed for finding optimal routes within acceptable computational time. Metaheuristics, including Simulated Annealing (Ghaffari-Nasab et al., 2013), Genetic Algorithm (Tasan & Gen, 2012 and C-Pop et al., 2013), Particle swarm optimization (MirHassani & Abolghasemi, 2011, Marinakis et al., 2010 and Ai & Kachitvichyanukul, 2009) have shown advantages in handling the VRPs. A recent comprehensive overview on metaheuristics for solving the VRP can be found in the work of Szeto et al. (2011). Nowadays, many industrial firms emphasize the need to use a decision support tool for solving VRPs. For illustration, E-Mendoza et al. (2009) proposed a DSS that integrates SAP/R3 and ArcGIS to handle the distance-constrained VRP. Manzini (2012) developed a DSS based on the top-down and multi-step approach to handle the management of logistic networks. The dynamic VRP variant has been solved by Dahl & Derigs (2011) using a web-based DSS that integrates decentralized databases and an on-line heuristic. The main contributions of this paper are (i) to solve the VRP using a modified ILS metaheuristic evaluated on several VRP benchmarks. (ii) to design a DSS that computationally outperforms other state of the art approaches. The remaining of the paper is organized as follows: Section 2 presents a detailed explanation of the proposed ILS algorithm. In section 3 a description of the DSS architecture is provided. In section 4 computational experiments highlight the effectiveness of the approach. 2 Architecture of the decision support system Decision Support Systems are computer-based information systems that aid different business or organisational processes involving decision-making. The conceptual design of the proposed DSS for integrated optimization routines is shown in Fig. 1, that encompasses four main steps: orders data extraction, geographical data extraction, optimization analysis and display geographical output. 1 Orders Data The DSS starts by the extraction of orders data for each customer to serve. The weights of cargos to deliver is known in order to fulfill vehicles capacity constraints. 2 Routing Data The DSS extracts the routing data from the geographical database to construct the adjacency matrix. The geographical data and transport information are the inputs for the resolution step. The two steps, Orders Data and Routing Data are achieved through the interface presented in Fig. 2 that allows the users to manager all inputs. 3 Resolution process Once all required information are sent to the optimization engine, the resolution process is initiated. The screenshot reported in Fig. 3 shows that the decision maker can select the solution approach that can be either CPLEX or ILS metaheuristic. 4 Display geographical output The solution obtained from the optimization engine is transformed to a geographical solution presented as routes on maps as shown in Fig 4.

3 An iterated local search platform for transportation logistics Fig. 1. Decision Support System Design 3 Iterated local search approach Iterated local search (ILS) approach, introduced by Lourenço et al. (2003), is applied to numerous combinatorial optimization problems successfully. Its performance is very competitive compared to other state-of-the art metaheuristics, such as particle swarm optimization, simulated annealing and genetic algorithm. The ILS is about combining phases of local search around the current solution and perturbations to diversify the search and avoid local optima. The algorithm starts its search from an initial solution S 0 computed by a greedy heuristic. This solution is then improved to obtain a first local optimum S using the local search procedure. Iteratively, a perturbation is applied to the current solution with the hope to escape from its attraction basin. The execution of the algorithm is stopped when a maximum number of iterations is reached. The pseudocode of the ILS algorithm (Grosso et al., 2009) that we im-

4 4 Takwa Tlili 1, and Saoussen Krichen 1 Fig. 2. Interface of the SDSS integrated in QGIS Fig. 3. Selecting either exact or approximate method plemented is sketched in Algorithm 1. Algorithm 1: ILS pseudocode 1: S 0 Initial solution(); 2: S Local search(s 0); 3: repeat 4: S Perturbation (S); 5: S Local search(s ); 6: if f(s ) < f(s) then 7: S S ; 8: end if 9: until termination condition met

5 An iterated local search platform for transportation logistics 5 Fig. 4. Geographical solution mapped 4 Simulation We analyze in what follows the results obtained on a set of experiments conducted to evaluate the performance of the developed algorithm. The ILS is coded in the Java programming language and experimentally evaluated on a laptop equipped with Core i5 processor and 2.5 GHz and 8 GB of RAM. The ILS is applied to some benchmark problems available in We select 20 problems from Augerat et al. (1995) benchmark, in which the number of customers is between 31 and 45. Instance Best Travel cost CPU time (s) Travel cost CPU time (s) Instance Best GA ILS GA ILS GA ILS GA ILS A-n32-k A-n45-k A-n33-k A-n45-k A-n33-k B-n31-k A-n34-k B-n34-k A-n36-k B-n35-k A-n37-k B-n38-k A-n37-k B-n39-k A-n38-k B-n41-k A-n39-k B-n43-k A-n39-k B-n44-k Table 1. Computational results on benchmark problems

6 6 Takwa Tlili 1, and Saoussen Krichen 1 Table 1 shows the experimental results on the instances and compares the performances of the ILS with the Genetic algorithm (GA) of Tsan & Gen (2012). In table 1, we report the travel costs as well as the CPUs of ILS and GA. It can be seen that the ILS algorithm, in half of the instances outperformed the GA for both travel cost and CPU time. In terms of runtime, our method is quite faster than the GA for the whole set of problems as shown in Figure 5. Fig. 5. CPU time of GA and ILS 5 Conclusion In this paper a prototype routing decision support system has been proposed in order to provide assistance to operating managers in transportation logistics. The architecture of the DSS consists of two key components: the geographical system and the optimization engine that applies a specifically designed ILS for solving the VRP. Comprehensive computational experiments and comparisons to an existing genetic algorithm showed that the ILS algorithm performs impressively, in terms of both solution quality and computational efficiency. References 1. T. J. Ai and V. Kachitvichyanukul. Particle swarm optimization and two solution representations for solving the capacitated vehicle routing problem. Computers & Industrial Engineering, 56: , C. Alabas-Uslu and B. Dengiz. A self-adaptive local search algorithm for the classical vehicle routing problem. Expert Systems with Applications, 38: , 2011.

7 An iterated local search platform for transportation logistics 7 3. S. Almoustafa, S. Hanafi, and N. Mladenovic. New exact method for large asymmetric distance-constrained vehicle routing problem. European Journal of Operational Research, 226: , C. Archetti, N. Bianchessi, and M. G. Speranza. Branch-and-cut algorithms for the split delivery vehicle routing problem. European Journal of Operational Research, 238: , D. Cattaruzza, N. Absi, D. Feillet, and T. Vidal. A memetic algorithm for the multi trip vehicle routing problem. European Journal of Operational Research, 236: , D. P. Cuervo, P. Goos, K. Sorensen, and E. Arraiz. An iterated local search algorithm for the vehicle routing problem with backhauls. European Journal of Operational Research, 237: , S. Dahl and U. Derigs. Cooperative planning in express carrier networks?an empirical study on the effectiveness of a real-time decision support system. Decision Support Systems, 51: , C. Erbao, L. Mingyong, and Y. Hongming. Open vehicle routing problem with demand uncertainty and its robust strategies. Expert Systems with Applications, 41: , N. Ghaffari-Nasab, S. G. Ahari, and M. Ghazanfari. A hybrid simulated annealing based heuristic for solving the location-routing problem with fuzzy demands. Scientia Iranica, 20: , A. Grosso, A. Jamali, and M. Locatelli. Finding maximin latin hypercube designs by iterated local search heuristics. European Journal of Operational Research, 197:541?547, J. Jiang, K. M. Ng, K. L. Poh, and K. M. Teo. Vehicle routing problem with a heterogeneous fleet and time windows. Expert Systems with Applications, 41: , J. Lenstra and A. Kan. Complexity of vehicle routing and scheduling problems. Networks, 11: , X. Li, S. C. Leung, and P. Tian. A multistart adaptive memorybased tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem. Expert Systems with Applications, 39: , H. Lourenço, O. Martin, and T. Stutzle. Iterated local search. Handbook of metaheuristics of international series in operations research & management science, 57:321?353, R. Manzini. A top-down approach and a decision support system for the design and management of logistic networks. Transportation Research Part E, 48: , Y. Marinakis and M. Marinaki. A bumble bees mating optimization algorithm for the open vehicle routing problem. Swarm and Evolutionary Computation, 15:80 94, Y. Marinakis, M. Marinaki, and G. Dounias. A hybrid particle swarm optimization algorithm for the vehicle routing problem. Engineering Applications of Artificial Intelligence, 23: , J. E. Mendoza, A. L. Medaglia, and N. Velasco. An evolutionarybased decision support system for vehicle routing: The case of a public utility. Decision Support Systems, 46: , S. MirHassani and N. Abolghasemi. A particle swarm optimization algorithm for open vehicle routing problem. Expert Systems with Applications, 38: , 2011.

8 8 Takwa Tlili 1, and Saoussen Krichen P. C. Pop, O. Matei, and C. P. Sitar. An improved hybrid algorithm for solving the generalized vehicle routing problem. Neurocomputing, 109:76?83, G. Ribeiro and G. Laporte. An adaptive large variable neighborhood search heuristic for cumulative capacitated vehicle routing problem. Computers & Operations Research, 39: , W. Szeto, Y. Wu, and S. C. Ho. An artificial bee colony algorithm for the capacitated vehicle routing problem. European Journal of Operational Research, 215: , A. S. Tasan and M. Gen. A genetic algorithm based approach to vehicle routing problem with simultaneous pick-up and deliveries. Computers & Industrial Engineering, 62: , W. Tu, Z. Fang, Q. Li, S.-L. Shaw, and B. Chen. A bi-level voronoi diagram-based metaheuristic for a large-scale multi-depot vehicle routing problem. Transportation Research Part E, 61:84 97, J. Wy and B.-I. Kim. A hybrid metaheuristic approach for the rollonrolloff vehicle routing problem. Computers & Operations Research, 40: , 2013.