DOI: 10.4018/IJAEC.2018010101 International Journal of Applied Evolutionary Computation Volume 9 • Issue 1 • January-March 2018 Copyright © 2018, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. 1 Efcient Golden-Ball Algorithm Based Clustering to solve the Multi- Depot VRP With Time Windows Lahcene Guezouli, University of Batna 2, Batna, Algeria Mohamed Bensakhria, University of Batna 2, Batna, Algeria Samir Abdelhamid, University of Batna 2, Batna, Algeria ABSTRACT In this article, the authors propose a decision support system which aims to optimize the classical Capacitated Vehicle Routing Problem by considering the existence of multiple available depots and a time window which must not be violated, that they call the Multi-Depot Vehicle Routing Problem with Time Window (MDVRPTW), and with respecting a set of criteria including: schedules requests from clients, the capacity of vehicles. The authors solve this problem by proposing a recently published technique based on soccer concepts, called Golden Ball (GB), with different solution representation from the original one, this technique was designed to solve combinatorial optimization problems, and by embedding a clustering algorithm. Computational results have shown that the approach produces acceptable quality solutions compared to the best previous results in similar problem in terms of generated solutions and processing time. Experimental results prove that the proposed Golden Ball algorithm is efficient and effective to solve the MDVRPTW problem. KEyWoRDS Clustering, Golden Ball Algorithm, Multi-Depot Vehicle Routing Problem, Routing, Scheduling 1. INTRoDUCTIoN Within the wide scope of logistics management, transportation plays a central role and is a crucial activity in the delivery of goods and services. The transport problem is one of the mainly essential combinatorial optimization problems that have taken the interest of several researchers. Huge research efforts have been devoted to the study of logistic problems and thousands of papers have been written on many variants of this problem such as Traveling Salesman Problem (TSP) (Toth, 2001), Vehicle Routing Problem (VRP) and supply chain management (SCM) (Pisinger, 2007). The Vehicle Routing Problem (VRP) has been one of the central topics in optimization since Dantzig proposed the problem in 1959(Dantzig, 1959). A simple general model of VRP can be described as follows: a set of service vehicles need to visit all customers in a geographical region with the minimum cost. The VRP is also named Single-depot VRP (SDVRP). In cases with more than one depot, VRPs are known as multi-depot VRPs (MDVRP) (Filipec, 2000), (Mirabi, 2014). Single-depot VRPs are not suitable for practical situations though they have attracted researchers in a wide sense. The Multi-Depot Vehicle Routing Problem (MDVRP) is a generalization of SDVRP in which the vehicles start from multiple depots and return to their original depots at the end of their assigned tours. As there are a large number of depots, it is a difficult task for decision makers to determine