represents service time needed by customer. Besides, each customer must be visited once and only once by exactly one vehicle. Therefore, the vehicle has to periodically returned to the depot for reloading or a new vehicle needed to be arranged for delivery. That is, the total demands of customers served by each vehicle cannot exceed units. customers are waiting to be served and each of the customers has a demands of ( ) units. Assume that there are vehicles in depot 0. If vehicles arrive before the time window “opens” or after the time window “closes,” there will be waiting cost and late cost. Each customer should be served exactly once. It starts from the depot and terminates at the depot.
#TIME MATLAB 2012 WINDOWS#
Vehicle routing problem with time windows (VRPTW) can be defined as choosing routes for limited number of vehicles to serve a group of customers in the time windows. Section 2 describes the VRPTW-SDP, Section 3 describes the MCPSO for the proposed problem, Section 4 presents experiment study, and Section 5 of the paper contains the conclusion. The rest of this paper is arranged as follows. Thus two dimensions encoding methods in MCPSO are proposed and used for the VRPTW-SDP. In MCPSO, each particle should contain two aspects of the customers, the order of served by which vehicle. In order to solve the VRPTW-SDP, we set the objective of VRPTW-SDP as the fitness function of MCPSO. The objective of the proposed VRPTW-SDP is minimizing the transport costs. In this paper, we study a case of the VRPTW both with uncertain number of vehicles and simultaneous delivery and pickup service. It takes a multi-swarm cooperative evolutionary strategy where the master swarms change their particles based on their own knowledge and the knowledge of the particles in the slave swarms, while the slave swarms carry out PSO independently. Then the multiswarm cooperative particle swarm optimization (MCPSO) was proposed as an improved PSO in. It sometimes immerses the local optimal value, thus the accuracy is limited. Among those algorithms, particle swarm optimization (PSO) has turned out to be an efficient algorithm in dealing with many complex optimization problems. Thus evolutionary algorithm (EA) is proposed to deal with optimization problems. However, those classical approaches less efficient in solving complex problems. Fisher proposed -trees to solve the VRP and VRPTW. Many researchers have made great effort in solving the VRPTW in recent years. VRPTW with simultaneous delivery and pick-up service (VRPTW-SDP) is an extension of VRPTW, where customers require simultaneous delivery and pick-up. This situation is very common in transport activity, because reduction of the number of the vehicles can save costs, while simultaneous delivery and pick-up can improve transport efficient. However, in reality, two factors need to be considered, the uncertain number of vehicles and simultaneous delivery and pick-up. Wang and Lang proposes multiperiod vehicle routing problem with recurring dynamic time windows. Feng divide the VRPTW with delivery and pickup into five categories. In 1981, Schrage proposed vehicle routing and scheduling problem with time window constraints as an important area for progress in handling realistic complications and generalizations of the basic routing model. Many researchers have contribute to the problem. The objective of the VRPTW is to minimize the total transport costs. The problem can be described as choosing routes for limited number of vehicles to serve a group of customers in the time windows. Vehicle routing problem with time windows (VRPTW) is an important issue in logistics system which has been researched widely in recent years. Finally, comparing with genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, the MCPSO algorithm performs best for solving this problem. And a new encoding method is proposed for the extension VRPTW. To solve the problem, an efficient multiswarm cooperative particle swarm optimization (MCPSO) algorithm is applied. Using minimization of the total transport costs as the objective of the extension VRPTW, a mathematic model is constructed. The two factors, which are very common characteristics in realworld, are uncertain number of vehicles and simultaneous delivery and pick-up service. This paper considers two additional factors of the widely researched vehicle routing problem with time windows (VRPTW).
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