text: This paper presents a parallel memetic algorithm for solving the vehicle routing problem with time windows (VRPTW). The VRPTW is a well-known NP-hard discrete optimization problem with two objectives. The main objective is to minimize the number of vehicles serving customers scattered on the map, and the second one is to minimize the total distance traveled by the vehicles. Here, the fleet size is minimized in the first phase of the proposed method using the parallel heuristic algorithm (PHA), and the traveled distance is minimized in the second phase by the parallel memetic algorithm (PMA). In both parallel algorithms, the parallel components co-operate periodically in order to exchange the best solutions found so far. An extensive experimental study performed on the Gehring and Homberger's benchmark proves the high convergence capabilities and robustness of both PHA and PMA. Also, we present the speedup analysis of the PMA.
  @cite_14: In this paper, according to the characteristics and influence factors of the distribution logistics and distribution center problem, a mathematical model of the distribution center of the LRTWP (Location and Routing with Time Window Problem) was established. An improved simulated annealing algorithm was used to solve the model, the parameter and selection operator in the algorithm is setted reasonably. Simulations and results indicate that the improved simulated annealing algorithm has better feasibility and validity for solving the LRTWP.
  @cite_10: Recently, routing and scheduling of vehicles represented a crucial issue in lots of logistic and transport systems due to the importance of selecting efficient distribution strategies with considering economic significance. Simulated annealing algorithm (SA) is a local search technique that can potentially yield near-optimal solutions to many difficult optimization problems, such as the vehicle routing problem with time windows (VRPTW). A hybrid optimization method that combines the evaluation function with the improved SA algorithm is proposed to treat the VRPTW in this paper. The simulated experiments demonstrate that it's an efficient solution to the large-scale VRPTW, and with regards to traditional SA algorithm, the computer costs are saved markedly.
  @cite_29: The vehicle routing problem with time windows (VRPTW) is a well-known and complex combinatorial problem. The primary objective of VRPTW is defined as the minimization of the number of routes or vehicles. Minimization of the total travel cost is secondary objective. This paper proposes an improved algorithm based on the ant colony system (ACS), which hybridized with randomized algorithm (RACS-VRPTW). In two objectives of VRPTW, only partial customers are randomly chosen to compute the transition probability. Experiments on various aspects of the algorithm and computational results for partial benchmark problems are reported. We compare our approach with some other meta-heuristics and show that our results are competitive.
  @cite_1: This paper surveys the research on the metaheuristics for the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval; all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. Metaheuristics are general solution procedures that explore the solution space to identify good solutions and often embed some of the standard route construction and improvement heuristics described in the first part of this article. In addition to describing basic features of each method, experimental results for Solomon's benchmark test problems are presented and analyzed.
  @cite_32: Abstract The routing of a fleet of vehicles to service a set of customers is important in the field of distribution. Vehicle routing problems (VRP) arise in many real-life applications within transportation and logistics. In this paper, we study a variant of the general VRP, VRP with time windows and split deliveries (VRPTWSD). Time constrained routing is relevant for applications where a schedule has to be followed. The option of splitting a demand makes it possible to service a customer whose demand exceeds the vehicle capacity. Splitting also allows to decrease costs. Although VRPTWSD is a relaxation of the VRP with time windows, the problem does not become easier to solve, and is still NP-hard. In this work, we propose a solution method based on tabu search for solving the VRPTWSD without imposing any restrictions on the split delivery options. We also give an analysis of experimental results on problems with 100 customers.
  @cite_15: Research on optimization of the vehicle routing problem with time windows (VRPTW) is one of the most significant and promising areas of investigation in ant colony system (ACS), since ACS is used to find a near-optimum solution for a discrete optimization problem. As VRPTW is the typical case of discrete optimization problem, in this paper, an ACS was proposed to optimize a VRPTW problem. The numerical experiments of ACS were implemented in the VRPTW problem. The optimized results of ACS are favorably compared with other optimization methods'
  @cite_16: 
  @cite_13: 
summary: Metaheuristic algorithms incorporate mechanisms to explore the search space and to exploit its most promising regions. They allow infeasible intermediate solutions and the solutions deteriorating during the search process in order to escape the local minima. A number of sequential and parallel algorithms were introduced during the recent years. The simulated annealing was successfully applied by Zhong and Pan @cite_10 , Debudaj-Grabysz and Czech @cite_13 , and recently by Li @cite_14 . The tabu searches were proposed by @cite_16 and @cite_32 . The ant colony approaches can be found in @cite_15 and Qi and Sun @cite_29 . A survey on the metaheuristic algorithms can be found in Br " a ysy and Gendreau @cite_1 .