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_18: Vehicle routing problem with time windows (VRPTW) is a generalisation of the classical vehicle routing problem, where a group of customers with given capacity demand are required to be serviced, and the servicing of the customer demands has to be started within a restricted available time window at the customer locations. This class of routing problems can be used to solve many practical problems such as container truck routing, delivery service scheduling and many logistics system problems. In this paper, we present a route construction heuristic with an adaptive parallel scheme. The result from extensive computation experiments shows the proposed parallel route construction heuristic is efficient and effective for routes construction, which is particularly useful for generation of the initial solutions for many metaheuristic approaches with improved solution quality and convergence of the solution process.
  @cite_26: This paper addresses the development of effective heuristics for solving the vehicle routing and scheduling problem with time window constraints. Both tour construction and local search tour improvement heuristics are developed. A major premise of the paper is that embedding global tour improvement procedures within the tour construction process can lead to improved solutions. Computational results are reported on test problems from the literature as well as real world applications. The hybrid construction improvement heuristic is more effective in reducing vehicle fleet size requirements than previously reported heuristics.
  @cite_4: This paper describes an insertion algorithm for the Vehicle Routing and Scheduling Problem with Time Windows (VRSPTW). This algorithm builds routes in parallel and uses a generalized regret measure over all unrouted customers in order to select the next candidate for insertion. Numerical results on the standard set of problems of Solomon are reported as well as comparisons with his sequential algorithm (Solomon, 1987).
  @cite_27: This paper considers the design and analysis of algorithms for vehicle routing and scheduling problems with time window constraints. Given the intrinsic difficulty of this problem class, approximation methods seem to offer the most promise for practical size problems. After describing a variety of heuristics, we conduct an extensive computational study of their performance. The problem set includes routing and scheduling environments that differ in terms of the type of data used to generate the problems, the percentage of customers with time windows, their tightness and positioning, and the scheduling horizon. We found that several heuristics performed well in different problem environments; in particular an insertion-type heuristic consistently gave very good results.
  @cite_23: 
  @cite_20: This paper investigates the application of a new class of neighborhood search algorithms—cyclic transfers—to multivehicle routing and scheduling problems. These algorithms exploit the two-faceted decision structure inherent to this problem class: First, assigning demands to vehicles and, second, routing each vehicle through its assigned demand stops. We describe the application of cyclic transfers to vehicle routing and scheduling problems. Then we determine the worst-case performance of these algorithms for several classes of vehicle routing and scheduling problems. Next, we develop computationally efficient methods for finding negative cost cyclic transfers. Finally, we present computational results for three diverse vehicle routing and scheduling problems, which collectively incorporate a variety of constraint and objective function structures. Our results show that cyclic transfer methods are either comparable to or better than the best published heuristic algorithms for several complex and important vehicle routing and scheduling problems. Most importantly, they represent a novel approach to solution improvement which holds promise in many vehicle routing and scheduling problem domains.
summary: Heuristic algorithms can be divided into two classes, namely the improvement and the construction techniques. In the construction heuristic algorithms the customers are iteratively inserted into a partial feasible solution without violating the time windows and capacity constraints. Several construction heuristics were proposed by Solomon @cite_27 , Potvin and Rousseau @cite_4 and recently by Pang @cite_18 . On the other hand, the improvement heuristics modify an initial solution and explore the search space by performing local search moves in order to decrease the fleet size and the total traveled distance. The examples of such heuristics can be found in @cite_20 , Russell @cite_26 and Potvin and Rousseau @cite_23 .