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.
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 .
@cite_18 @cite_26 @cite_4 @cite_27 @cite_23 @cite_20
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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. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . A Green Vehicle Routing Problem (G-VRP) is formulated and solution techniques are developed to aid organizations with alternative fuel-powered vehicle fleets in overcoming difficulties that exist as a result of limited vehicle driving range in conjunction with limited refueling infrastructure. The G-VRP is formulated as a mixed integer linear program. Two construction heuristics, the Modified Clarke and Wright Savings heuristic and the Density-Based Clustering Algorithm, and a customized improvement technique, are developed. Results of numerical experiments show that the heuristics perform well. Moreover, problem feasibility depends on customer and station location configurations. Implications of technology adoption on operations are discussed. 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.