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物流配送路径英文文献

物流配送路径英文文献
物流配送路径英文文献

A Memetic Algorithm for the Vehicle Routing Problem with Time Windows

Jean Berger and Mohamed Barkaoui

Defence Research and Development Canada一Valcartier, Decision Support System Section 2459 Pie-XI Blvd. North, Val-Belair, PQ, Canada, G3J 1X5

email: jean.berger@drdc-rddc.gc.ca, barkaoui@oricom.ca

Abstract

Serial and parallel versions of a new memetic algorithm to address the Vehicle Routing Problem with Time Windows are presented. The underlying approach involves parallel co-evolution of two populations. The first population evolves individuals to minimize total traveled distance while the second focuses on minimizing temporal constraint violation to generate a feasible solution. New genetic operators have been designed to incorporate key concepts emerging from recent promise techniques such as insertion heuristics, large neighborhood search and ant colony systems to further diversify and intensify the search. The parallel version of the method is based on a master-slave message-passing paradigm. The master controls the execution of the algorithm, synchronizes atomic genetic operations and handles parent selection while the slaves concurrently execute genetic operations. Results from a computational experiment show that the serial version of the proposed technique matches or outperforms the best-known heuristic routing procedures, providing six new best-known solutions. In comparison, the method proved to be fast, cost-effective and highly competitive. Alternatively, simulation results obtained for the parallel version show a significant improvement over the serial algorithm, matching or even improving solution quality. The parallel algorithm shows a speed-up of five in computing solution having near similar quality.

1 .Introduction

Vehicle routing problems are well known combinatorial considerable economic significance. The Vehicle Routing optimization Problem with problems with Time Windows(VRPTW) has

received a lot of attention in the literature recently. This is mostly due to the wide applicability of time window constraints in real-world cases. In VRPTW, customers with known demands are serviced by a homogeneous fleet of vehicles of limited capacity. Routes are ssumed to start and end at the central depot. Each customer provides a time interval during which a particular task must be completed such as loading/unloading the vehicle. It is worth noting that the time window requirement does not prevent any vehicle from arriving before the allowed start of service at a customer location. The objective is to minimize the number of tours or routes, and then for the same number of tours, to minimize the total traveled distance, such that each customer is serviced within its time window and the total load on any vehicle associated with a given route does not exceed the vehicle capacity.

A variety of algorithms including exact methods and efficient heuristics have already been proposed for VRPTW. For excellent surveys on exact, heuristic and metaheuristic methods, see [Desrosiers et al.1995], [Cordeau et al.,2001] and [Braysy and Gendreau, 2001a and 2001b] respectively. In particular, evolutionary and genetic algorithms have been among the most suitable approaches to tackle the VRPTW, and are of particular interest to us. Genetic algorithms [Holland, 1975;[De Jong, 1975] and [Goldberg, 1989] are adaptive heuristic search methods that mimic evolution through natural selection. They work by combining selection, recombination and mutation operations. The selection pressure drives the population toward better solutions while recombination uses genes of selected parents to produce offspring that will form the next generation. Mutation is used to escape from local minima. Routing techniques based on genetic algorithms to solve VRPTW emerge from the work of [Blanton and Wainwright,1993], [Thangiah, 1995a and 1995b], [Thangiah et al., 1995], [Potvin and Bengio, 1996], [Berger et al., 1998, 1999, 2000] and [Tan et2001].Alternate methods using evolutionary metaheuristics have been proposed by [Homberger and G1999],[Gehring and Homberger, 1999 and 2001],and [Braysy et al., 2000]. Other recent studies on vmetaheuristics for VRPTW can be found in [Rochat and Taillard, 1995], [Taillard etal.1997], [Chiang and Russell, 1997], [Cordeau et al., 2001](tabu searches), [Gambardella et al.,1999] (ant colony optimization),

and [Liu and Shen, 1999].Proposed metaheuristics so far show significant variability in performance. They often require

considerable computational effort and therefore fail to convincingly provide a single robust and successful technique. Recently, a new memetic or parallel hybrid genetic algorithm (PHGA) for the VRPTW has been successfully developed [Bergen Barkaoui and Braysy, 2002]. Algorithms is a population-based approach for heuristic search in optimization problems[Moscato, 1989]. They have shown that they are orders of magnitude faster than traditional genetic algorithms for some problem domains. Basically, they combine local search heuristics with mutation and crossover operators. For this reason, some researchers have viewed them as hybrid genetic algorithms or genetic local search. Our approach is based on a new concept that combines constrained parallel co-evolution of two populations and partial temporal constraint relaxation to improve solution quality. The firs population evolves individuals to minimize the total traveled distance while the second focuses on minimizing temporal constraint violation in trying to generate a feasible solution. Imposing a constant number of tours for each solution of a given population, temporal constraint relaxation allows escaping local minima while progressively moving toward a better solution. Populations interact with one another whenever a new feasible solution emerges, reducing by one the number of tours imposed on future solutions. New genetic operators have been designed to maximize the number of customers served within their time intervals first, and then temporal constraint relaxation is used to insert remaining unvisited customers. Key principles and variants emerging from recent promising techniques are also captured to further diversify and intensify the search. As a result, even though the algorithm is more robust, efficient, stable and highly competitive, prohibitive computational cost of key genetic operators and overall run-time still remain a sensitive issue to be satisfactorily addressed.

The main contribution of this paper is to further improve the PHGA technique by developing an efficient parallel implementation based upon a master-slave message-passing

paradigm(networked parallel computing) in order to significantly reduce run-time. The master

processing element controls the execution of the algorithm, synchronizes atomic genetic operations and handles the parent selection process while the slave processing elements concurrently execute reproduction and mutation operators. Current and new genetic operators have been designed and revisited to reduce processor starvation over each generation. The paper is outlined as follows. Section 2 introduces the basic concepts of the proposed parallel hybrid genetic algorithm. The basic principles and features of the algorithm are first described. Details on the parallel implementation of the algorithm are then given. Section 3 presents the results of a computational experiment to assess the value of the proposed approach and reports a comparative performance analysis to alternate methods. Finally, a summary is presented in Section 4.

2. Parallel Hybrid Genetic Algorithm

2.1 General Description

The proposed algorithm relies upon constrained parallel co-evolution and partial constraint relaxation. Two populations Pop, and Pope, primarily formed of non-feasible solution individuals, are evolving concurrently, each with their own objective functions. Pop, contains at least one feasible solution and is used to minimize total traveled distance while Pope focuses on minimizing constraint violation. Constrained to a fixed number of tours over the some population, solution individuals differ by exactly one route across both populations. Parallel evolution is interrupted whenever a new best feasible solution is obtained. Populations are then reinitialized and co-evolution resumed, while decreasing the number of routes associated with solution individuals by one. The number of tours imposed on solution individuals in Pop, and Pope are R-,;- and R-,;。一1,respectively. R-,;- refers to the number of routes found in the best feasible solution obtained so far. As a new feasible solution emerges from Pope, population Pop, is replaced by Pope, R-,;- is updated and, Pope is reinitialized with the revised number of tours (R.-.。一1),using the RSS_ M mutation operator. In addition, a post-processing procedure (RC_ M) aimed at reordering customers, is applied to further improve the

new best solution. Theevolutionary process is repeated until a predefined stopping condition is met. The proposed approach uses a steady-state genetic algorithm that involves overlapping populations. At first, new individuals are generated and added to the current population Popp. The process continues until the overlapping population outnumbers the initial population by up. Then, the up worst individuals are eliminated to maintain population size using the following individual evaluation:The proposed evaluation expression indicates that better individuals generally (but notnecessarily) include fewer routes, and smaller total traveled distance, while satisfying temporal constraints. The general algorithm is as follows:

Initialization

Repeat

p=1

Repeat {evolve population Pope一new generation }

For j=1二n,, do

Select two parents from Pope

Generate a new solution S} using recombination and mutation operators associated with Pope

Add S} to Pope

end for

Remove the n,, worst individuals from Pope using the evaluation function (1).

P=P刊

Until (all populations Pope have been considered)

if (Pops includes a new best feasible solution) then

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Mercury (Hg2+) effect on enzyme activities and hepatopancreas histo structures of juvenile Chinese mitten crab Eriocheir sinensis* Abstract We studied the effects of mercury (Hg2+) on antioxidant and digestive enzyme activities in terms of LC50 value and on hepatopancreas histo structures of juvenile Chinese mitten crabs Eriocheir sinensis in 40-day exposure to various concentrations of Hg2+ (0, 0.01, 0.05, 0.10, 0.20, and 0.30 mg/L). The results show that the activities of superoxide dismutase (SOD), glutathione peroxidase (GPX) and catalase (CAT) significantly increased in the concentrations of 0.01 and 0.05 mg/L, while that of enzyme decreased in 0.10, 0.20 and 0.30 mg/L treatments. Meanwhile, Hg2+ disrupted the histo structures of the hepatopancreas, causing decreases in activities of pepsin, tryptase, amylase, and cellulose, which are synthesized in the hepatopancreas. Moreover, as the Hg2+ concentration increased, the survival rate of the crabs decreased, worst at 56.57% in 0.30 mg/L. Therefore, although crabs are able to tolerate low levels of mercury pollution, high levels lead to cellular injury and tissue damage in hepatopancreas, which then loses some of its vital physiological functions such as absorption, storage, and secretion. Keyword: Eriocheir sinensis; mercury; hepatopancreas; antioxidant enzymes; histo structure; digestive ; enzymes 1 INTRODUCTION Mercury is a nonessential metal for aquatic animals (Bano et al., 1989). Due to anthropogenic input and environmental transport of mercury, pollution of the aquatic environment has increased significantly in the past decade (Mason et al., 1994; Botton, 2000). Waterborne mercury penetrates into aquatic animals, accumulates in different tissues, and induces adverse effects at the molecular, cellular and tissue levels (Bianchini et al., 1996; St-Amand et al., 1999; Chou et al., 2002). The Chinese mitten crab, Eriocheir sinensis (Edwards, 1853), is one of the most economically important crab species in China, with annual production reaching 500 000 tons and valued at US$2.2 billion in 2005. Previous investigations have described acute toxicity (Bianchini et al., 1996) and morphological changes in the gills of E. sinensis exposed to mercury (Zhao et al., 2008). However, the mechanism of mercury toxicity to E. sinensis is still largely unknown. Previous studies show that ambient mercury exposure leads to the generation of reactive oxygen species (ROS) including O2-, OH-, O2-and H2O2 (Ali et al., 2000). ROS are very unstable and highly reactive, and can induce alterations in the structure of cellular macromolecules, such as proteins, lipids, nucleic acids, etc. (Michiels et al., 1988). ROS formation can also induce cellular damage (Verlecar et al., 2008). Superoxide dismutase (SOD), catalase (CAT) and glutathione peroxidase (GPX) are the primary enzymes responsible for scavenging ROS. Homeostatic mechanisms act to equilibrate the amount of ROS generated under stress conditions in order to protect an organism from adverse effects(Pan et al., 2006; Yan et al., 2007). In addition, the activity of these enzymes is regulated by health status and environmental stress (Winston et al., 1991). Although several studies have reported ROS formation, antioxidant enzyme activity, and scavenger responses in crustaceans (Sridevi et al., 1998; Yan et al., 2007), little is known about the relationship between ambient Hg2+ and the antioxidant defensive systems of Eriocheir sinensis. * Supported by the National Basic Research Program of China (973 Program) (No. 2007CB407306);

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