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2.
The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study 总被引:1,自引:0,他引:1
Bram Verweij Shabbir Ahmed Anton J. Kleywegt George Nemhauser Alexander Shapiro 《Computational Optimization and Applications》2003,24(2-3):289-333
The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 21694 scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time. 相似文献
3.
Consider a network where two routes are available for users wishing to travel from a source to a destination. On one route (which could be viewed as private transport) service slows as traffic increases. On the other (which could be viewed as public transport) the service frequency increases with demand. The Downs-Thomson paradox occurs when improvements in service produce an overall decline in performance as user equilibria adjust. Using the model proposed by Calvert [10], with a ⋅|M|1 queue corresponding to the private transport route, and a bulk-service infinite server queue modelling the public transport route, we give a complete analysis of this system in the setting of probabilistic routing. We obtain the user equilibria (which are not always unique), and determine their stability.AMS subject classification: 60K30, 90B15, 90B20, 91A10, 91A13This revised version was published online in June 2005 with corrected coverdate 相似文献
4.
Han-xing Wang Xi Hu Qin Zhang 《应用数学学报(英文版)》2007,23(2):235-244
In this paper,we present a random graph model with spatial reuse for a mobile ad hoc network(MANET) based on the dynamic source routing protocol.Many important performance parameters of theMANET are obtained,such as the average flooding distance (AFD),the probability generating function of theflooding distance,and the probability of a flooding route to be symmetric.Compared with the random graphmodel without spatial reuse,this model is much more effective because it has a smaller value of AFD and alarger probability for finding a symmetric valid route. 相似文献
5.
Rafael Caballero Mercedes González Flor M Guerrero Julián Molina Concepción Paralera 《European Journal of Operational Research》2007
In this work we present a multiobjective location routing problem and solve it with a multiobjective metaheuristic procedure. In this type of problem, we have to locate some plants within a set of possible locations to meet the demands of a number of clients with multiple objectives. This type of model is used to solve a problem with real data in the region of Andalusia (Spain). Thus, we study the location of two incineration plants for the disposal of solid animal waste from some preestablished locations in Andalusia, and design the routes to serve the different slaughterhouses in this region. This must be done while taking into account certain economic objectives (start-up, maintenance, and transport costs) and social objectives (social rejection by towns on the truck routes, maximum risk as an equity criterion, and the negative implications for towns close to the plant). 相似文献
6.
首先将无线传感器网络的路由问题转化成求解最小Steiner树问题,然后给出了求解无线传感器网络路由的蚁群优化算法,并对算法的收敛性进行了证明.最后对找到最优解后信息素值的变化进行了分析.即在限制信息素取值的条件下,当迭代次数充分大时,该算法能以任意接近于1的概率找到最优解,并且当最优解找到后,最优树边上的信息素单调增加,而最优解以外边上的信息素在有限步达到最小值. 相似文献
7.
A Hybrid Multiobjective Evolutionary Algorithm for Solving Vehicle Routing Problem with Time Windows 总被引:2,自引:0,他引:2
Vehicle routing problem with time windows (VRPTW) involves the routing of a set of vehicles with limited capacity from a central
depot to a set of geographically dispersed customers with known demands and predefined time windows. The problem is solved
by optimizing routes for the vehicles so as to meet all given constraints as well as to minimize the objectives of traveling
distance and number of vehicles. This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates
various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective
optimization in VRPTW. The proposed HMOEA is featured with specialized genetic operators and variable-length chromosome representation
to accommodate the sequence-oriented optimization in VRPTW. Unlike existing VRPTW approaches that often aggregate multiple
criteria and constraints into a compromise function, the proposed HMOEA optimizes all routing constraints and objectives simultaneously,
which improves the routing solutions in many aspects, such as lower routing cost, wider scattering area and better convergence
trace. The HMOEA is applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances, which yields 20 routing solutions
better than or competitive as compared to the best solutions published in literature. 相似文献
8.
Martin Skutella 《Mathematical Programming》2002,91(3):493-514
In the single source unsplittable min-cost flow problem, commodities must be routed simultaneously from a common source vertex
to certain destination vertices in a given graph with edge capacities and costs; the demand of each commodity must be routed
along a single path so that the total flow through any edge is at most its capacity. Moreover, the total cost must not exceed
a given budget. This problem has been introduced by Kleinberg [7] and generalizes several NP-complete problems from various
areas in combinatorial optimization such as packing, partitioning, scheduling, load balancing, and virtual-circuit routing.
Kolliopoulos and Stein [9] and Dinitz, Garg, and Goemans [4] developed algorithms improving the first approximation results
of Kleinberg for the problem of minimizing the violation of edge capacities and for other variants. However, known techniques
do not seem to be capable of providing solutions without also violating the cost constraint. We give the first approximation
results with hard cost constraints. Moreover, all our results dominate the best known bicriteria approximations. Finally,
we provide results on the hardness of approximation for several variants of the problem.
Received: August 23, 2000 / Accepted: April 20, 2001?Published online October 2, 2001 相似文献
9.
Kenneth Sörensen 《Central European Journal of Operations Research》2006,14(2):193-207
In this paper, we argue that vehicle routing solutions are often tactical decisions, that should not be changed too often
or too much. For marketing or other reasons, vehicle routing solutions should be stable, i.e. a new solution (when e.g. new customers require service) should be as similar as possible to a solution already in
use. Simultaneously however, this new solution should still have a good quality in the traditional sense (e.g. small total
travel cost). In this paper, we develop a way to measure the difference between two vehicle routing solutions. We use this
distance measure to create a metaheuristic approach that will find solutions that are “close” (in the solution space) to a
given baseline solution and at the same time have a high quality in the sense that their total distance traveled is small.
By using this approach, the dispatcher is offered a choice of Pareto-optimal solutions, allowing him to make a trade-off between
changing his existing solution and allowing a longer travel distance. Some experiments are performed to show the effectiveness
of the approach. 相似文献
10.
Fabien Tricoire 《4OR: A Quarterly Journal of Operations Research》2007,5(2):165-168
We present an overview of the author’s Ph.D. thesis, supervised by P. Dejax and N. Bostel, which was defended in February
2006 at école des Mines de Nantes, France. The thesis is written in French, and is available at . It was conducted in the context of a research contract with a water distribution company. In a first section, we define
multiperiod routing problems for service technicians. In a second section, we present some heuristics and a memetic algorithm
used to solve these problems. The third section introduces optimal and near-optimal approaches based on column generation.
Finally, we present some applications to the real-life case. The methods presented in Sects. 2, 3 and 4 were tested over several
sets of problems, based on real-life statistics provided by the company.
相似文献