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1.
A Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows 总被引:6,自引:0,他引:6
Michael Polacek Richard F. Hartl Karl Doerner Marc Reimann 《Journal of Heuristics》2004,10(6):613-627
The aim of this paper is to propose an algorithm based on the philosophy of the Variable Neighborhood Search (VNS) to solve Multi Depot Vehicle Routing Problems with Time Windows. The paper has two main contributions. First, from a technical point of view, it presents the first application of a VNS for this problem and several design issues of VNS algorithms are discussed. Second, from a problem oriented point of view the computational results show that the approach is competitive with an existing Tabu Search algorithm with respect to both solution quality and computation times. 相似文献
2.
Peter Francis Guangming Zhang Karen Smilowitz 《European Journal of Operational Research》2007,180(3):1045-1059
This paper presents modeling and solution method improvements for the Multi-Resource Routing Problem (MRRP) with flexible tasks. The MRRP with flexible tasks is used to model routing and scheduling problems for intermodal drayage operations in which two resources (tractors and trailers) perform tasks to transport loaded and empty equipment. Tasks may be either well defined, in which both the origin and the destination of a movement are given, or flexible, in which the origin or the destination is chosen by the model. This paper proposes methods to effectively manage the number of options considered for flexible tasks (either feasible origins for a known destination or feasible destinations for a known origin). This modeling change generates sufficient options to allow for low-cost solutions while maintaining reasonable computational effort. We also propose a new solution method that uses randomized route generation. Computational results from test cases show that these changes improve the quality of solutions by at least 5% in the test cases as compared to methods from previous studies. 相似文献
3.
M. Abbad R. El. Azouzi M. El. Kamili 《Mathematical Methods of Operations Research》2006,63(3):461-471
In this paper we consider some properties on prices under flow control in a network that is to be shared by noncooperative users. Each user is faced with an optimization problem which is formulated as the minimization of its own criterion subject to constraint on the flows of the other users. The operating points of the network are the Nash equilibria of the underlying routing game. Our objective is to study the behavior of prices of all users when the network designer needs to allocate capacities to network links. For parallel links topologies, we show that degradation of the performances such as prices will not take place, as well as the users may find it beneficial to improve their requests 相似文献
4.
本文研究并揭示了L_(2~a)(2~(2~a-1))型正交表行(列)间的递推规律,提出了一种泛函梯度数值计算的新方法——正交试验法,该方法在计算速度和精度上优于直接梯度法;在通用性及节省内存方面优于伴随算子法。 相似文献
5.
本文根据汉寿县1960─1988年洪涝灾害资料,应用加权列联表分析法,与前期气候因子建立洪涝趋势预测模式。最后对1989─1990年洪涝试报,取得了满意的效果。 相似文献
6.
We study the effect of arrival model uncertainties on the optimal routing in a system of parallel queues. For exponential service time distributions and Bernoulli routing, the optimal mean system delay generally depends on the interarrival time distribution. Any error in modeling the arriving process will cause a model-based optimal routing algorithm to produce a mean system delay higher than the true optimum. In this paper, we present an asymptotic analysis of the behavior of this error under heavy traffic conditions for a general renewal arrival process. An asymptotic analysis of the error in optimal mean delay due to uncertainties in the service time distribution for Poisson arrivals was reported in Ref. 6, where it was shown that, when the first moment of the service time distribution is known, this error in performance vanishes asymptotically as the traffic load approaches the system capacity. In contrast, this paper establishes the somewhat surprising result that, when only the first moment of the arrival distribution is known, the error in optimal mean delay due to uncertainties in the arrival model is unbounded as the traffic approaches the system capacity. However, when both first and second moments are known, the error vanishes asymptotically. Numerical examples corroborating the theoretical results are also presented.This work was supported by the National Science Foundation under Grants ECS-88-01912 and EID-92-12122 and by NASA under Contract NAG 2-595.The authors wish to thank an anonymous referee for pointing out Ref. 20, thus avoiding the need for an explicit proof of convexity of the cost function considered in the paper. 相似文献
7.
M. R. Darafsheh Y. Farjami A. R. Ashrafi M. Hamadanian 《Journal of mathematical chemistry》2007,41(3):315-326
The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is
a new field in chemistry. Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine
with inversion and proved that the r-NRG of this molecule is a group of order 648, containing a subgroup of order 324 without
inversions (see J. Math. Chem. 28(4) (2000) 377–388). In this work, a computational method is described, by means of which it is possible to calculate the
symmetry group of molecules. We study the full non-rigid group (f-NRG) of Sponge and Pina molecules with C
2 and C
i point groups, respectively. It proved that these are groups of order 162 and 13122 with 54 and 3240 conjugacy classes, respectively.
The character tables of these groups are also computed. 相似文献
8.
本文提出一个以(10~(△pe)-1)~(-1)对△pe表示的离子选择电极一次加入标准法结果处理数值表。该表简单明了,不含电极斜率因素,适用于具有各种斜率的电极和不同价态离子的测定。 相似文献
9.
Guillermo Restrepo Eugenio J. Llanos Héber Mesa 《Journal of mathematical chemistry》2006,39(2):401-416
We carried out a mathematical study of 72 chemical elements taking advantage of the chemotopological method. We selected 128
properties to define the elements (physico-chemical, geochemical and chemical properties). Then, we looked for correlated
properties and we reduced the number of them to 90. In this way we defined each element as a 90-tuple. Afterwards, we applied
principal component analysis and cluster analysis (4 similarity functions and 5 grouping methodologies). Then, we calculated
a consensus tree for the 20 dendrograms generated by the CA. Afterwards, we extracted the similarity relationships from the
consensus tree and built up a basis for a topology on the set of chemical elements. Finally, we calculated some topological
properties (closures, derived sets, boundaries, interiors and exteriors) of several subsets of chemical elements. We found
that alkali metals, alkaline earth metals and noble gases appear not related to the rest of the elements. Also, we found that
the boundary of non-metals are the semimetals with a stair-shape on the periodic table 相似文献
10.
The graphical unitary group approach has been applied in an efficient implementation of a general multireference configuration interaction (MRCI) method for use with small active molecular orbital spaces in a semiempirical framework. Gradients can be computed analytically for molecular orbitals from a closed-shell or a half-electron open-shell Hartree-Fock calculation. CPU times for single point energy and gradient calculations are reported. The code allows MRCI geometry optimizations of large molecules, as illustrated for the singlet ground state and the four lowest triplet states of fullerene C(76). 相似文献