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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.
构造一个求解椭圆型边值问题的多子域D—N交替算法,导出对应的容度方程和等价的迭代法,证明算法的收敛性。 相似文献
3.
ADegenerateStefanProblemwithTwoFreeBoundaries¥(李辉来)LiHuilai(DepartmentofMathematics,JilinUniversity,Changchun,130023)Abstract... 相似文献
4.
Alexandra Shlapentokh 《Compositio Mathematica》2002,132(1):99-120
Let F be a function field of characteristic p > 2, finitely generated over a field C algebraic over a finite field C
p
and such that it has an extension of degree p. Then Hilbert's Tenth Problem is not decidable over F. 相似文献
5.
6.
Optimale Quantisierung 总被引:1,自引:0,他引:1
Peter M. Gruber 《Mathematische Semesterberichte》2002,49(2):227-251
Zusammenfassung. Optimale Quantisierungen oder – damit ?quivalent – minimale Summen von Momenten spielen in mehreren Zweigen der Mathematik
und ihrer Anwendungen eine Rolle. Ausgehend von der Fejes Tóth'schen Ungleichung für Summen von Momenten in der euklidischen
Ebene und einem zugeh?rigen Stabilit?tssatz, werden gewisse Erweiterungen auf normierte R?ume und riemannsche Mannigfaltigkeiten
h?herer Dimension besprochen. Die Ergebnisse werden dann auf Probleme aus folgenden Bereichen angewendet: (i) Datenübertragung,
(ii) Wahrscheinlichkeitstheorie, (iii) numerische Integration, (iv) Approximation konvexer K?rper und (v) isoperimetrische
Probleme.
Eingegangen am 29. Mai 2002 / Angenommen am 8. Juli 2002 相似文献
7.
Christofides [1] proposes a heuristic for the traveling salesman problem that runs in polynomial time. He shows that when the graphG = (V, E) is complete and the distance matrix defines a function onV × V that is metric, then the length of the Hamiltonian cycle produced by the heuristic is always smaller than 3/2 times the length of an optimal Hamiltonian cycle. The purpose of this note is to refine Christofides' worst-case analysis by providing a tight bound for everyn 3, wheren is the number of vertices of the graph. We also show that these bounds are still tight when the metric is restricted to rectilinear distances, or to Euclidean distances for alln 6.This work was supported, in part, by NSF Grant ENG 75-00568 to Cornell University. This work was done when the authors were affiliated with the Center for Operations Research and Econometrics, University of Louvain, Belgium. 相似文献
8.
Ludo Van der Heyden 《Mathematical Programming》1980,19(1):328-346
A variable dimension algorithm is presented for the linear complementarity problems – Mz = q; s,z 0; s
i
z
i
= 0 fori = 1,2, ,n. The algorithm solves a sequence of subproblems of different dimensions, the sequence being possibly nonmonotonic in the dimension of the subproblem solved. Every subproblem is the linear complementarity problem defined by a leading principal minor of the matrixM. Index-theoretic arguments characterize the points at which nonmonotonic behavior occurs. 相似文献
9.
A primal transportation algorithm is devised via post-optimization on the costs of a modified problem. The procedure involves altering the costs corresponding to the basic cells of the initial (primal feasible) solution so that it is dual feasible as well. The altered costs are then successively restored to their true values with appropriate changes in the optimal solution by the application of cell or area cost operators discussed elsewhere. The cell cost operator algorithm converges to optimum within (2T – 1) steps for primal nondegenerate transportation problems and [(2T + 1) min (m, n)] – 1 steps for primal degenerate transportation problems, whereT is the sum of the (integer) warehouse availabilities (also the sum of the (integer) market requirements) andm andn denote the number of warehouses and markets respectively. For the area cost operator algorithm the corresponding bounds on the number of steps areT and (T + 1) min (m, n) respectively.This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie—Mellon University, under Contract N00014-67-A-0314-0007 NR 047-048 with the U.S. Office of Naval Research. 相似文献
10.
We investigate several classes of inequalities for the symmetric travelling salesman problem with respect to their facet-defining properties for the associated polytope. A new class of inequalities called comb inequalities is derived and their number shown to grow much faster with the number of cities than the exponentially growing number of subtour-elimination constraints. The dimension of the travelling salesman polytope is calculated and several inequalities are shown to define facets of the polytope. In part II (On the travelling salesman problem II: Lifting theorems and facets) we prove that all subtour-elimination and all comb inequalities define facets of the symmetric travelling salesman polytope. 相似文献