On the windy postman problem

Guan, Meigu

doi:10.1016/0166-218x(84)90089-1

Cited by 45 publications

(20 citation statements)

References 3 publications

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“…Let us suppose that, after applying Gaussian elimination to system (16) there are a number f of free variables. Given the values for these variables can be chosen in {0, 1}, we have 2 f different solutions for (16), although the corresponding mod-2 cuts may not be different. A nice description of different strategies to select the cuts that are added to the LP can be found in Wenger (2004).…”

Section: Mod-2 Cuts Separation Proceduresmentioning

confidence: 99%

“…A nice description of different strategies to select the cuts that are added to the LP can be found in Wenger (2004). We have used the procedure implemented by Fricke and Oswald (2006) to solve (16). When a solution with free variables is obtained, we take the cut resulting from setting all free variables to 0 and the cuts resulting from setting exactly one of the free variables to 1 and the remaining ones to 0, up to a maximum of 50 cuts.…”

Section: Mod-2 Cuts Separation Proceduresmentioning

confidence: 99%

“…Given an undirected and connected graph G = (V, E) with two non-negative costs c ij and c ji associated with each edge (i, j) ∈ E corresponding to the cost of traversing it from i to j and from j to i, respectively, find the tour on G traversing each edge at least once, at minimum cost. This problem was first introduced by Minieka (1979), is an N P -hard problem (Guan 1984 andBrucker 1981) which can be solved in polynomial time if G is Eulerian (Win, 1987).…”

Section: Introductionmentioning

confidence: 99%

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New results on the Windy Postman Problem

et al. 2010

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In this paper we study the Windy Postman Problem. This is a well known Arc Routing Problem which contains the Mixed Chinese Postman Problem as a special case. We present here a full description of the polyhedron associated to the Windy Postman Problem over graphs with up to 4 vertices and 10 edges. We introduce two new families of facet-inducing inequalities and we prove that these inequalities and the already known Odd Zigzag inequalities are mod-2 cut inequalities. Moreover, a Branch & Cut (B&C) algorithm that incorporates two new separation algorithms for all the previously mentioned inequalities and a new heuristic procedure to obtain upper bounds are presented. Finally, the performance of the B&C algorithm over several sets of large WPP and MCPP instances, with up to 3000 nodes and 9000 links, shows that up to our knowledge this is the best algorithm for the exact resolution of the WPP and the MCPP.

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Section: Mod-2 Cuts Separation Proceduresmentioning

confidence: 99%

Section: Mod-2 Cuts Separation Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New results on the Windy Postman Problem

et al. 2010

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“…Finally, we have the Windy Postman Problem (WPP), proposed by Minieka (1979) and also studied by Guan (1984), Win (1987) and Grötschel & Win (1988, 1992. This problem consists of finding a minimum cost traversal of all the edges of an undirected graph in which the cost of traversing an edge (i, j) in a given direction, c ij , can be different to the cost of traversing it in the opposite direction, c ji .…”

Section: Introductionmentioning

confidence: 99%

The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra

Corberán¹,

Plana²,

Sanchis³

2008

SIAM J. Discrete Math.

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The Windy Postman Problem consists of finding a minimum cost traversal of all the edges of an undirected graph with two costs associated with each edge, representing the costs of traversing it in each direction. In this paper we deal with the Windy General Routing Problem (WGRP), in which only a subset of edges must be traversed and a subset of vertices must be visited. This is also an NP-hard problem that generalizes many important Arc Routing Problems (ARP's) and has some interesting real-life applications. Here we study the description of the WGRP polyhedron, for which some general properties and some large families of facet-inducing inequalities are presented. Moreover, since the WGRP contains many well-known routing problems as special cases, this paper also provides a global view of their associated polyhedra. Finally, for the first time, some polyhedral results for several ARP's defined on mixed graphs formulated using two variables per edge are presented.

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“…Therefore, since the Mixed Chinese Postman Problem (MCPP) is N P -hard, the WPP is also a N P -hard problem (Brucker, 1981 andGuan, 1984), although some particular cases can be solved in polynomial time (Guan, 1984 andWin, 1989). An integer linear programming formulation of the WPP was given in Grötschel & Win (1992).…”

Section: Introductionmentioning

confidence: 99%

New heuristic algorithms for the windy rural postman problem

Benavent

Corberán

Piñana

et al. 2005

Computers & Operations Research

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In this paper we deal with the Windy Rural Postman Problem. This problem generalizes several important Arc Routing Problems and has interesting real-life applications. Here, we present several heuristics whose study has lead to the design of a Scatter Search algorithm for the Windy Rural Postman Problem. Extensive computational experiments over different sets of instances, with sizes up to 988 nodes and 3952 edges, are also presented.

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On the windy postman problem

Cited by 45 publications

References 3 publications

New results on the Windy Postman Problem

New results on the Windy Postman Problem

The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra

New heuristic algorithms for the windy rural postman problem

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