13 research outputs found
New Heuristic Algorithms for the Windy Rural Postman Problem
[EN] 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. (c) 2004 Elsevier Ltd. All rights reserved.Benavent, E.; Corberán, A.; Piñana, E.; Plana. I.; Sanchís Llopis, JM. (2005). New Heuristic Algorithms for the Windy Rural Postman Problem. Computers & Operations Research. 32(12):3111-3128. doi:10.1016/j.cor.2004.04.007S31113128321
New results on the Windy Postman Problem
[EN] In this paper, we study the Windy Postman Problem (WPP). This is a well-known Arc Routing Problem that contains the Mixed Chinese Postman Problem (MCPP) as a special case. We extend to arbitrary dimension some new inequalities that complete the description of the polyhedron associated with the Windy Postman Problem over graphs with up to four vertices and ten edges. We introduce two new families of facet-inducing inequalities and prove that these inequalities, along with the already known odd zigzag inequalities, are Chvátal-Gomory inequalities of rank at most 2. Moreover, a branch-and-cut 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 a branch-and-cut algorithm over several sets of large WPP and MCPP instances, with up to 3,000 nodes and 9,000 edges (and arcs in the MCPP case), shows that, to our knowledge, this is the best algorithm to date for the exact resolution of the WPP and the MCPP. © 2010 Springer and Mathematical Optimization Society.The authors want to thank the three referees for their careful reading of the manuscript and for their many comments and suggestions that have contributed to improve the paper content and readability. In particular, several remarks regarding the discussion of C-G and mod-k inequalities were pointed out by one of the referees. A. Corberan, I. Plana and J.M. Sanchis wish to thank the Ministerio de Educacion y Ciencia of Spain (projects MTM2006-14961-C05-02 and MTM2009-14039-C06-02) for its support.Corberán, A.; Oswald, M.; Plana, I.; Reinelt, G.; Sanchís Llopis, JM. (2012). New results on the Windy Postman Problem. Mathematical Programming. 132(1-2):309-332. https://doi.org/10.1007/s10107-010-0399-xS3093321321-2Benavent E., Carrotta A., Corberán A., Sanchis J.M., Vigo D.: Lower bounds and heuristics for the windy rural postman problem. Eur. J. Oper. Res. 176, 855–869 (2007)Brucker P. The Chinese postman problem for mixed graphs. In Proceedings of international workshop. Lecture Notes in Computer Science 100, 354–366 (1981)Caprara A., Fischetti M.: -Chvátal-Gomory cuts. Math. Program. 74, 221–235 (1996)Caprara A., Fischetti M., Letchford A.N.: On the separation of maximally violated mod-k cuts. Math. Program. 87, 37–56 (2000)Christof, T., Loebel, A.: PORTA—a polyhedron representation algorithm www.informatik.uni-heidelberg.de/groups/comopt/software/PORTA/ (1998)Christofides, N., Benavent, E., Campos, V., Corberán, A., Mota, E.: An optimal method for the mixed postman problem. In Thoft-Christensen, P. (ed.) System Modelling and Optimization. Lecture Notes in Control and Information Sciences 59, Springer (1984)Corberán A., Plana I., Sanchis J.M.: Zigzag inequalities: a new class of facet-inducing inequalities for arc routing problems. Math. Program. 108, 79–96 (2006)Corberán A., Plana I., Sanchis J.M.: A branch & cut algorithm for the windy general routing problem and special cases. Networks 49, 245–257 (2007)Corberán, A., Plana I., Sanchis, J.M.: Arc routing problems: data instances. www.uv.es/corberan/instancias.htm (2007)Corberán A., Plana I., Sanchis J.M.: The windy general routing polyhedron: a global view of many known arc routing polyhedra. SIAM J. Discrete Math. 22, 606–628 (2008)Grötschel, M., Win, Z.: On the windy postman polyhedron. Report No. 75, Schwerpunktprogram der Deutschen Forschungsgemeinschaft, Universität Augsburg, Germany (1988)Grötschel M., Win Z.: A cutting plane algorithm for the Windy Postman Problem. Math. Program. 55, 339–358 (1992)Guan M.: On the Windy Postman Problem. Discrete Appl. Math. 9, 41–46 (1984)Minieka E.: The Chinese postman problem for mixed networks. Manage. Sci. 25, 643–648 (1979)Naddef D., Rinaldi G.: The symmetric traveling salesman polytope and its graphical relaxation: composition of valid inequalities. Math. Program. 51, 359–400 (1991)Oswald M., Reinelt G., Seitz H.: Applying mod-k cuts for solving linear ordering problems. TOP 17, 158–170 (2009)Papadimitriou C.H.: On the complexity of edge traversing. J. Assoc. Comput. Mach. 23, 544–554 (1976)Ralphs T.K.: On the mixed Chinese postman problem. Oper. Res. Lett. 14, 123–127 (1993)Wenger, K.: Generic Cut Generation Methods for Routing Problems. PhD Dissertation, University of Heidelberg, Germany (2004)Win, Z.: Contributions to Routing Problems. PhD Dissertation, University of Augsburg, Germany (1987)Win Z.: On the Windy Postman Problem on eulerian graphs. Math. Program. 44, 97–112 (1989)Zaragoza Martínez F.J.: Series-parallel graphs are windy postman perfect. Discrete Math. 308, 1366–1374 (2008
Parameterized complexity of the k-arc Chinese Postman Problem
In the Mixed Chinese Postman Problem (MCPP), given an edge-weighted mixed
graph ( may have both edges and arcs), our aim is to find a minimum
weight closed walk traversing each edge and arc at least once. The MCPP
parameterized by the number of edges was known to be fixed-parameter tractable
using a simple argument. Solving an open question of van Bevern et al., we
prove that the MCPP parameterized by the number of arcs is also fixed-parameter
tractable. Our proof is more involved and, in particular, uses a well-known
result of Marx, O'Sullivan and Razgon (2013) on the treewidth of torso graphs
with respect to small separators. We obtain a small cut analog of this result,
and use it to construct a tree decomposition which, despite not having bounded
width, has other properties allowing us to design a fixed-parameter algorithm
A branch-and-cut algorithm for the maximum benefit Chinese postman problem
[EN] The Maximum Benefit Chinese Postman Problem (MBCPP) is an NP-hard problem that considers several benefits associated with each edge, one for each time the edge is traversed with a service. The objective is to find a closed walk with maximum benefit.We propose an IP formulation for the undirected MBCPP and, based on the description of its associated polyhedron, we propose a branch-and-cut algorithm and present computational results on instances with up to 1,000 vertices and 3,000 edges.The authors wish to thank the Ministerio de Innovacion y Ciencia/FEDER of Spain (projects MTM2009-14039-C06-02, MTM2010-19576-C02-02 and DE2009-0057) and Junta de Andalucia/FEDER (grant number FQM-5849) for its support. They also thank two anonymous referees for their careful reading of the manuscript and for their many suggestions and comments that have helped to improve the contents and readability of the paper.Corberán, A.; Plana, I.; Rodríguez-Chía, AM.; Sanchís Llopis, JM. (2013). A branch-and-cut algorithm for the maximum benefit Chinese postman problem. Mathematical Programming. 141(1-2):21-48. https://doi.org/10.1007/s10107-011-0507-6S21481411-2Aráoz J., Fernández E., Franquesa C.: The clustered price-collecting arc-routing problem. Transp. Sci. 43, 287–300 (2009)Aráoz J., Fernández E., Meza O.: Solving the prize-collecting rural postman problem. Eur. J. Oper. Res. 196, 886–896 (2009)Aráoz J., Fernández E., Zoltan C.: Privatized rural postman problems. Comput. Oper. Res. 33, 3432–3449 (2006)Archetti C., Feillet D., Hertz A., Speranza M.G.: The undirected capacitated arc routing problem with profits. Comput. Oper. Res. 37, 1860–1869 (2010)Barahona F., Grötschel M.: On the cycle polytope of a binary matroid. J. Comb. Theory B 40, 40–62 (1986)Fernández E., Fernández E., Franquesa C., Sanchis J.M.: The windy clustered prize-collecting problem. Transp. Sci. 45, 317–334 (2011)Letchford A.N., Letchford A.N., Sanchis J.M.: A cutting-plane algorithm for the general routing problem. Math. Progr. 90, 291–316 (2001)Plana I., Plana I., Sanchis J.M.: A branch & cut algorithm for the windy general routing problem and special cases. Networks 49, 245–257 (2007)Corberán, Á., Plana, I., Sanchis, J.M.: Arc Routing Problems: Data Instances. http://www.uv.es/corberan/instancias.htmSanchis J.M., Sanchis J.M.: A polyhedral approach to the rural postman problem. Eur. J. Oper. Res. 79, 95–114 (1994)Feillet D., Dejax P., Gendreau M.: The profitable arc tour problem: solution with a branch-and-price algorithm. Transp. Sci. 39, 539–552 (2005)Franquesa, C.: The Clustered Prize-collecting Arc Routing Problem. PhD Thesis, Technical University of Catalonia, Barcelona (2008)Ghiani G., Laporte G.: A branch-and-cut algorithm for the undirected rural postman problem. Math. Progr. 87, 467–481 (2000)Lenstra J.K., Rinnooy Kan A.H.G.: On general routing problems. Networks 6, 593–597 (1976)Letchford A.N., Reinelt G., Theis D.O.: Odd minimum cut-sets and b-matchings revisited. SIAM J. Discret. Math. 22, 1480–1487 (2008)Malandraki C., Daskin M.S.: The maximum benefit chinese postman problem and the maximum benefit traveling salesman problem. Eur. J. Oper. Res. 65, 218–234 (1993)Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley, New York (1988)Orloff C.S.: A fundamental problem in vehicle routing. Networks 4, 35–64 (1974)Pearn W.L., Chiu W.C.: Approximate solutions for the maximum benefit Chinese postman problem. Int. J. Syst. Sci. 36, 815–822 (2005)Pearn W.L., Wang K.H.: On the maximum benefit Chinese postman problem. OMEGA 31, 269–273 (2003)Reinelt G., Theis D.O.: Transformation of facets of the general routing problem polytope. SIAM J. Optim. 16, 220–234 (2005
Solution methodologies for debris : removal during disaster response phase
Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent University, 2014.Thesis (Master's) -- Bilkent University, 2014.Includes bibliographical references leaves 79-85.During the disaster response phase of the emergency relief, the aim is to reduce
loss of human life by reaching disaster affected areas with relief items as soon as
possible. Debris caused by the disaster blocks the roads and prevents emergency
aid teams to access the disaster affected regions. Deciding which roads to clean in
order to transport relief items is crucial to diminish the negative impact of a disaster
on human health. Despite the significance of the problem during response,
in the literature debris removal is mostly studied in recovery or reconstruction
phases of a disaster. The aim of this study is providing solution methodologies for
debris removal problem in response phase. In particular, debris removal activities
on certain blocked arcs have to be scheduled in order to reach a set of critical
nodes such as schools and hospitals. Two mathematical models are developed
with different objectives. The first model aims to minimize the total time spent
to reach all critical nodes whereas the second minimizes weighted sum of visiting
times where weights indicate the priorities of critical nodes. Since obtaining solutions
quickly is important in the early post-disaster, heuristic algorithms are also
proposed. Two data sets belonging to Kartal and Bakırk¨oy districts of ˙Istanbul
are used to test the mathematical models and heuristics.Berktaş, NihalM.S
Debris removal during disaster response phase : a case for Turkey
Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 88-93.In this study, a methodology to provide emergency relief supplies to the disaster affected
regions is developed. As a result of destructive effects of disasters, debris, which is the
ruin and wreckage of the structures, occurs. Proper removal of debris has significant
importance since it blocks the roads and prohibits emergency aid teams to access the
disaster affected regions. Wrong disaster management, lack of efficiency and delays in
debris removal cause disruptions in providing sheltering, nutrition, healthcare and
communication services to the disaster victims, and more importantly they result in loss
of lives. Due to the importance of a systematic and efficient way of debris removal from
the point of improving disaster victims’ life quality and its contributions to
transportation of emergency relief materials to the disaster affected regions, the focus of
this study is providing emergency relief supplies to the disaster affected regions as soon
as possible, by considering unblocking operations of roads through removing the
accumulated debris.
To come up with a scientific solution methodology to the problem, mathematical models
that select the paths in order to transport emergency aid materials in the presence of
debris to the pre-determined disaster affected regions are developed. The performances
of the models are tested on two distinct data sets from İstanbul. Since it is crucial to act quickly in an emergency case, a constructive and an improvement heuristic are also
proposed.Şahin, HalenurM.S
A study on two arc routing problems
Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal