New Facets and an Enhanced Branch-and-Cut for the Min-Max K-Windy Rural Postman Problem

[EN] The min-max windy rural postman problem is a multiple vehicle version of the windy rural postman problem, WRPP, which consists of minimizing the length of the longest route to find a set of balanced routes for the vehicles. In a previous paper, an ILP formulation and a partial polyhedral study were presented, and a preliminary branch-and-cut algorithm that produced some promising computational results was implemented. In this article, we present further results for this problem. We describe several new facet-inducing inequalities obtained from the WRPP, as well as some inequalities that have to be satisfied by any optimal solution. We present an enhanced branch-and-cut algorithm that takes advantage of both these new inequalities and high quality min-max K-WRPP feasible solutions obtained by a metaheuristic. Computational results on a large set of instances are also reported. © 2011 Wiley Periodicals, Inc.Contract grant sponsor: Ministerio de Ciencia e Innovacion of Spain; Contract grant numbers: MTM2006-14961-C05-02, MTM2009-14039-C06-02Benavent López, E.; Corberán, A.; Plana, I.; Sanchís Llopis, JM. (2011). New Facets and an Enhanced Branch-and-Cut for the Min-Max K-Windy Rural Postman Problem. Networks. 58(4):255-272. https://doi.org/10.1002/net.20469S255272584D. Ahr Contributions to multiple postmen problems 2004Ahr, D., & Reinelt, G. (2002). New Heuristics and Lower Bounds for the Min-Max k-Chinese Postman Problem. Lecture Notes in Computer Science, 64-74. doi:10.1007/3-540-45749-6_10Ahr, D., & Reinelt, G. (2006). A tabu search algorithm for the min–max k-Chinese postman problem. Computers & Operations Research, 33(12), 3403-3422. doi:10.1016/j.cor.2005.02.011D. Applegate R. E. Bixby V. Chvátal W. Cook Finding cuts in the TSP 1995Benavent, E., Carrotta, A., Corberán, A., Sanchis, J. M., & Vigo, D. (2007). Lower bounds and heuristics for the Windy Rural Postman Problem. European Journal of Operational Research, 176(2), 855-869. doi:10.1016/j.ejor.2005.09.021Benavent, E., Corberán, A., Plana, I., & Sanchis, J. M. (2009). Min-Max K -vehicles windy rural postman problem. Networks, 54(4), 216-226. doi:10.1002/net.20334Benavent, E., Corberán, Á., & Sanchis, J. M. (2009). A metaheuristic for the min–max windy rural postman problem with K vehicles. Computational Management Science, 7(3), 269-287. doi:10.1007/s10287-009-0119-2Corberáan, A., Letchford, A. N., & Sanchis, J. M. (2001). A cutting plane algorithm for the General Routing Problem. Mathematical Programming, 90(2), 291-316. doi:10.1007/pl00011426Corberán, A., Plana, I., & Sanchis, J. M. (2007). A branch & cut algorithm for the windy general routing problem and special cases. Networks, 49(4), 245-257. doi:10.1002/net.20176Corberán, A., Plana, I., & Sanchis, J. M. (2008). The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra. SIAM Journal on Discrete Mathematics, 22(2), 606-628. doi:10.1137/050640886Frederickson, G. N., Hecht, M. S., & Kim, C. E. (1978). Approximation Algorithms for Some Routing Problems. SIAM Journal on Computing, 7(2), 178-193. doi:10.1137/0207017Pearn, W. L. (1994). Solvable cases of the k-person Chinese postman problem. Operations Research Letters, 16(4), 241-244. doi:10.1016/0167-6377(94)90073-6I. Plana The windy general routing problem 200

The stacker crane problem and the directed general routing problem

This is the peer reviewed version of the following article: Ávila, Thais , Corberán, Angel, Plana, Isaac, Sanchís Llopis, José María. (2015). The stacker crane problem and the directed general routing problem.Networks, 65, 1, 43-55. DOI: 10.1002/net.21591 , which has been published in final form at http://doi.org/10.1002/net.21591. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving[EN] This article deals with the polyhedral description and the resolution of the directed general routing problem (DGRP) and the stacker crane problem (SCP). The DGRP contains a large number of important arc and node routing problems as special cases, including the SCP. Large families of facet-defining inequalities for the DGRP are described and a branch-and-cut algorithm for these problems is presented. Extensive computational experiments over different sets of DGRP and SCP instances are included.Contract grant sponsor: Ministerio de Economía y Competitividad (project MTM2012-36163-C06-02) of Spain Contract grant sponsor: Generalitat Valenciana (project GVPROMETEO2013-049)Ávila, T.; Corberán, A.; Plana, I.; Sanchís Llopis, JM. (2015). The stacker crane problem and the directed general routing problem. Networks. 65(1):43-55. https://doi.org/10.1002/net.21591S435565

In situ optimization methodology for the water circulation pumps frequency of ground source heat pump systems

[EN] This paper presents an experimental study of the influence of the water circulation pumps frequency atthe indoor and outdoor loops in the overall system performance of a ground source heat pump moni-tored plant, and describes a three steps new methodology to optimize the system energy performanceand obtain the values of the optimal frequencies when ON/OFF regulation is employed. The first stepconsists of several experimental tests of pseudo-random sequence of frequency steps for both, internaland external circulation pumps, carried out during a single day. The second step is the characterization ofthe quasi-steady state system performance as a function of circulation pumps frequencies. The final stepconsists of, by means of an analytical expression, the extrapolation of results to any partial load ratio,what allows finding the optimal frequency as a function of the instantaneous thermal load. The advantageof the proposed methodology is that it can be carried out on site and is able to consider the phenomenaoccurring at the heat pump and the ground source heat exchanger when the flow rates are varied. Themethodology can be applied to any installation incorporating variable speed circulation pumps. Resultsindicate large energy savings potential for this kind of installation.This work was supported by the European Commission under the FP7 framework project GROUND-MED: "Advanced ground source heat pump systems for heating and cooling in Mediterranean climate".Montagud Montalvá, CI.; Corberán Salvador, JM.; Montero Reguera, ÁE. (2014). In situ optimization methodology for the water circulation pumps frequency of ground source heat pump systems. Energy and Buildings. 68, A:42-53. https://doi.org/10.1016/j.enbuild.2013.09.030S425368,

Min-Max K-vehicles Windy Rural Postman Problem

[EN] In this article the Min-Max version of the windy rural postman problem with several vehicles is introduced. For this problem, in which the objective is to minimize the length of the longest tour in order to find a set of balanced tours for the vehicles, we present here an ILP formulation and study its associated polyhedron. Based on its partial description, a branch-and-cut algorithm has been implemented and computational results on a large set of instances are finally presented. (C) 2009 Wiley Periodicals, Inc. NETWORKS, Vol. 54(4),216-226 2009Contract grant sponsor: Ministerio de Education y Ciencia of Spain: Contract gram number: MTM2006-14961-C05-02Benavent López, E.; Corberan, A.; Plana, I.; Sanchís Llopis, JM. (2009). Min-Max K-vehicles Windy Rural Postman Problem. Networks. 54(4):216-226. https://doi.org/10.1002/net.20334S216226544D. Ahr Contributions to multiple postmen problems 2004D. Ahr G. Reinelt “New heuristics and lower bounds for the min-max k -Chinese postman problem” Algorithms-ESA 2002, 10th Annual European Symposium, Rome, Italy, 2002, Lecture Notes in Computer Science 2461 R. Möring R. Raman Springer Berlin 2002 64 74Ahr, D., & Reinelt, G. (2006). A tabu search algorithm for the min–max k-Chinese postman problem. Computers & Operations Research, 33(12), 3403-3422. doi:10.1016/j.cor.2005.02.011D. Applegate R.E. Bixby V. Chvátal W. Cook Finding cuts in the TSP 1995Barahona, F., & Grötschel, M. (1986). On the cycle polytope of a binary matroid. Journal of Combinatorial Theory, Series B, 40(1), 40-62. doi:10.1016/0095-8956(86)90063-8Belenguer, J. M., & Benavent, E. (1998). Computational Optimization and Applications, 10(2), 165-187. doi:10.1023/a:1018316919294Benavent, E., Carrotta, A., Corberán, A., Sanchis, J. M., & Vigo, D. (2007). Lower bounds and heuristics for the Windy Rural Postman Problem. European Journal of Operational Research, 176(2), 855-869. doi:10.1016/j.ejor.2005.09.021N. Christofides V. Campos A. Corberán E. Mota An algorithm for the rural postman problem 1981Christofides, N., Campos, V., Corberán, A., & Mota, E. (1986). An algorithm for the Rural Postman problem on a directed graph. Netflow at Pisa, 155-166. doi:10.1007/bfb0121091Corberán, A., Plana, I., & Sanchis, J. M. (2008). The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra. SIAM Journal on Discrete Mathematics, 22(2), 606-628. doi:10.1137/050640886Corberán, A., Plana, I., & Sanchis, J. M. (2007). A branch & cut algorithm for the windy general routing problem and special cases. Networks, 49(4), 245-257. doi:10.1002/net.20176Eiselt, H. A., Gendreau, M., & Laporte, G. (1995). Arc Routing Problems, Part II: The Rural Postman Problem. Operations Research, 43(3), 399-414. doi:10.1287/opre.43.3.399Frederickson, G. N., Hecht, M. S., & Kim, C. E. (1978). Approximation Algorithms for Some Routing Problems. SIAM Journal on Computing, 7(2), 178-193. doi:10.1137/0207017G. Ghiani D. Laganá G. Laporte R. Musmanno A branch-and-cut algorithm for the undirected capacitated arc routing problem 2007Ghiani, G., & Laporte, G. (2000). A branch-and-cut algorithm for the Undirected Rural Postman Problem. Mathematical Programming, 87(3), 467-481. doi:10.1007/s101070050007Golden, B. L., & Wong, R. T. (1981). Capacitated arc routing problems. Networks, 11(3), 305-315. doi:10.1002/net.3230110308Padberg, M. W., & Rao, M. R. (1982). Odd Minimum Cut-Sets andb-Matchings. Mathematics of Operations Research, 7(1), 67-80. doi:10.1287/moor.7.1.67Pearn, W. L. (1994). Solvable cases of the k-person Chinese postman problem. Operations Research Letters, 16(4), 241-244. doi:10.1016/0167-6377(94)90073-

50 Años de Arc Routing

Hace poco más de 50 años, un matemático chino, Meigu Guan, planteó el problema de encontrar un recorrido de las aristas de un grafo no dirigido que fuera el más corto posible. Guan buscaba minimizar la longitud de un camino cerrado que pasara por cada arista del grafo al menos una vez y, así, encontrar una ruta de longitud mínima para un cartero que debe recorrer cada calle de la zona que tiene asignada para repartir el correo. El artículo de Guan, sobre lo que posteriormente se conoció como el Problema del Cartero Chino, fue el primero de una larga serie de contribuciones en el área de las Rutas por Arcos (Arc Routing). Básicamente, los problemas de rutas por arcos consisten en determinar un recorrido de coste mínimo de todos o algunos arcos y/o aristas de un grafo, posiblemente sujeto a algunas condiciones adicionales. Estos problemas definen un área apasionante porque, por una parte, la mayoría de ellos son problemas que plantean un desafío desde el punto de vista de su estudio y resolución y, por otro lado, porque aparecen en muchas situaciones prácticas de la vida real como la recogida de basuras, la limpieza de las calles y el mantenimiento de carreteras o vías de tren y, puesto que el dinero involucrado en estas operaciones representa millones de euros, existe un considerable potencial para el ahorro. Esta charla es sobre el recorrido de los arcos (y aristas) de un grafo, los problemas de rutas por arcos, su historia y resolución, y sus aplicaciones a problemas de la vida real.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Evaluation of different heat pump systems for sanitary hot water production using natural refrigerants

[EN] Heat pumps that work with a high degree of subcooling in subcritical systems have shown a significant margin of improvement when working with sanitary hot water applications. Recently, two different approaches to overcome the high degree of subcooling have been presented in the literature: with a subcooler (separate from the condenser) and by making all the subcooling in the condenser. In this paper, a comparative evaluation between both alternatives is presented, and the obtained results are compared with a representative solution already available on the market using natural refrigerants for this application. The results of this analysis have shown that in a system with subcooling in the condenser, it is possible to obtain a COP comparable to that of transcritical CO2 heat pump water heaters. Furthermore, the system with subcooling has been demonstrated experimentally as being capable of producing water up to 90ºC and has shown a COP up to 20% higher than some CO2 commercial products (catalogue data reference).This work has been developed in the Seventh Framework Program of the European Union by the project, Next Generation of Heat Pump Technologies (NEXTGHP), grant agreement 307169. The authors thank the support given. Part of the work presented was carried by Miquel Pitarch-Mocholí with the financial support of a PhD scholarship from the Universitat Politècnica de València. The authors would like also to acknowledge the Spanish ‘MINISTERIO DE ECONOMIA Y COMPETITIVIDAD’, through the project ref-ENE2014-53311-C2-1-P-AR ‘‘Aprovechamiento del calor residual a baja temperatura mediante bombas de calor para la produccion de agua caliente” for the given supportPitarch, M.; Navarro-Peris, E.; Gonzálvez-Maciá, J.; Corberán, JM. (2017). Evaluation of different heat pump systems for sanitary hot water production using natural refrigerants. Applied Energy. 190:911-919. https://doi.org/10.1016/j.apenergy.2016.12.166S91191919

A comparison of two different formulations for Arc Routing Problems on Mixed graphs

[EN] Arc routing problems on mixed graphs have been modelled in the literature either using just one variable per edge or associating to each edge two variables, each one representing its traversal in the corresponding direction. In this paper, and using the mixed general routing problem as an example, we compare theoretical and computationally both formulations as well as the lower bounds obtained from them using Linear Programming based methods. Extensive computational experiments, including some big and newly generated random instances, are presented.Authors want to thank two anonymous referees for their careful reading of the manuscript. Also we thank the support given by the Ministerio de Ciencia y Tecnología of Spain through Grant TIC2003-05982-C05-01 and by the Generalitat Valenciana (Grupos 03/189).Corberán, A.; Mota, E.; Sanchís Llopis, JM. (2006). A comparison of two different formulations for Arc Routing Problems on Mixed graphs. Computers & Operations Research. 33(12):3384-3402. https://doi.org/10.1016/j.cor.2005.02.010S33843402331

Zigzag inequalities:a new class of facet-inducing inequalities for Arc Routing Problems

[EN] In this paper we introduce a new class of facet-inducing inequalities for the Windy Rural Postman Problem and the Windy General Routing Problem. These inequalities are called Zigzag inequalities because they cut off fractional solutions containing a zigzag associated with variables with 0.5 value. Two different types of inequalities, the Odd Zigzag and the Even Zigzag inequalities, are presented. Finally, their application to other known Arc Routing Problems is discussed.The authors wish to thank the Ministerio de Ciencia y Tecnología of Spain (project TIC2003-05982-C05-01) and the Generalitat Valenciana (Ref: GRUPOS03/189) their support.Corberán, A.; Plana, I.; Sanchís Llopis, JM. (2006). Zigzag inequalities:a new class of facet-inducing inequalities for Arc Routing Problems. Mathematical Programming. 108(1):79-96. https://doi.org/10.1007/s10107-005-0643-yS79961081Benavent, E., Carrotta, A., Corberán, A., Sanchis, J.M., Vigo, D.: Lower Bounds and Heuristics for the Windy Rural Postman Problem. Technical Report TR03-2003. Department of Statistics and OR, University of Valencia (Spain). Submitted to EJOR 2003Benavent, E., Corberán, A., Piñana, E., Plana, I., Sanchis, J.M.: New Heuristics for the Windy Rural Postman Problem. To appear in Comput. Oper. Res. 2005Chopra, S., Rinaldi, G.: The Graphical Asymmetric Traveling Salesman Polyhedron: Symmetric Inequalities. SIAM J. Discrete Math. 9 (4), 602–624 (1996)Christofides, N., Benavent, E., Campos, V., Corberán, A., Mota, E.: An Optimal Method for the Mixed Postman Problem. In: P. Thoft-Christensen (ed.) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, 59. Berlin: Springer-Verlag 1984Christofides, N., Campos, V., Corberán, A., Mota, E.: An Algorithm for the Rural Postman Problem. Report IC.OR. 81.5. Imperial College, London 1981Corberán, A., Mejía, G., Sanchis, J.M.: New Results on the Mixed General Routing Problem. To appear in Oper. Res. 2005Corberán, A., Mota, E., Sanchis, J.M.: A Comparison of Two Different Formulations for Arc Routing Problems on Mixed Graphs. To appear in Comput. Oper. Res. 2005Corberán, A., Plana, I., Sanchis, J.M.: On the Windy General Routing Polyhedron. In preparation 2005Corberán, A., Romero, A., Sanchis, J.M.: The Mixed General Routing Problem Polyhedron. Math. Programming 96, 103–137 (2003)Cornuèjols, G., Fonlupt, J., Naddef, D.: The traveling salesman problem on a graph and some related integer polyhedra. Math. Programming 33, 1–27 (1985)Eiselt, H.A., Gendreau, M., Laporte, G.: Arc-Routing Problems, Part 2: the Rural Postman Problem. Oper. Res. 43, 399–414 (1995)Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton, NJ 1962Grötschel, M., Win, Z.: On the Windy Postman Polyhedron. Report No. 75, Schwerpunktprogram der Deutschen Forschungsgemeinschaft, Universität Augsburg, Germany 1988Grötschel, M., Win, Z.: A Cutting Plane Algorithm for the Windy Postman Problem. Math. Programming 55, 339–358 (1992)Guan, M.: On the Windy Postman Problem. Discrete Applied Mathematics 9, 41–46 (1984)Letchford, A.: New inequalities for the General Routing Problem. Eur. J. Oper. Res. 96, 317–322 (1997)Minieka, E.: The Chinese Postman Problem for Mixed Networks. Management Sci. 25, 643–648 (1979)Naddef, D., Rinaldi, G.: The Symmetric Traveling Salesman Polytope and its Graphical Relaxation: Composition of Valid Inequalities. Math. Programming 51, 359–400 (1991)Nobert, Y., Picard, J.C.: An Optimal Algorithm for the Mixed Chinese Postman Problem. Networks 27, 95–108 (1996)Ralphs, T.K.: On the Mixed Chinese Postman Problem. Oper. Res. Lett. 14, 123–127 (1993)Win, Z.: Contributions to Routing Problems. PhD Dissertation, University of Augsburg, Germany 198

Development of an experimental method to generate a non-uniform air flow distribution at the inlet of a heat exchanger

As already demonstrated by many authors, the non-uniformity of the air distribution at the inlet of both condensers and evaporators entails not negligible performance degradation. Its experimental quantification is mainly complicated by the difficulties connected to the air velocity measurement in a traditional air-conditioning installation. For this reason, many works are supported by the application of CFD models or others simulation tools. In order to analyze experimentally the effect of the nonuniform air distribution on the performance of a condenser, in this work a simple method for generating a specific air velocity profile at the inlet of a heat exchanger will be presented. It consist in allocating several filters along the heat exchanger height. Once characterized the filter, identifying the relation between the length of the filters, the pressure drop and the air velocity, any type of air velocity profile can be generated. The method presents high flexibility and allows being used with any typology of heat exchanger. In this work, the method will be used for generating a non-uniform air velocity profile at the inlet of two condenser: a round tube plate fins heat exchanger and a microchannel heat exchanger. The results show that, with a specific distribution of the filters, the nonuniform air velocity profile characterizing the A-shape condensation units has been reproduced with a very good agreement.The work of Alessandro Pisano on this project was partially supported by the Ministry for Economy and Finance of Spain, under the Training of Researcher program (FPI). Financial support from the Ministry for Economy and Finance of Spain, project numbers: DPI2011-26771-C02-01 is gratefully acknowledged

Transferencia de resultados de investigación sobre enseñanza y aprendizaje de la geometría al aula

En este trabajo presentamos algunos ítems del test que hemos diseñado con objeto de obtener información sobre la Geometría que se enseña en escuelas de primaria de algunos estados de México y así poder, por un lado, valorar si la Geometría que se contempla en el currículum de primaria mexicano se corresponde con la que imparten estos maestros y, por otor, determinar las posibles causas que han llevado a la enseñanza de la geometría a la situación actual. En este informe hacemos también referencia a un estudio que estamos realizando en el que analizamos algunos libros de texto de primaria mexicanos y algunos de los test utilizados en este país para la evaluación de los estudiantes de este nivel