The Experts below are selected from a list of 84 Experts worldwide ranked by ideXlab platform
José M. Sanchis - One of the best experts on this subject based on the ideXlab platform.
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A branch-and-cut algorithm for the Profitable Windy Rural Postman Problem
European Journal of Operational Research, 2016Co-Authors: Thais Ávila, Ángel Corberán, Isaac Plana, José M. SanchisAbstract:Abstract In this paper we study the profitable windy rural postman problem. This is an arc routing problem with profits defined on a windy graph in which there is a profit Associated with some of the edges of the graph, consisting of finding a route maximizing the difference between the total profit collected and the total cost. This problem generalizes the rural postman problem and other well-known arc routing problems and has real-life applications, mainly in snow removal operations. We propose here a formulation for the problem and study its Associated Polyhedron. Several families of facet-inducing inequalities are described and used in the design of a branch-and-cut procedure. The algorithm has been tested on a large set of benchmark instances and compared with other existing algorithms. The results obtained show that the branch-and-cut algorithm is able to solve large-sized instances optimally in reasonable computing times.
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A branch-and-cut algorithm for the Orienteering Arc Routing Problem
Computers & Operations Research, 2016Co-Authors: Claudia Archetti, Ángel Corberán, Isaac Plana, José M. Sanchis, M. Grazia SperanzaAbstract:In arc routing problems, customers are located on arcs, and routes of minimum cost have to be identified. In the Orienteering Arc Routing Problem (OARP), in addition to a set of regular customers that have to be serviced, a set of potential customers is available. From this latter set, customers have to be chosen on the basis of an Associated profit. The objective is to find a route servicing the customers which maximize the total profit collected while satisfying a given time limit on the route. In this paper, we describe large families of facet-inducing inequalities for the OARP and present a branch-and-cut algorithm for its solution. The exact algorithm embeds a procedure which builds a heuristic solution to the OARP on the basis of the information provided by the solution of the linear relaxation. Extensive computational experiments over different sets of OARP instances show that the exact algorithm is capable of solving to optimality large instances, with up to 2000 vertices and 14,000 arcs, within 1h and often within a few minutes. HighlightsWe study a hard arc routing problem with profits.We provide an integer programming formulation for the problem.The Associated Polyhedron is partially described.We implement a branch-and-cut algorithm based on the partial description.The proposed algorithm can solve instances with up to 2000 vertices and 14,000 arcs
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The Team Orienteering Arc Routing Problem
Transportation Science, 2014Co-Authors: Claudia Archetti, Ángel Corberán, José M. Sanchis, M. Grazia Speranza, Isaac PlanaAbstract:The team orienteering arc routing problem (TOARP) is the extension to the arc routing setting of the team orienteering problem. In the TOARP, in addition to a possible set of regular customers that have to be serviced, another set of potential customers is available. Each customer is Associated with an arc of a directed graph. Each potential customer has a profit that is collected when it is serviced, that is, when the Associated arc is traversed. A fleet of vehicles with a given maximum traveling time is available. The profit from a customer can be collected by one vehicle at most. The objective is to identify the customers that maximize the total profit collected while satisfying the given time limit for each vehicle. In this paper we propose a formulation for this problem and study a relaxation of its Associated Polyhedron. We present some families of valid and facet-inducing inequalities that we use in the implementation of a branch-and-cut algorithm for the resolution of the problem. Computational ex...
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A branch-and-cut algorithm for the maximum benefit Chinese postman problem
Mathematical Programming, 2013Co-Authors: Ángel Corberán, Isaac Plana, Antonio M. Rodríguez-chía, José M. SanchisAbstract: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.
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A branch-and-cut algorithm for the maximum benefit Chinese postman problem
Mathematical Programming, 2011Co-Authors: Ángel Corberán, Isaac Plana, Antonio M. Rodríguez-chía, José M. SanchisAbstract:[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-
Isaac Plana - One of the best experts on this subject based on the ideXlab platform.
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A branch-and-cut algorithm for the Profitable Windy Rural Postman Problem
European Journal of Operational Research, 2016Co-Authors: Thais Ávila, Ángel Corberán, Isaac Plana, José M. SanchisAbstract:Abstract In this paper we study the profitable windy rural postman problem. This is an arc routing problem with profits defined on a windy graph in which there is a profit Associated with some of the edges of the graph, consisting of finding a route maximizing the difference between the total profit collected and the total cost. This problem generalizes the rural postman problem and other well-known arc routing problems and has real-life applications, mainly in snow removal operations. We propose here a formulation for the problem and study its Associated Polyhedron. Several families of facet-inducing inequalities are described and used in the design of a branch-and-cut procedure. The algorithm has been tested on a large set of benchmark instances and compared with other existing algorithms. The results obtained show that the branch-and-cut algorithm is able to solve large-sized instances optimally in reasonable computing times.
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A branch-and-cut algorithm for the Orienteering Arc Routing Problem
Computers & Operations Research, 2016Co-Authors: Claudia Archetti, Ángel Corberán, Isaac Plana, José M. Sanchis, M. Grazia SperanzaAbstract:In arc routing problems, customers are located on arcs, and routes of minimum cost have to be identified. In the Orienteering Arc Routing Problem (OARP), in addition to a set of regular customers that have to be serviced, a set of potential customers is available. From this latter set, customers have to be chosen on the basis of an Associated profit. The objective is to find a route servicing the customers which maximize the total profit collected while satisfying a given time limit on the route. In this paper, we describe large families of facet-inducing inequalities for the OARP and present a branch-and-cut algorithm for its solution. The exact algorithm embeds a procedure which builds a heuristic solution to the OARP on the basis of the information provided by the solution of the linear relaxation. Extensive computational experiments over different sets of OARP instances show that the exact algorithm is capable of solving to optimality large instances, with up to 2000 vertices and 14,000 arcs, within 1h and often within a few minutes. HighlightsWe study a hard arc routing problem with profits.We provide an integer programming formulation for the problem.The Associated Polyhedron is partially described.We implement a branch-and-cut algorithm based on the partial description.The proposed algorithm can solve instances with up to 2000 vertices and 14,000 arcs
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The Team Orienteering Arc Routing Problem
Transportation Science, 2014Co-Authors: Claudia Archetti, Ángel Corberán, José M. Sanchis, M. Grazia Speranza, Isaac PlanaAbstract:The team orienteering arc routing problem (TOARP) is the extension to the arc routing setting of the team orienteering problem. In the TOARP, in addition to a possible set of regular customers that have to be serviced, another set of potential customers is available. Each customer is Associated with an arc of a directed graph. Each potential customer has a profit that is collected when it is serviced, that is, when the Associated arc is traversed. A fleet of vehicles with a given maximum traveling time is available. The profit from a customer can be collected by one vehicle at most. The objective is to identify the customers that maximize the total profit collected while satisfying the given time limit for each vehicle. In this paper we propose a formulation for this problem and study a relaxation of its Associated Polyhedron. We present some families of valid and facet-inducing inequalities that we use in the implementation of a branch-and-cut algorithm for the resolution of the problem. Computational ex...
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A branch-and-cut algorithm for the maximum benefit Chinese postman problem
Mathematical Programming, 2013Co-Authors: Ángel Corberán, Isaac Plana, Antonio M. Rodríguez-chía, José M. SanchisAbstract: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.
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A branch-and-cut algorithm for the maximum benefit Chinese postman problem
Mathematical Programming, 2011Co-Authors: Ángel Corberán, Isaac Plana, Antonio M. Rodríguez-chía, José M. SanchisAbstract:[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-
Ángel Corberán - One of the best experts on this subject based on the ideXlab platform.
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A branch-and-cut algorithm for the Profitable Windy Rural Postman Problem
European Journal of Operational Research, 2016Co-Authors: Thais Ávila, Ángel Corberán, Isaac Plana, José M. SanchisAbstract:Abstract In this paper we study the profitable windy rural postman problem. This is an arc routing problem with profits defined on a windy graph in which there is a profit Associated with some of the edges of the graph, consisting of finding a route maximizing the difference between the total profit collected and the total cost. This problem generalizes the rural postman problem and other well-known arc routing problems and has real-life applications, mainly in snow removal operations. We propose here a formulation for the problem and study its Associated Polyhedron. Several families of facet-inducing inequalities are described and used in the design of a branch-and-cut procedure. The algorithm has been tested on a large set of benchmark instances and compared with other existing algorithms. The results obtained show that the branch-and-cut algorithm is able to solve large-sized instances optimally in reasonable computing times.
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A branch-and-cut algorithm for the Orienteering Arc Routing Problem
Computers & Operations Research, 2016Co-Authors: Claudia Archetti, Ángel Corberán, Isaac Plana, José M. Sanchis, M. Grazia SperanzaAbstract:In arc routing problems, customers are located on arcs, and routes of minimum cost have to be identified. In the Orienteering Arc Routing Problem (OARP), in addition to a set of regular customers that have to be serviced, a set of potential customers is available. From this latter set, customers have to be chosen on the basis of an Associated profit. The objective is to find a route servicing the customers which maximize the total profit collected while satisfying a given time limit on the route. In this paper, we describe large families of facet-inducing inequalities for the OARP and present a branch-and-cut algorithm for its solution. The exact algorithm embeds a procedure which builds a heuristic solution to the OARP on the basis of the information provided by the solution of the linear relaxation. Extensive computational experiments over different sets of OARP instances show that the exact algorithm is capable of solving to optimality large instances, with up to 2000 vertices and 14,000 arcs, within 1h and often within a few minutes. HighlightsWe study a hard arc routing problem with profits.We provide an integer programming formulation for the problem.The Associated Polyhedron is partially described.We implement a branch-and-cut algorithm based on the partial description.The proposed algorithm can solve instances with up to 2000 vertices and 14,000 arcs
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The Team Orienteering Arc Routing Problem
Transportation Science, 2014Co-Authors: Claudia Archetti, Ángel Corberán, José M. Sanchis, M. Grazia Speranza, Isaac PlanaAbstract:The team orienteering arc routing problem (TOARP) is the extension to the arc routing setting of the team orienteering problem. In the TOARP, in addition to a possible set of regular customers that have to be serviced, another set of potential customers is available. Each customer is Associated with an arc of a directed graph. Each potential customer has a profit that is collected when it is serviced, that is, when the Associated arc is traversed. A fleet of vehicles with a given maximum traveling time is available. The profit from a customer can be collected by one vehicle at most. The objective is to identify the customers that maximize the total profit collected while satisfying the given time limit for each vehicle. In this paper we propose a formulation for this problem and study a relaxation of its Associated Polyhedron. We present some families of valid and facet-inducing inequalities that we use in the implementation of a branch-and-cut algorithm for the resolution of the problem. Computational ex...
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A branch-and-cut algorithm for the maximum benefit Chinese postman problem
Mathematical Programming, 2013Co-Authors: Ángel Corberán, Isaac Plana, Antonio M. Rodríguez-chía, José M. SanchisAbstract: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.
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A branch-and-cut algorithm for the maximum benefit Chinese postman problem
Mathematical Programming, 2011Co-Authors: Ángel Corberán, Isaac Plana, Antonio M. Rodríguez-chía, José M. SanchisAbstract:[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-
Luis Gouveia - One of the best experts on this subject based on the ideXlab platform.
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Balanced vehicle routing: Polyhedral analysis and branch-and-cut algorithm
European Journal of Operational Research, 2019Co-Authors: Tolga Bektaş, Luis Gouveia, Antonio Martinez-sykora, Juan-josé Salazar-gonzálezAbstract:This paper studies a variant of the unit-demand Capacitated Vehicle Routing Problem, namely the Balanced Vehicle Routing Problem, where each route is required to visit a maximum and a minimum number of customers. A polyhedral analysis for the problem is presented, including the dimension of the Associated Polyhedron, description of several families of facet-inducing inequalities and the relationship between these inequalities. The inequalities are used in a branch-and-cut algorithm, which is shown to computationally outperform the best approach known in the literature for the solution of this problem.
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On the convex piecewise linear unsplittable multicommodity flow problem
2016Co-Authors: Bernard Fortz, Luis Gouveia, Martim Joyce-monizAbstract:We consider the problem of finding the cheapest routing for a set of commodities over a directed graph, such that: i) each commodity flows through a single path, ii) the routing cost of each arc is given by a convex piecewise linear function of the load (i.e. the total flow) traversing it. We propose a new mixed-integer programming formulation for this problem. This formulation gives a complete description of the Associated Polyhedron for the single commodity case, and produces very tight linear programming bounds for the multi-commodity case.
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DRCN - On the convex piecewise linear unsplittable multicommodity flow problem
2016 12th International Conference on the Design of Reliable Communication Networks (DRCN), 2016Co-Authors: Bernard Fortz, Luis Gouveia, Martim Joyce-monizAbstract:We consider the problem of finding the cheapest routing for a set of commodities over a directed graph, such that: i) each commodity flows through a single path, ii) the routing cost of each arc is given by a convex piecewise linear function of the load (i.e. the total flow) traversing it. We propose a new mixed-integer programming formulation for this problem. This formulation gives a complete description of the Associated Polyhedron for the single commodity case, and produces very tight linear programming bounds for the multi-commodity case.
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Extended Node-Arc Formulations for the K-Edge Disjoint Hop-Constrained Network Design Problem
2008Co-Authors: Quentin Botton, Bernard Fortz, Luis GouveiaAbstract:This paper considers the K-edge-disjoint hop-constrained Network Design Problem (HCNDP) which consistsin finding a minimum cost subgraph such that there exists at least K-edge-disjoint paths betweenorigins and destinations of demands, and such that the length of these paths is at most equal to a givenparameter L. This problem was considered in the past using only design variables. Here, we consideran extended node-arc formulation, introducing flow variables to model the paths. We conjecture that ourformulation leads to the complete description of the Associated Polyhedron and we provide an algorithmleading to good performances in terms of computing times.
Martim Joyce-moniz - One of the best experts on this subject based on the ideXlab platform.
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On the convex piecewise linear unsplittable multicommodity flow problem
2016Co-Authors: Bernard Fortz, Luis Gouveia, Martim Joyce-monizAbstract:We consider the problem of finding the cheapest routing for a set of commodities over a directed graph, such that: i) each commodity flows through a single path, ii) the routing cost of each arc is given by a convex piecewise linear function of the load (i.e. the total flow) traversing it. We propose a new mixed-integer programming formulation for this problem. This formulation gives a complete description of the Associated Polyhedron for the single commodity case, and produces very tight linear programming bounds for the multi-commodity case.
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DRCN - On the convex piecewise linear unsplittable multicommodity flow problem
2016 12th International Conference on the Design of Reliable Communication Networks (DRCN), 2016Co-Authors: Bernard Fortz, Luis Gouveia, Martim Joyce-monizAbstract:We consider the problem of finding the cheapest routing for a set of commodities over a directed graph, such that: i) each commodity flows through a single path, ii) the routing cost of each arc is given by a convex piecewise linear function of the load (i.e. the total flow) traversing it. We propose a new mixed-integer programming formulation for this problem. This formulation gives a complete description of the Associated Polyhedron for the single commodity case, and produces very tight linear programming bounds for the multi-commodity case.
