ABSTRACT The quadratic minimum spanning tree problem (QMSTP) consists of finding a spanning tree of a graph G such that a quadratic cost function is minimized. In its adjacent only version (AQMSTP), interaction costs only apply for edges... more
ABSTRACT The quadratic minimum spanning tree problem (QMSTP) consists of finding a spanning tree of a graph G such that a quadratic cost function is minimized. In its adjacent only version (AQMSTP), interaction costs only apply for edges that share an endpoint. Motivated by the weak lower bounds provided by formulations in the literature, we present a new linear integer programming formulation for AQMSTP. In addition to decision variables assigned to the edges, it also makes use of variables assigned to the stars of G. In doing so, the model is naturally linear (integer), without the need of implementing usual linearization steps, and its linear programming relaxation better estimates the interaction costs between edges. We also study a reformulation derived from the new model, obtained by projecting out the decision variables associated with the stars. Two exact solution approaches are presented: a branch-and-cut-and-price algorithm, based on the first formulation, and a branch-and-cut algorithm, based on its projection. Our computational results indicate that the lower bounds introduced here are much stronger than previous bounds in the literature. Being designed for the adjacent only case, our duality gaps are one order of magnitude smaller than the Gilmore–Lawler lower bounds for AQMSTP. As a result, the two exact algorithms introduced here outperform the previous exact solution approaches in the literature. In particular, the branch-and-cut method we propose managed to solve AQMSTP instances with as many as 50 vertices to proven optimality. © 2015 Wiley Periodicals, Inc. NETWORKS, 2015
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A group of young researchers from the ESI X summer school, HEC, Jouy-en-Josas 1994, give their personal views on the current status of, and prospects for, Combinatorial Optimisation. Several issues are considered and discussed with... more
A group of young researchers from the ESI X summer school, HEC, Jouy-en-Josas 1994, give their personal views on the current status of, and prospects for, Combinatorial Optimisation. Several issues are considered and discussed with emphasis on a selected ...
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@MISC\{IMM2006-04717, author = "J. Clausen and J. Larsen and J. Bang-Jensen and D. Pisinger", title = "Forretningsviden + it + matematik = effektivitet", year =... more
@MISC\{IMM2006-04717, author = "J. Clausen and J. Larsen and J. Bang-Jensen and D. Pisinger", title = "Forretningsviden + it + matematik = effektivitet", year = "2006", month = "jan", publisher = "", address = "", note = "Kronik", url = "http://www2.imm.dtu.dk/pubdb/p.php?4717" }
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Driver scheduling based on” driver-friendly” vehicle schedules......... 323 Viktor Argilan, Janos Balogh, Jozsef Bekesi, Balazs David, Miklos Kresz, Attila Toth Optimizing ordered median functions with applications to single facility... more
Driver scheduling based on” driver-friendly” vehicle schedules......... 323 Viktor Argilan, Janos Balogh, Jozsef Bekesi, Balazs David, Miklos Kresz, Attila Toth Optimizing ordered median functions with applications to single facility location........................................................ 329 Victor Blanco, Justo Puerto, Safae El Haj Ben Ali A Column-and-Row Generation Algorithm for a Crew Planning Problem in Railways............................................. 335 AC. Suyabatmaz and G. Sahin
PhD Dissertation Proposal. Three essays on applied metaheuristics for logistical challenges in congested urban areas. ...
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We consider the problem of planning the shunting of train units at a railway workshop area. Before and after the maintenance check, a train unit is parked at a depository track. The problem is to schedule the trains to workshops and depot... more
We consider the problem of planning the shunting of train units at a railway workshop area. Before and after the maintenance check, a train unit is parked at a depository track. The problem is to schedule the trains to workshops and depot tracks in order to complete the repairs as soon as possible, while avoiding train blockings at the tracks.
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ABSTRACT
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ABSTRACT This paper considers the Capacitated Profitable Tour Problem (CPTP) which is a special case of the Elementary Shortest Path Problem with Resource Constraints (ESPPRC). The CPTP belongs to the group of problems known as traveling... more
ABSTRACT This paper considers the Capacitated Profitable Tour Problem (CPTP) which is a special case of the Elementary Shortest Path Problem with Resource Constraints (ESPPRC). The CPTP belongs to the group of problems known as traveling salesman problems with profits. In CPTP each customer is associated with a profit and a demand and the objective is to find a capacitated tour (rooted in a depot node) that minimizes the total travel distance minus the profit of the visited customers. The CPTP can be recognized as the sub-problem in many column generation applications, where it is traditionally solved through dynamic programming. In this paper we present an alternative framework based on a formulation for the undirected CPTP and solved through branch-and-cut. Valid inequalities are presented among which we introduce a new family of inequalities for the CPTP denoted rounded multistar inequalities and we prove their validity. Computational experiments are performed on a set of instances known from the literature and a set of newly generated instances. The results indicate that the presented algorithm is highly competitive with the dynamic programming algorithms. In particular, we are able to solve instances with 800 nodes to optimality where the dynamic programming algorithms cannot solve instances with more than 200 nodes. Moreover dynamic programming and branch-and-cut complement each other well, giving us hope for solving more general problems through hybrid approaches. The paper is intended to serve as a platform for further development of branch-and-cut algorithms for CPTP hence also acting as a survey/tutorial.