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A RelaxandCut Framework for Gomory MixedInteger Cuts
"... Gomory MixedInteger Cuts (GMICs) are widely used in modern branchandcut codes for the solution of MixedInteger Programs. Typically, GMICs are iteratively generated from the optimal basis of the current Linear Programming (LP) relaxation, and immediately added to the LP before the next round of ..."
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Gomory MixedInteger Cuts (GMICs) are widely used in modern branchandcut codes for the solution of MixedInteger Programs. Typically, GMICs are iteratively generated from the optimal basis of the current Linear Programming (LP) relaxation, and immediately added to the LP before the next round of cuts is generated. Unfortunately, this approach is prone to instability. In this paper we analyze a different scheme for the generation of rank1 GMICs read from a basis of the original LP—the one before the addition of any cut. We adopt a relaxandcut approach where the generated GMICs are not added to the current LP, but immediately relaxed in a Lagrangian fashion. Various elaborations of the basic idea are presented, that lead to very fast— yet accurate—variants of the basic scheme. Very encouraging computational results are presented, with a comparison with alternative techniques from the literature also aimed at improving the GMIC quality. We also show how our method can be integrated with other cut generators, and successfully used in a cutandbranch enumerative framework.
Solving RealWorld Vehicle Routing Problems with Evolutionary Algorithms
 Natural Intelligence for Scheduling, Planning and Packing Problems, volume 250 of Studies in Computational Intelligence, chapter 2
, 2009
"... Thisdocument is a preview version and not necessarily identical with the original. ..."
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Thisdocument is a preview version and not necessarily identical with the original.
Delayminimized route design for wireless sensoractuator networks
 In Proc. of IEEE Wireless Communications and Networking Conference (WCNC’07
, 2007
"... Abstract — Wireless sensoractuator networks (WSANs) have recently been suggested as an enhancement to the traditional sensor networks by employing powerful and mobile actuators. Multiple actuators can patrol along different routes and communicate with the static sensors. To minimize the data collec ..."
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Abstract — Wireless sensoractuator networks (WSANs) have recently been suggested as an enhancement to the traditional sensor networks by employing powerful and mobile actuators. Multiple actuators can patrol along different routes and communicate with the static sensors. To minimize the data collection time, an effective route design is crucial for the actuators to travel in the sensing field. In this paper, we present a mathematical formulation of the route design problem, and show that the general problem is computationally intractable. We then develop a practically efficient algorithm to reduce the waiting time for the sensors. Our algorithm adaptively differentiates the actuator visiting frequencies to the sensors according to their relative weights and data generation patterns. Simulation results demonstrate that our algorithm can effectively reduce the overall data collection time. I.
Automating the Generation of VNS Components with Grammatical Evolution
"... Abstract. The vehicle routing problem (VRP) is a family of problems whereby a fleet of vehicles must service the commodity demands of a set of geographically scattered customers from one or more depots, subject to a number of constraints. Early hyperheuristic research focussed on selecting and appl ..."
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Abstract. The vehicle routing problem (VRP) is a family of problems whereby a fleet of vehicles must service the commodity demands of a set of geographically scattered customers from one or more depots, subject to a number of constraints. Early hyperheuristic research focussed on selecting and applying a lowlevel heuristic at a given stage of an optimisation process. Recent trends have led to a number of approaches being developed to automatically generate heuristics for a number of combinatorial optimisation problems. Previous work on the VRP has shown that the application of hyperheuristic approaches can yield successful results. In this paper we investigate the potential of grammatical evolution as a method to evolve the components of a variable neighbourhood search (VNS) framework. In particular two components are generated; constructive heuristics to create initial solutions and neighbourhood move operators to change the state of a given solution. The proposed method is tested on standard benchmark instances of two common VRP variants. 1
A SetPartitioningBased Model for the Stochastic Vehicle Routing Problem
, 2006
"... The objective of the Vehicle Routing Problem (VRP) is to construct a minimum cost set of vehicle routes that visits all customers and satisfies demands without violating the vehicle capacity constraints. The Stochastic Vehicle Routing Problem (SVRP) results when one or more elements of the VRP are m ..."
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The objective of the Vehicle Routing Problem (VRP) is to construct a minimum cost set of vehicle routes that visits all customers and satisfies demands without violating the vehicle capacity constraints. The Stochastic Vehicle Routing Problem (SVRP) results when one or more elements of the VRP are modeled as random variables. In this paper, we present a setpartitioningbased modeling framework for the VRP with stochastic demands (VRPSD). The framework can be adapted easily for routing problems with randomness in other problem elements, such as random customers and random travel times. We formulate the VRPSD as a twostage stochastic program and introduce an extended recourse strategy in which vehicles are allowed to serve additional customers from failed routes prior to returning to the depot or to serve customers from failed routes on a new route after returning to the depot. Computational experiments show that route plans generated using the new recourse function perform quite well, especially for problems with few customers per route, where cost savings of roughly 5 % are possible. 1
Optimizing the Cargo Express Service of Swiss Federal Railways
, 2006
"... doi 10.1287/trsc.1080.0246 ..."
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Decomposition in Integer Linear Programming
, 2009
"... Both cutting plane methods and traditional decomposition methods are procedures that compute a bound on the optimal value of an integer linear program (ILP) by constructing an approximation to the convex hull of feasible solutions. This approximation is obtained by intersecting the polyhedron associ ..."
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Both cutting plane methods and traditional decomposition methods are procedures that compute a bound on the optimal value of an integer linear program (ILP) by constructing an approximation to the convex hull of feasible solutions. This approximation is obtained by intersecting the polyhedron associated with the continuous relaxation, which has an explicit representation, with an implicitly defined polyhedron having a description of exponential size. In this paper, we first review these classical procedures and then introduce a new class of bounding methods called integrated decomposition methods, in which the bound yielded by traditional approaches is potentially improved by introducing a second implicitly defined polyhedron. We also discuss the concept of structured separation, which is related to the wellknown template paradigm for dynamically generating valid inequalities and is central to our algorithmic framework. Finally, we briefly introduce a software framework for implementing the methods discussed in the paper and illustrate the concepts through the presentation of applications. 1
An adaptive delayminimized route design for wireless sensoractuator networks
 IEEE Trans. Veh. Technol
, 2009
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Modelling of capacitated transportation systems for integral scheduling
 OR spectrum
, 2004
"... Abstract. Motivated by a planned automated cargo transportation network, we consider transportation problems in which the finite capacity of resources (such as vehicles, docks, parking places) has to be taken into account. For such problems, it is often even difficult to construct a good feasible so ..."
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Abstract. Motivated by a planned automated cargo transportation network, we consider transportation problems in which the finite capacity of resources (such as vehicles, docks, parking places) has to be taken into account. For such problems, it is often even difficult to construct a good feasible solution. We present a flexible modeling methodology which allows to construct, evaluate, and improve feasible solutions. This new modeling approach is evaluated on instances stemming from a simulation model of the planned cargo transportation system.