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33
Implementing the DantzigFulkersonJohnson Algorithm for Large Traveling Salesman Problems
, 2003
"... Dantzig, Fulkerson, and Johnson (1954) introduced the cuttingplane method as a means of attacking the traveling salesman problem; this method has been applied to broad classes of problems in combinatorial optimization and integer programming. In this paper we discuss an implementation of Dantzig et ..."
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Cited by 36 (6 self)
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Dantzig, Fulkerson, and Johnson (1954) introduced the cuttingplane method as a means of attacking the traveling salesman problem; this method has been applied to broad classes of problems in combinatorial optimization and integer programming. In this paper we discuss an implementation of Dantzig et al.'s method that is suitable for TSP instances having 1,000,000 or more cities. Our aim is to use the study of the TSP as a step towards understanding the applicability and limits of the general cuttingplane method in largescale applications.
A twophase local search for the biobjective traveling salesman problem
 in EMO, 2003
, 2003
"... lpaquete,tom¡ Abstract. This article proposes the TwoPhase Local Search for finding a good approximate set of nondominated solutions. The two phases of this procedure are to (i) generate an initial solution by optimizing only one single objective, and then (ii) to start from this solution a search ..."
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Cited by 17 (6 self)
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lpaquete,tom¡ Abstract. This article proposes the TwoPhase Local Search for finding a good approximate set of nondominated solutions. The two phases of this procedure are to (i) generate an initial solution by optimizing only one single objective, and then (ii) to start from this solution a search for nondominated solutions exploiting a sequence of different formulations of the problem based on aggregations of the objectives. This second phase is a single chain, using the local optimum obtained in the previous formulation as a starting solution to solve the next formulation. Based on this basic idea, we propose some further improvements and report computational results on several instances of the biobjective TSP that show competitive results with stateoftheart algorithms for this problem. 1
TSP  Infrastructure for the Traveling Salesperson Problem
 JOURNAL OF STATISTICAL SOFTWARE
, 2006
"... The traveling salesperson or salesman problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP ..."
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Cited by 9 (2 self)
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The traveling salesperson or salesman problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP is difficult since it belongs to the class of NPcomplete problems. The importance of the TSP arises besides from its theoretical appeal from the variety of its applications. In addition to vehicle routing, many other applications, e.g., computer wiring, cutting wallpaper, job sequencing or several data visualization techniques, require the solution of a TSP. In this paper we introduce the R package TSP which provides a basic infrastructure for handling and solving the traveling salesperson problem. The package features S3 classes for specifying a TSP and its (possibly optimal) solution as well as several heuristics to find good solutions. In addition, it provides an interface to Concorde, one of the best exact TSP solvers currently available.
A Memetic Algorithm for the Generalized Traveling Salesman Problem ∗
"... The generalized traveling salesman problem (GTSP) is an extension of the wellknown traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The recent studies on this subject ..."
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Cited by 9 (2 self)
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The generalized traveling salesman problem (GTSP) is an extension of the wellknown traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The recent studies on this subject consider different variations of a memetic algorithm approach to the GTSP. The aim of this paper is to present a new memetic algorithm for GTSP with a powerful local search procedure. The experiments show that the proposed algorithm clearly outperforms all of the known heuristics with respect to both solution quality and running time. While the other memetic algorithms were designed only for the symmetric GTSP, our algorithm can solve both symmetric and asymmetric instances. 1
Temporal Message Ordering in Wireless Sensor Networks
, 2002
"... Wireless sensor networks (WSN) are envisioned to fulfill complex monitoring tasks in the near future. A typical WSN application like object tracking fuses sensor readings produced by nodes throughout the network to obtain a highlevel sensing result such as the current speed of a tracked vehicle. In ..."
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Cited by 8 (4 self)
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Wireless sensor networks (WSN) are envisioned to fulfill complex monitoring tasks in the near future. A typical WSN application like object tracking fuses sensor readings produced by nodes throughout the network to obtain a highlevel sensing result such as the current speed of a tracked vehicle. In order to produce correct results, the application typically has to process sensor events in the order of their occurrence at the sensor nodes. Temporal message ordering ensures that sensor events arrive at the application in this order. Due to the requirements and characteristics of sensor networks, temporal message ordering is a nontrivial problem in this environment. We motivate the need for temporal message ordering in WSN and present an energy efficient temporal message ordering scheme for sensor networks.
On the Integrality Ratio for the Asymmetric Traveling Salesman Problem
 Mathematics of Operations Research
, 2006
"... informs ® doi 10.1287/moor.1060.0191 ..."
Hybrid metaheuristics for the vehicle routing problem with stochastic demands
 JOURNAL OF MATHEMATICAL
, 2006
"... ..."
A Note on Single Alternating Cycle Neighborhoods for the TSP
 JOURNAL OF HEURISTICS
, 2004
"... This paper investigates two different local search approaches for the TSP. Both approaches are based on the general concept of singlealternating cycle neighborhoods. The first approach, stems from the famous heuristic suggested by Lin and Kernighan and the second is based on the notion of stemandc ..."
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Cited by 7 (0 self)
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This paper investigates two different local search approaches for the TSP. Both approaches are based on the general concept of singlealternating cycle neighborhoods. The first approach, stems from the famous heuristic suggested by Lin and Kernighan and the second is based on the notion of stemandcycles developed by Glover in the early nineties. We show that the corresponding neighborhoods are not identical and that only a subset of moves can be found when Lin & Kernighan’s gain criterion is applied.
Analyzing Heuristic Performance with Response Surface Models: Prediction, Optimization and Robustness
 In Proceedings of the Genetic and Evolutionary Computation Conference. ACM
, 2007
"... This research uses a Design of Experiments (DOE) approach to build a predictive model of the performance of a combinatorial optimization heuristic over a range of heuristic tuning parameter settings and problem instance characteristics. The heuristic is Ant Colony System (ACS) for the Travelling Sal ..."
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Cited by 6 (5 self)
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This research uses a Design of Experiments (DOE) approach to build a predictive model of the performance of a combinatorial optimization heuristic over a range of heuristic tuning parameter settings and problem instance characteristics. The heuristic is Ant Colony System (ACS) for the Travelling Salesperson Problem. 10 heurstic tuning parameters and 2 problem characteristics are considered. Response Surface Models (RSM) of the solution quality and solution time predicted ACS performance on both new instances from a publicly available problem generator and new realworld instances from the TSPLIB benchmark library. A numerical optimisation of the RSMs is used to find the tuning parameter settings that yield optimal performance in terms of solution quality and solution time. This paper is the first use of desirability functions, a wellestablished technique in DOE, to simultaneously optimise these conflicting goals. Finally, overlay plots are used to examine the robustness of the performance of the optimised heuristic across a range of problem instance characteristics. These plots give predictions on the range of problem instances for which a given solution quality can be expected within a given solution time.
Training Simultaneous Recurrent Neural Network with Resilient Propagation for Combinatorial Optimization
 Nos 3
, 2002
"... This paper proposes a nonrecurrent training algorithm, resilient propagation, for the Simultaneous Recurrent Neural network operating in relaxationmode for computing high quality solutions of static optimization problems. Implementation details related to adaptation of the recurrent neural network ..."
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Cited by 6 (3 self)
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This paper proposes a nonrecurrent training algorithm, resilient propagation, for the Simultaneous Recurrent Neural network operating in relaxationmode for computing high quality solutions of static optimization problems. Implementation details related to adaptation of the recurrent neural network weights through the nonrecurrent training algorithm, resilient backpropagation, are formulated through an algebraic approach. Performance of the proposed neurooptimizer on a wellknown static combinatorial optimization problem, the Traveling Salesman problem, is evaluated on the basis of computational complexity measures and, subsequently, compared to performance of the Simultaneous Recurrent Neural network trained with the standard backpropagation, and recurrent backpropagation for the same static optimization problem. Simulation results indicate that the Simultaneous Recurrent Neural network trained with the resilient backpropagation algorithm is able to locate superior quality solutions through comparable amount of computational effort for the Traveling Salesman problem.