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26
Exact solutions to linear programming problems
 Operations Research Letters
, 2007
"... The use of floatingpoint calculations limits the accuracy of solutions obtained by standard LP software. We present a simplexbased algorithm that returns exact rational solutions, taking advantage of the speed of floatingpoint calculations and attempting to minimize the operations performed in ra ..."
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Cited by 19 (8 self)
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The use of floatingpoint calculations limits the accuracy of solutions obtained by standard LP software. We present a simplexbased algorithm that returns exact rational solutions, taking advantage of the speed of floatingpoint calculations and attempting to minimize the operations performed in rational arithmetic. Extensive computational results are presented.
An Effective Implementation of Kopt Moves for the LinKernighan TSP
 Roskilde University, 2007. Case
, 2006
"... Local search with kchange neighborhoods, kopt, is the most widely used heuristic method for the traveling salesman problem (TSP). This report presents an effective implementation of kopt for the LinKernighan TSP heuristic. The effectiveness of the implementation is demonstrated with extensive ex ..."
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Cited by 12 (1 self)
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Local search with kchange neighborhoods, kopt, is the most widely used heuristic method for the traveling salesman problem (TSP). This report presents an effective implementation of kopt for the LinKernighan TSP heuristic. The effectiveness of the implementation is demonstrated with extensive experiments on instances ranging from 10,000 to 10,000,000 cities. 1.
Certification of an optimal TSP tour through 85,900 cities
, 2007
"... We describe a computer code and data that together certify the optimality of a solution to the 85,900city traveling salesman problem pla85900, the largest instance in the TSPLIB collection of challenge problems. ..."
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Cited by 8 (1 self)
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We describe a computer code and data that together certify the optimality of a solution to the 85,900city traveling salesman problem pla85900, the largest instance in the TSPLIB collection of challenge problems.
Screening the Parameters Affecting Heuristic Performance
 In Proceedings of the Genetic and Evolutionary Computation Conference
, 2007
"... This research screens the tuning parameters of a combinatorial optimization heuristic. Specifically, it presents a Design of Experiments (DOE) approach that uses a Fractional Factorial Design to screen the tuning parameters of Ant Colony System (ACS) for the Travelling Salesperson problem. Screening ..."
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Cited by 7 (4 self)
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This research screens the tuning parameters of a combinatorial optimization heuristic. Specifically, it presents a Design of Experiments (DOE) approach that uses a Fractional Factorial Design to screen the tuning parameters of Ant Colony System (ACS) for the Travelling Salesperson problem. Screening is a preliminary step to building a Response Surface Model (RSM) [20, 18]. It identifies those parameters that need not be included in a Response Surface Model, thus reducing the complexity and expense of the RSM design. 10 algorithm parameters and 2 problem characteristics are considered. Open questions on the effect of 3 parameters on performance are answered. Ant placement and choice of ant for pheromone update have no effect. However, the choice of parallel or sequential solution construction does indeed influence performance. A further parameter, sometimes assumed important, was shown to have no effect on performance. A new problem characteristic that effects performance was identified. The importance of measuring solution time was highlighted by helping identify the prohibitive cost of noninteger parameters where those parameters are exponents in the ACS algorithm’s computations. All results are obtained with a publicly available algorithm and problem generator.
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.
An Analysis of Problem Difficulty for a Class of Optimisation Heuristics
 In Proceedings of the Seventh European Conference on Evolutionary Computation in Combinatorial Optimisation, volume 4446 of LNCS
, 2007
"... Abstract. This paper investigates the effect of the cost matrix standard deviation of Travelling Salesman Problem (TSP) instances on the performance of a class of combinatorial optimisation heuristics. Ant Colony Optimisation (ACO) is the class of heuristic investigated. Results demonstrate that for ..."
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Cited by 4 (3 self)
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Abstract. This paper investigates the effect of the cost matrix standard deviation of Travelling Salesman Problem (TSP) instances on the performance of a class of combinatorial optimisation heuristics. Ant Colony Optimisation (ACO) is the class of heuristic investigated. Results demonstrate that for a given instance size, an increase in the standard deviation of the cost matrix of instances results in an increase in the difficulty of the instances. This implies that for ACO, it is insufficient to report results on problems classified only by problem size, as has been commonly done in most ACO research to date. Some description of the cost matrix distribution is also required when attempting to explain and predict the performance of these algorithms on the TSP. 1
Not every GTSP facet induces an STSP facet
 Integer Programming and Combinatorial Optimization 11, volume 3509 of LNCS
, 2005
"... Abstract. The graphical traveling salesman problem (GTSP) has been studied as a variant of the classical symmetric traveling salesman problem (STSP) suited particularly for sparse graphs. In addition, it can be viewed as a relaxation of the STSP and employed for solving the latter to optimality as o ..."
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Cited by 3 (2 self)
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Abstract. The graphical traveling salesman problem (GTSP) has been studied as a variant of the classical symmetric traveling salesman problem (STSP) suited particularly for sparse graphs. In addition, it can be viewed as a relaxation of the STSP and employed for solving the latter to optimality as originally proposed by Naddef and Rinaldi. There is a close natural connection between the two associated polyhedra. Until now, it was not known whether there are facets in TTform of the GTSP polyhedron which are not facets of the STSP polytope as well. In this paper we give an affirmative answer to this question for n ≥ 9 and provide a general method for constructing such facets.
On the Graphical Relaxation of the Symmetric Traveling Salesman
, 2007
"... Abstract. The Graphical Traveling Salesman Polyhedron (GTSP) has been proposed by Naddef and Rinaldi to be viewed as a relaxation of the Symmetric Traveling Salesman Polytope (STSP). It has also been employed by Applegate, Bixby, Chvátal, and Cook for solving the latter to optimality by the Brancha ..."
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Cited by 3 (3 self)
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Abstract. The Graphical Traveling Salesman Polyhedron (GTSP) has been proposed by Naddef and Rinaldi to be viewed as a relaxation of the Symmetric Traveling Salesman Polytope (STSP). It has also been employed by Applegate, Bixby, Chvátal, and Cook for solving the latter to optimality by the BranchandCut method. There is a close natural connection between the two polyhedra. Until now, it was not known whether there are facets in TTform of the GTSP polyhedron which are not facets of the STSP polytope as well. In this paper we give an affirmative answer to this question for n ≥ 9. We provide a general method for proving the existence of such facets, at the core of which lies the construction of a continuous curve on a polyhedron. This curve starts in a vertex, walks along edges, and ends in a vertex not adjacent to the starting vertex. Thus there must have been a third vertex on the way.