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116
An effective implementation of the linkernighan traveling salesman heuristic
 European Journal of Operational Research
, 2000
"... This report describes an implementation of the LinKernighan heuristic, one of the most successful methods for generating optimal or nearoptimal solutions for the symmetric traveling salesman problem. Computational tests show that the implementation is highly effective. It has found optimal solution ..."
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Cited by 120 (1 self)
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This report describes an implementation of the LinKernighan heuristic, one of the most successful methods for generating optimal or nearoptimal solutions for the symmetric traveling salesman problem. Computational tests show that the implementation is highly effective. It has found optimal solutions for all solved problem instances we have been able to obtain, including a 7397city problem (the largest nontrivial problem instance solved to optimality today). Furthermore, the algorithm has improved the best known solutions for a series of largescale problems with unknown optima, among these an 85900city problem. 1.
Some NPcomplete Geometric Problems
"... We show that the STEINER TREE problem and TRAVELING SALESMAN problem for points in the plane are NPcomplete when distances are measured either by the rectilinear (Manhattan) metric or by a natural discretized version of the Euclidean metric. Our proofs also indicate that the problems are NPhard i ..."
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Cited by 83 (2 self)
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We show that the STEINER TREE problem and TRAVELING SALESMAN problem for points in the plane are NPcomplete when distances are measured either by the rectilinear (Manhattan) metric or by a natural discretized version of the Euclidean metric. Our proofs also indicate that the problems are NPhard if the distance I~asure is the (unmodified) Euclidean metric. However, for reasons we discuss, there is some question as to whether these problems, or even the wellsolved MINIMUM SPANNING TREE problem, are in NP when the distance measure is the Euclidean metric.
Computing MinimumWeight Perfect Matchings
 INFORMS
, 1999
"... We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the ..."
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Cited by 83 (2 self)
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We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the use of multiple search trees with an individual dualchange � for each tree. As a benchmark of the algorithm’s performance, solving a 100,000node geometric instance on a 200 Mhz PentiumPro computer takes approximately 3 minutes.
Physical Mapping of Chromosomes: A Combinatorial Problem in Molecular Biology
 Algorithmica
, 1993
"... This paper is concerned with algorithms for the reassembly process. ..."
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Cited by 51 (5 self)
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This paper is concerned with algorithms for the reassembly process.
Job Shop Scheduling by Local Search
 INFORMS JOURNAL ON COMPUTING
, 1994
"... We survey solution methods for the job shop scheduling problem with an emphasis on local search. Both deterministic and randomized local search methods as well as the proposed neighborhoods are discussed. We compare the computational performance of the various methods in terms of their effectiveness ..."
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Cited by 50 (0 self)
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We survey solution methods for the job shop scheduling problem with an emphasis on local search. Both deterministic and randomized local search methods as well as the proposed neighborhoods are discussed. We compare the computational performance of the various methods in terms of their effectiveness and efficiency on a standard set of problem instances.
On Traveling Salesperson Problems for Dubins' vehicle: stochastic and dynamic environments
 CDC 2005, TO APPEAR
, 2005
"... In this paper we propose some novel planning and routing strategies for Dubins’ vehicle, i.e., for a nonholonomic vehicle moving along paths with bounded curvature, without reversing direction. First, we study a stochastic version of the Traveling Salesperson Problem (TSP): given n targets randomly ..."
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Cited by 42 (13 self)
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In this paper we propose some novel planning and routing strategies for Dubins’ vehicle, i.e., for a nonholonomic vehicle moving along paths with bounded curvature, without reversing direction. First, we study a stochastic version of the Traveling Salesperson Problem (TSP): given n targets randomly sampled from a uniform distribution in a rectangle, what is the shortest Dubins ’ tour through the targets and what is its length? We show that the expected length of such a tour is Ω(n 2/3) and we propose a novel algorithm that generates a tour of length O(n 2/3 log(n) 1/3) with high probability. Second, we study a dynamic version of the TSP (known as “Dynamic Traveling Repairperson Problem” in the Operations Research literature): given a stochastic process that generates targets, is there a policy that allows a Dubins vehicle to stabilize the system, in the sense that the number of unvisited targets does not diverge over time? If such policies exist, what is the minimum expected waiting period between the time a target is generated and the time it is visited? We propose a novel recedinghorizon algorithm whose performance is almost within a constant factor from the optimum.
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.
Cost Versus Distance In the Traveling Salesman Problem
, 1995
"... This paper studies the distribution of good solutions for the traveling salesman problem (TSP) on a wellknown 532city instance that has been solved optimally by Padberg and Rinaldi [16]. For each of five local search heuristics, solutions are obtained from 2,500 different random starting points. C ..."
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Cited by 36 (0 self)
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This paper studies the distribution of good solutions for the traveling salesman problem (TSP) on a wellknown 532city instance that has been solved optimally by Padberg and Rinaldi [16]. For each of five local search heuristics, solutions are obtained from 2,500 different random starting points. Comparisons of these solutions show that lowercost solutions have a strong tendency to be both closer to the optimal tour and closer to other good solutions. (Distance between two solutions is defined in terms of the number of edges they have in common.) These results support the conjecture of Boese, Kahng and Muddu [3] that the solution spaces of TSP instances have a "globally convex" or "big valley" character. This observation was used by [3] to motivate a new multistart strategy for global optimization called Adaptive MultiStart (AMS). 1 Introduction Local search is probably the most successful approach to finding heuristic solutions to combinatorial global optimization problems. In gl...
Yet Another Local Search Method for Constraint Solving
 In AAAI Fall Symposium on Using Uncertainty within Computation, Cape Cod
, 2001
"... We propose a generic, domainindependent local search method called adaptive search for solving Constraint Satisfaction Problems (CSP). We design a new heuristics that takes advantage of the structure of the problem in terms of constraints and variables and can guide the search more precisely th ..."
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Cited by 33 (4 self)
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We propose a generic, domainindependent local search method called adaptive search for solving Constraint Satisfaction Problems (CSP). We design a new heuristics that takes advantage of the structure of the problem in terms of constraints and variables and can guide the search more precisely than a global cost function to optimize (such as for instance the number of violated constraints). We also use an adaptive memory in the spirit of Tabu Search in order to prevent stagnation in local minima and loops. This method is generic, can apply to a large class of constraints (e.g. linear and nonlinear arithmetic constraints, symbolic constraints, etc) and naturally copes with overconstrained problems. Preliminary results on some classical CSP problems show very encouraging performances. 1
Asynchronous Teams: Cooperation Schemes for Autonomous Agents
 Journal of Heuristics
, 1998
"... Experiments over a variety of optimization problems indicate that scaleeffective convergence is an emergent behavior of certain computerbased agents, provided these agents are organized into an asynchronous team (ATeam). An ATeam is a problemsolving architecture in which the agents are autonomo ..."
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Cited by 32 (7 self)
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Experiments over a variety of optimization problems indicate that scaleeffective convergence is an emergent behavior of certain computerbased agents, provided these agents are organized into an asynchronous team (ATeam). An ATeam is a problemsolving architecture in which the agents are autonomous and cooperate by modifying one another’s trialsolutions. These solutions circulate continually. Convergence is said to occur if and when a persistent solution appears. Convergence is said to be scaleeffective if the quality of the persistent solution increases with the number of agents, and the speed of its appearance increases with the number of computers. This paper uses a traveling salesman problem to illustrate scaleeffective behavior and develops Markov models that explain its occurrence in ATeams, particularly, how autonomous agents, without strategic planning or centralized coordination, can converge to solutions of arbitrarily high quality. The models also predict two properties that remain to be experimentally confirmed: • construction and destruction are dual processes. In other words, adept destruction can compensate for inept construction in an ATeam, and viceversa. (Construction refers to the process of creating or changing solutions, destruction, to the process of erasing solutions.) • solutionquality is independent of agentphylum. In other words, ATeams provide an organizational framework in which humans and autonomous mechanical agents can cooperate effectively. 2 1.