TSPLIB—A Traveling Salesman Problem Library

Reinelt, Gerhard

doi:10.1287/ijoc.3.4.376

Cited by 2,189 publications

(1,214 citation statements)

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“…Since there are no open-source benchmarks for testing the algorithms of the MTSP, we computed some instances presented in TSPLIB [30], which is the standard public library for the TSP. Although the MTSP is different to the TSP, typical instances and optimal results of these can reflect the performance of MDCP to a great extent.…”

Section: Experiments and Computational Resultsmentioning

confidence: 99%

A novel method for solving the multiple traveling salesmen problem with multiple depots

Hou

Liu

2012

Chin. Sci. Bull.

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Multi-traveling salesman problem (MTSP) is an extension of traveling salesman problem, which is a famous NP hard problem, and can be used to solve many real world problems, such as railway transportation, routing and pipeline laying. In this paper, we analyze the general properties of MTSP, and find that the multiple depots and closed paths in the graph is a big issue for MTSP. Thus, a novel method is presented to solve it. We transform a complicated graph into a simplified one firstly, then an effective algorithm is proposed to solve the MTSP based on the simplified results. In addition, we also propose a method to optimize the general results by using 2-OPT. Simulation results show that our method can find the global solution for MTSP efficiently. The traveling salesman problem (TSP) is a typical combinatorial optimization problem. A generalization of the TSP is the multiple traveling salesmen problem (MTSP), which determines a set of routes enabling multiple salesmen to start at and return to depots. [17] used a competition-based neural network to solve a minmax MTSP. Thus far, GAs have been applied to a wide range of application areas, including solving the MTSP. Liaw et al. [18] proposed a hybrid genetic algorithm, which is based on tabu search, to solve the MTSP. Carter et al. [19] researched chromosome representation and related genetic operators to find an applicable method for solving the MTSP. Additionally, the ant system, which was proved by [7], is a perfectly acceptable meta-heuristic for a number of NP-hard problems. In [20], an ant system is applied to the MTSP.The MTSP seems to be more appropriate than the TSP for practical applications and can be used to simulate many everyday applications such as transportation logistics, job planning, vehicle scheduling, and so on. Some reported applications are presented in [10]. The main applications include print press scheduling [21], crew scheduling [22], school bus routing [23], mission planning [24], and the de-

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Section: Experiments and Computational Resultsmentioning

confidence: 99%

A novel method for solving the multiple traveling salesmen problem with multiple depots

Hou

Liu

2012

Chin. Sci. Bull.

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“…The algorithm runs on a Pentium 1Ghz, 256 MB RAM, and uses CPLEX 6.5 as LP solver. The two sets of test instances are taken from the TSPLIB [23] and Ascheuer's asymmetric TSPTW problem instances [1]. Table 4 shows the results for small TSP instances.…”

Section: Computational Resultsmentioning

confidence: 99%

“…In Tables 2 and 3 we report the quality of the heuristic with respect to the ratio. The TSP instances are taken from TSPLIB [23] and the asymmetric TSPTW instances are due to Ascheuer [1]. All subproblems are solved to optimality with a fixed strategy, as to make a fair comparison.…”

Section: Quality Of Heuristicmentioning

confidence: 99%

Reduced Cost-Based Ranking for Generating Promising Subproblems

Milano

Hoeve

2002

Lecture Notes in Computer Science

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Abstract. In this paper, we propose an effective search procedure that interleaves two steps: subproblem generation and subproblem solution. We mainly focus on the first part. It consists of a variable domain value ranking based on reduced costs. Exploiting the ranking, we generate, in a Limited Discrepancy Search tree, the most promising subproblems first. An interesting result is that reduced costs provide a very precise ranking that allows to almost always find the optimal solution in the first generated subproblem, even if its dimension is significantly smaller than that of the original problem. Concerning the proof of optimality, we exploit a way to increase the lower bound for subproblems at higher discrepancies. We show experimental results on the TSP and its time constrained variant to show the effectiveness of the proposed approach, but the technique could be generalized for other problems.

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“…The Held-Karp Lower Bound (HKLB) is calculated by using a 1-tree with modified edge weights. Johnson et al showed in [31] that for randomly generated instances the optimal tour length is on average less than 0.8% above the Held-Karp bound and for most instances from the TSPLIB [40] collection less than 2%. So, the Held-Karp bound can be used as an evaluation criterion for TSP instances where no optimal solution is known.…”

Section: Algorithmsmentioning

confidence: 99%

“…• From Reinelt's TSPLIB [40] the following instances were taken: fl1577, fl3795 (both clustered instances), pr2392, pcb3038 (both drilling problems), fnl4461 (map of East Germany), usa13509 (map of the United States), pla33810 and pla85900 (both programmed logic array). The number in the instance names denotes the number of cities in the instances.…”

Section: Testbedmentioning

confidence: 99%

Embedding a Chained Lin-Kernighan Algorithm into a Distributed Algorithm

Fischer

Merz

Metaheuristics

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The Chained Lin-Kernighan algorithm (CLK) is one of the best heuristics to solve Traveling Salesman Problems (TSP). In this paper a distributed algorithm is proposed, were nodes in a network locally optimize TSP instances by using the CLK algorithm. Within an Evolutionary Algorithm (EA) network-based framework the resulting tours are modified and exchanged with neighboring nodes. We show that the distributed variant finds better tours compared to the original CLK given the same amount of computation time. For instance fl3795, the original CLK got stuck in local optima in each of 10 runs, whereas the distributed algorithm found optimal tours in each run requiring less than 10 CPU minutes per node on average in an 8 node setup. For instance sw24978, the distributed algorithm had an average solution quality of 0.050% above the optimum, compared to CLK's average solution of 0.119% above the optimum given the same total CPU time (10 4 seconds). Considering the best tours of both variants for this instance, the distributed algorithm is 0.033% above the optimum and the CLK algorithm 0.099%.

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TSPLIB—A Traveling Salesman Problem Library

Cited by 2,189 publications

References 0 publications

A novel method for solving the multiple traveling salesmen problem with multiple depots

A novel method for solving the multiple traveling salesmen problem with multiple depots

Reduced Cost-Based Ranking for Generating Promising Subproblems

Embedding a Chained Lin-Kernighan Algorithm into a Distributed Algorithm

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