Minimization and maximization versions of the quadratic travelling salesman problem

Aichholzer, Oswin; Fischer, Anja; Fischer, Frank; Meier, J. Fabian; Pferschy, Ulrich; Pilz, Alexander; Staněk, Rostislav

doi:10.1080/02331934.2016.1276905

Cited by 14 publications

(6 citation statements)

References 20 publications

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“…The difference between the two instance sets lies in how the cost of the AngleTSP and of the AngleDistanceTSP instance is computed. To guarantee the comparability of the results, we adopted the same cost computation as done in the literature (see [5,6,20]). In the AngleTSP, the cost for each triplet of vertices

i,j,k\in V

corresponds to the turning angle

{\alpha}_{ijk}

multiplied by 1000.…”

Section: Computational Experimentsmentioning

confidence: 99%

A tabu search with geometry‐based sparsification methods for angular traveling salesman problems

Cavagnini,

Schneider,

Theiß

2023

Networks

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The angular‐metric traveling salesman problem (AngleTSP) aims to find a tour visiting a given set of vertices in the Euclidean plane exactly once while minimizing the cost given by the sum of all turning angles. If the cost is obtained by combining the sum of all turning angles and the traveled distance, the problem is called angular‐distance‐metric traveling salesman problem (AngleDistanceTSP). In this work, we study the symmetric variants of these problems. Because both the AngleTSP and AngleDistanceTSP are NP‐hard, multiple heuristic approaches have been proposed in the literature. Nevertheless, a good tradeoff between solution quality and runtime is hard to find. We propose a granular tabu search (GTS) that considers the geometric features of the two problems in the design of starting solutions and sparsification methods. We further enrich the GTS with components that guarantee both intensification and diversification during the search. The computational results on benchmark instances from the literature show that (i) for the AngleTSP, our GTS lies on the Pareto frontier of the best performing‐heuristics, and (ii) for the AngleDistanceTSP, our GTS provides the best solution quality across all existing heuristics in competitive runtimes. In addition, new best‐known solutions are found for most benchmark instances for which an optimal solution is not available.

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i,j,k\in V

corresponds to the turning angle

{\alpha}_{ijk}

multiplied by 1000.…”

Section: Computational Experimentsmentioning

confidence: 99%

A tabu search with geometry‐based sparsification methods for angular traveling salesman problems

Cavagnini,

Schneider,

Theiß

2023

Networks

View full text Add to dashboard Cite

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“…It is motivated by the applications of permuted Markov model [11] and permuted variable length Markov model [45] in bioinformatics. We study the minimization version of QTSP [31]. Fischer et al [12] proposed the exact and heuristic approaches to solve QTSP.…”

Section: A Experiments On Qtspmentioning

confidence: 99%

Enhanced Branch-and-Bound Framework for a Class of Sequencing Problems

Zhang

Teng

Zhou

et al. 2021

IEEE Trans. Syst. Man Cybern, Syst.

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In this paper, we propose an enhanced branch-andbound (B&B) framework for a class of sequencing problems, which aim to find a permutation of all involved elements to minimize a given objective function. We require that the sequencing problems satisfy three conditions: 1) incrementally computable; 2) monotonic; and 3) overlapping subproblems. Our enhanced B&B framework is built on the classical B&B process by introducing two techniques, i.e., dominance rules and caching search states. Following the enhanced B&B framework, we conduct empirical studies on three typical and challenging sequencing problems, i.e., quadratic traveling salesman problem, traveling repairman problem, and talent scheduling problem. The computational results demonstrate the effectiveness of our enhanced B&B framework when compared to classical B&B and some exact approaches, such as dynamic programming and constraint programming. Additional experiments are carried out to analyze different configurations of the algorithm. Index Terms-Branch-and-bound (B&B), caching states, dominance rules, dynamic programming (DP), talent scheduling problem, traveling salesman/repairman problem. I. INTRODUCTION T HE SEARCH techniques for solving combinatorial optimization problems (COPs) have been widely studied in the communities of artificial intelligence, industrial engineering, and operations research during the last century. The simplest and standard framework for solving COPs is to use branch-and-bound (B&B) algorithms [3], [8], [14]. Its basic idea is to systematically and implicitly enumerate all possible candidate solutions, where large subsets of fruitless candidates Manuscript

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“…We select the constraint with the smaller number of nonnegative coefficients on the left-hand side in the hope of creating the lighter model that is easier to solve. This idea is also used to propose the Integer Linear Program based method tackling the TSP in [7].…”

Section: Branch-and-cut Algorithmmentioning

confidence: 99%

An efficient branch-and-cut algorithm for the parallel drone scheduling traveling salesman problem

Nguyen¹,

Luong²,

Hà³

et al. 2021

Preprint

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We propose an efficient branch-and-cut algorithm to exactly solve the parallel drone scheduling traveling salesman problem. Our algorithm can find optimal solutions for all but two existing instances with up to 229 customers in a reasonable running time. To make the problem more challenging for future methods, we introduce two new sets of 120 larger instances with the number of customers varying from 318 to 783 and test our algorithm and investigate the performance of state-of-the-art metaheuristics on these instances.

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Minimization and maximization versions of the quadratic travelling salesman problem

Cited by 14 publications

References 20 publications

A tabu search with geometry‐based sparsification methods for angular traveling salesman problems

A tabu search with geometry‐based sparsification methods for angular traveling salesman problems

Enhanced Branch-and-Bound Framework for a Class of Sequencing Problems

An efficient branch-and-cut algorithm for the parallel drone scheduling traveling salesman problem

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