Effective Tour Searching for TSP by Contraction of Pseudo Backbone Edges

Dong, Changxing; Jäger, Gerold; Richter, Dirk; Molitor, Paul

doi:10.1007/978-3-642-02158-9_16

Cited by 12 publications

(2 citation statements)

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“…The TSP has been intensively studied and many solution algorithms have been developed to solve this problem, e.g., the Concorde exact solver (Applegate et al, 2006a,b), the Lin-Kernighan heuristic method (Lin & Kernighan, 1973;Helsgaun, 2000) and the "backbone" based heuristics (Dong et al, 2009;Jäger et al, 2014). Recently, there has been a growing interest in using machine learning to automatically learn a solution algorithm to solve combinatorial optimization problems (Bengio et al, 2018).…”

Section: Travelling Salesman Problemmentioning

confidence: 99%

Generalization of Machine Learning for Problem Reduction: A Case Study on Travelling Salesman Problems

Sun,

Ernst,

et al. 2020

Preprint

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Combinatorial optimization plays an important role in real-world problem solving. In the big data era, the dimensionality of a combinatorial optimization problem is usually very large, which poses a significant challenge to existing solution methods. In this paper, we examine the generalization capability of a machine learning model for problem reduction on the classic traveling salesman problems (TSP). We demonstrate that our method can greedily remove decision variables from an optimization problem that are predicted not to be part of an optimal solution. More specifically, we investigate our model's capability to generalize on test instances that have not been seen during the training phase. We consider three scenarios where training and test instances are different in terms of: 1) problem characteristics; 2) problem sizes; and 3) problem types. Our experiments show that this machine learning based technique can generalize reasonably well over a wide range of TSP test instances with different characteristics or sizes. While the accuracy of predicting unused variables naturally deteriorates the further an instance is from the training set, we observe that even when solving a different TSP problem variant than was used in the training, the machine learning model still makes useful predictions about which variables can be eliminated without significantly impacting solution quality.

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Section: Travelling Salesman Problemmentioning

confidence: 99%

Generalization of Machine Learning for Problem Reduction: A Case Study on Travelling Salesman Problems

Sun,

Ernst,

et al. 2020

Preprint

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“…The theory of single tolerances has been formalized by Goldengorin, Jäger, Molitor [11,12] for three different types of cost functions, namely of types sum, product and maximum. Based on this theory, effective heuristics and exact algorithms have been created and implemented [6,9,10,13,14,20,29,34] for the TSP as well as for related problems [2,17,22], proving the usefulness of the concept of tolerances. In 2010, Libura introduced and investigated the so-called robustness tolerance [24] where one not only determines for which changes a solution remains optimal, but also where it remains robust, i.e., gives the lowest regret.…”

Section: Introductionmentioning

confidence: 99%

Extending single tolerances to set tolerances

Jäger

Turkensteen

2018

Discrete Applied Mathematics

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The theory of single upper and lower tolerances for combinatorial minimization problems was formalized in 2005 for the three types of cost functions sum, product, and maximum, and since then it has shown to be rather useful in creating heuristics and exact algorithms. However, such single tolerances are often used because the assessment of multiple cost changes is considered too complicated. This paper addresses that issue. In this paper we extend this theory from single to set tolerances for these three types of cost functions. In particular, we characterize specific values of set upper and lower tolerances as positive and infinite, and we show a criterion for the uniqueness of an optimal solution to a combinatorial minimization problem. Furthermore, we present one exact formula and several bounds for computing set upper and lower tolerances using the relation to their corresponding single tolerance counterparts.

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