Improved Filtering for the Euclidean Traveling Salesperson Problem in CLP(FD)

Bertagnon, Alessandro; Gavanelli, Marco

doi:10.1609/aaai.v34i02.5498

Cited by 6 publications

(1 citation statement)

References 25 publications

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“…Since the target TSP instances have a 2D Euclidean metric given by coordinates, we can take advantage of this geometric information, as already pointed out by Bertagnon and Gavanelli (2020). For the initial tour generation we suggest a Double Local optimization With recursion (DoLoWire) procedure.…”

Section: Introductionmentioning

confidence: 99%

Travelling Santa Problem: Optimization of a Million-Households Tour Within One Hour

Strutz

2021

Front. Robot. AI

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Finding the shortest tour visiting all given points at least ones belongs to the most famous optimization problems until today [travelling salesman problem (TSP)]. Optimal solutions exist for many problems up to several ten thousand points. The major difficulty in solving larger problems is the required computational complexity. This shifts the research from finding the optimum with no time limitation to approaches that find good but sub-optimal solutions in pre-defined limited time. This paper proposes a new approach for two-dimensional symmetric problems with more than a million coordinates that is able to create good initial tours within few minutes. It is based on a hierarchical clustering strategy and supports parallel processing. In addition, a method is proposed that can correct unfavorable paths with moderate computational complexity. The new approach is superior to state-of-the-art methods when applied to TSP instances with non-uniformly distributed coordinates.

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Section: Introductionmentioning

confidence: 99%

Travelling Santa Problem: Optimization of a Million-Households Tour Within One Hour

Strutz

2021

Front. Robot. AI

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Improving the Efficiency of Euclidean TSP Solving in Constraint Programming by Predicting Effective Nocrossing Constraints

Bellodi

Bertagnon

Gavanelli

et al. 2021

Lecture Notes in Computer Science

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The Traveling Salesperson Problem (TSP) is a well-known problem addressed in the literature through various techniques, including Integer Linear Programming, Constraint Programming (CP) and Local Search. Many real life instances belong to the subclass of Euclidean TSPs, in which the nodes to be visited are associated with points in the Euclidean plane, and the distance between them is the Euclidean distance. A well-known property of the Euclidean TSP is that no crossings can exist in an optimal solution. In a previous publication, we exploited this property to speedup the solution of Euclidean instances in CP, by imposing a number of so-called no-overlapping constraints. The number of imposed constraints is quadratic in the number of nodes of the TSP. In this work, we observe that not all the no-overlapping constraints are equally useful: by experimental analysis, some of them provide a speedup, while others only introduce overhead. We use a supervised machine learning approach on them to learn a binary classifier, with the objective to impose only those no-overlapping constraints that have been classified as effective. Preliminary experiments support the validity of the idea.

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Geometric reasoning on the euclidean traveling salesperson problem in answer set programming1

Bertagnon,

Gavanelli

2024

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The Traveling Salesperson Problem (TSP) is one of the best-known problems in computer science. Many instances and real world applications fall into the Euclidean TSP special case, in which each node is identified by its coordinates on the plane and the Euclidean distance is used as cost function. It is worth noting that in the Euclidean TSP more information is available than in the general case; in a previous publication, the use of geometric information has been exploited to speedup TSP solving for Constraint Logic Programming (CLP) solvers. In this work, we study the applicability of geometric reasoning to the Euclidean TSP in the context of an ASP computation. We compare experimentally a classical ASP approach to the TSP and the effect of the reasoning based on geometric properties. We also compare the speedup of the additional filtering based on geometric information on an ASP solver and a CLP on Finite Domain (CLP(FD)) solver.

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Improved Filtering for the Euclidean Traveling Salesperson Problem in CLP(FD)

Cited by 6 publications

References 25 publications

Travelling Santa Problem: Optimization of a Million-Households Tour Within One Hour

Travelling Santa Problem: Optimization of a Million-Households Tour Within One Hour

Improving the Efficiency of Euclidean TSP Solving in Constraint Programming by Predicting Effective Nocrossing Constraints

Geometric reasoning on the euclidean traveling salesperson problem in answer set programming1

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