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Open AccessArticle

Simple Constructive, Insertion, and Improvement Heuristics Based on the Girding Polygon for the Euclidean Traveling Salesman Problem

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Centro de Investigación en Ciencias UAEMor, Universidad Autónoma del Estado de Morelos, 62209 Cuernavaca, Mexico
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Facultad de Contaduría, Administración e Informática UAEMor, 62209 Cuernavaca, Mexico
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Facultad de Matemáticas UAGro, Universidad Autónoma de Guerrero, 39650 Acapulco, Mexico
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Author to whom correspondence should be addressed.
Algorithms 2020, 13(1), 5; https://doi.org/10.3390/a13010005
Received: 15 November 2019 / Revised: 13 December 2019 / Accepted: 17 December 2019 / Published: 21 December 2019
(This article belongs to the Special Issue Exact and Heuristic Scheduling Algorithms)
The Traveling Salesman Problem (TSP) aims at finding the shortest trip for a salesman, who has to visit each of the locations from a given set exactly once, starting and ending at the same location. Here, we consider the Euclidean version of the problem, in which the locations are points in the two-dimensional Euclidean space and the distances are correspondingly Euclidean distances. We propose simple, fast, and easily implementable heuristics that work well, in practice, for large real-life problem instances. The algorithm works on three phases, the constructive, the insertion, and the improvement phases. The first two phases run in time O ( n 2 ) and the number of repetitions in the improvement phase, in practice, is bounded by a small constant. We have tested the practical behavior of our heuristics on the available benchmark problem instances. The approximation provided by our algorithm for the tested benchmark problem instances did not beat best known results. At the same time, comparing the CPU time used by our algorithm with that of the earlier known ones, in about 92% of the cases our algorithm has required less computational time. Our algorithm is also memory efficient: for the largest tested problem instance with 744,710 cities, it has used about 50 MiB, whereas the average memory usage for the remained 217 instances was 1.6 MiB. View Full-Text
Keywords: heuristic algorithm; traveling salesman problem; computational experiment; time complexity heuristic algorithm; traveling salesman problem; computational experiment; time complexity
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Pacheco-Valencia, V.; Hernández, J.A.; Sigarreta, J.M.; Vakhania, N. Simple Constructive, Insertion, and Improvement Heuristics Based on the Girding Polygon for the Euclidean Traveling Salesman Problem. Algorithms 2020, 13, 5.

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