Evolving Hard and Easy Traveling Salesman Problem Instances: A Multi-objective Approach

2014 ◽  
pp. 216-227 ◽  
Author(s):  
He Jiang ◽  
Wencheng Sun ◽  
Zhilei Ren ◽  
Xiaochen Lai ◽  
Yong Piao
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Multi Objective ◽  
Problem Instances

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

Algorithms ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 5 ◽  
Author(s):  
Víctor Pacheco-Valencia ◽  
José Alberto Hernández ◽  
José María Sigarreta ◽  
Nodari Vakhania
Keyword(s):  
Traveling Salesman Problem ◽  
Real Life ◽  
Traveling Salesman ◽  
Computational Time ◽  
Problem Instance ◽  
Dimensional Euclidean Space ◽  
Benchmark Problem ◽  
Small Constant ◽  
Euclidean Traveling Salesman Problem ◽  
Problem Instances

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.

Multi-objective traveling salesman problem: an ABC approach

2020 ◽  
Vol 50 (11) ◽  
pp. 3942-3960
Author(s):  
Indadul Khan ◽  
Manas Kumar Maiti ◽  
Krishnendu Basuli
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Multi Objective
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