On Randomness and Structure in Euclidean TSP Instances: A Study With Heuristic Methods

Crişan, Gloria Cerasela; Nechita, Elena; Simian, Dana

doi:10.1109/access.2020.3048774

Cited by 3 publications

(3 citation statements)

References 62 publications

(110 reference statements)

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“…Some other complex features, such as the highest edge features [28], the clustering features [29], Weibull distribution of distances [30], are proposed to assess the TSP hardness to some heuristic algorithms such as Ant Colony Optimization (ACO). In [31], researchers find that the regularity of the TSP structure can indicate the TSP hardness to ACO, but this type of feature cannot predict the hardness to the local search Lin-Kernighan algorithm. It implies that the valuable features may vary across algorithms.…”

Section: B Hardness Prediction For Optimization Problemsmentioning

confidence: 99%

“…With post-analysis, researchers have shown that the standard deviation (SD) or Coefficient of Variation (CV) of the distance matrix is one of the most significant features [27], [28], [31] in algorithm selection or hardness prediction for TSP. Intuitively, when the SD of the TSP distance matrix is very high, it is easy to tell the difference between candidate solutions, and the TSP is easy to solve.…”

Section: B Ginesmentioning

confidence: 99%

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Revisit the Algorithm Selection Problem for TSP with Spatial Information Enhanced Graph Neural Networks

Ye¹,

Bliek²,

Zhang³

2023

Preprint

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Algorithm selection is a well-known problem where researchers investigate how to construct useful features representing the problem instances and then apply feature-based machine learning models to predict which algorithm works best with the given instance. However, even for simple optimization problems such as Euclidean Traveling Salesman Problem (TSP), there lacks a general and effective feature representation for problem instances.The important features of TSP are relatively well understood in the literature, based on extensive domain knowledge and post-analysis of the solutions. In recent years, Convolutional Neural Network (CNN) has become a popular approach to select algorithms for TSP. Compared to traditional feature-based machine learning models, CNN has an automatic feature-learning ability and demands less domain expertise. However, it is still required to generate intermediate representations, i.e., multiple images to represent TSP instances first.In this paper, we revisit the algorithm selection problem for TSP, and propose a novel Graph Neural Network (GNN), called GINES. GINES takes the coordinates of cities and distances between cities as input. It is composed of a new message-passing mechanism and a local neighborhood feature extractor to learn spatial information of TSP instances. We evaluate GINES on two benchmark datasets. The results show that GINES outperforms CNN and the original GINE models. It is better than the traditional handcrafted feature-based approach on one dataset. The code and dataset will be released in the final version of this paper.

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Section: B Hardness Prediction For Optimization Problemsmentioning

confidence: 99%

Section: B Ginesmentioning

confidence: 99%

Revisit the Algorithm Selection Problem for TSP with Spatial Information Enhanced Graph Neural Networks

Ye¹,

Bliek²,

Zhang³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…More comparisons for the performance of heuristics have been conducted by Gupta ( 39 ), Ansari et al ( 2 ), Abdulkarim and Alshammari ( 41 ), and Gupta et al ( 42 ). Crisan et al examined the quality of the TSP solutions based on a structure of a TSP instance; the instances were classified as semistructured, and unstructured (randomly uniform) ( 43 ). The study then used a population-based ant colony optimization and a local search Lin–Kernighan heuristic for n ranging from 100 to 2,900.…”

Section: Literature Reviewmentioning

confidence: 99%

Review of Length Approximations for Tours with Few Stops

Choi

Schonfeld

2021

Transportation Research Record: Journal of the Transportation R

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The shortest tour distance for visiting all points exactly once and returning to the origin is computed by solving the well-known traveling salesman problem (TSP). Owing to the large computational effort needed for optimizing TSP tours, researchers have developed approximations that relate the average length of TSP tours to the number of points, n, visited per tour. The existing approximations are used in transportation system planning and evaluation for estimating the distance for vehicles with large capacities (e.g., delivery trucks) where n is relatively large. However, the average TSP tour lengths would be inaccurately estimated if the approximations were derived for a wide range of n values since the tour lengths increase at a decreasing rate (i.e., with [Formula: see text]) as n increases. A comprehensive review is presented here of existing studies approximating TSP tour lengths for low n values, which have become important for some recently favored delivery alternatives (e.g., deliveries by bikes, drones, and robots).

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