Approximative graph pyramid solution of the E-TSP

Haxhimusa, Yll; Kropatsch, Walter G.; Pizlo, Zygmunt; Ion, Adrian

doi:10.1016/j.imavis.2008.06.016

Cited by 15 publications

(21 citation statements)

References 40 publications

(60 reference statements)

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“…Global solution for this sample has 4.8% above best known solution compare to TSPLIB and it is a promising solution according to our objectives as drawn in figure 5. Compared to another method [1] [3], this initial result has promising result. MST pyramid method by Haxhimusa [1] and hierarchical model by Graham [3] has error up to 7% for number nodes up to 50, while this method has 3% maximum as shown in Table 1.…”

Section: Methodsmentioning

confidence: 90%

“…Let R be the threshold value for this graph G, and obtained from equation (1). Threshold R equal to 97.7575 and delete more than 50% edges that will be excluded to form clusters.…”

Section: Methodsmentioning

confidence: 99%

“…al formulated a pyramid algorithm [1] for E-TSP motivated by the failure to identify an existing algorithm that could provide a good fit to the subjects data. More recently, hierarchical (pyramid) algorithms have been used to model mental mechanisms involved in other types of visual problems.…”

Section: Literature Backgroundmentioning

confidence: 99%

“…This is a capability to organize data which is received everyday into cluster, so that they may draw important conclusions. However making computer to solve clustering problem is quite difficult and demanding the attentions of computer scientist and engineers all over the world until now [1].…”

Section: Introductionmentioning

confidence: 99%

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Initial Result of Clustering Strategy to Euclidean TSP

Fajar

Abu

Suryana

2009

2009 International Conference of Soft Computing and Pattern Recognition

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There has been growing interest in studying combinatorial optimization problems by clustering strategy, with a special emphasis on the traveling salesman problem (TSP). Since TSP naturally arises as a sub problem in many transportation, manufacturing and various logistics application, this problem has caught much attention of mathematicians and computer scientists. A clustering strategy will decompose TSP into subgraph and form clusters, so it may reduce the TSP graph to smaller problem. The primary objective of this research is to produce a better clustering strategy that fit into Euclidean TSP. General approach for this research is to produce an algorithm for generating clusters and able to handle large size cluster. The next step is to produce Hamilton path algorithm and followed by inter cluster connection algorithm to form global tour. The significant of this research is solution result error less than 10% compare to best known solution (TSPLIB) and there is an improvement to a hierarchical clustering strategy in order to fit in such the Euclidean TSP method.

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Section: Methodsmentioning

confidence: 90%

“…Let R be the threshold value for this graph G, and obtained from equation (1). Threshold R equal to 97.7575 and delete more than 50% edges that will be excluded to form clusters.…”

Section: Methodsmentioning

confidence: 99%

Section: Literature Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Initial Result of Clustering Strategy to Euclidean TSP

Fajar

Abu

Suryana

2009

2009 International Conference of Soft Computing and Pattern Recognition

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“…human solvers) have access to the actual inter-node distances and related geometric properties of the stimuli (e.g., Best, 2005;Graham, et al, 2000;Haxhimusa, et al, 2011;Haxhimusa, Kropatsch, Pizlo, & Ion, 2009;Hill, 1982;MacGregor & Ormerod, 1996;MacGregor, Ormerod, & Chronicle, 1999Pizlo et al, 2006;Tak, Plaiser, & van Rooij, 2008;Vickers, Butavicius, Lee, & Medvedev, 2001). …”

Section: Figurementioning

confidence: 99%

Fast and Efficient Discrimination of Traveling Salesperson Problem Stimulus Difficulty.

Dry¹,

Fontaine²

2014

The Journal of Problem Solving

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The Traveling Salesperson Problem (TSP) is a computationally difficult combinatorial optimization problem. In spite of its relative difficulty, human solvers are able to generate close-to-optimal solutions in a close-to-linear time frame, and it has been suggested that this is due to the visual system's inherent sensitivity to certain geometric properties of TSP stimuli. In the current study we employed a novel experimental paradigm in which we presented participants with sets of four TSP stimuli that varied in terms of their relative solution difficulty and asked them to indicate which of the four stimuli they would prefer to solve. The results indicated that the participants' choice frequencies followed the same ordering as the stimuli's empirical solution difficulty; that is, easy-to-solve stimuli were chosen with a higher frequency than hard-to-solve stimuli. It is suggested that these results provide further evidence of the speed and efficiency of human processing of TSPs, and provide further evidence implicating the role of rapid visuo-perceptual organization in generating TSP solutions. An analysis of the geometric properties of the stimuli uncovered a number of factors that may have influenced the choice preferences of participants in the current experiment, and the performance quality of participants in previous experiments.

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Death of the (traveling) salesman: Primates do not show clear evidence of multi‐step route planning

Janson

2013

American J Primatol

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Several comparative studies have linked larger brain size to a fruit-eating diet in primates and other animals. The general explanation for this correlation is that fruit is a complex resource base, consisting of many discrete patches of many species, each with distinct nutritional traits, the production of which changes predictably both within and between seasons. Using this information to devise optimal spatial foraging strategies is among the most difficult problems to solve in all of mathematics, a version of the famous Traveling Salesman Problem. Several authors have suggested that primates might use their large brains and complex cognition to plan foraging strategies that approximate optimal solutions to this problem. Three empirical studies have examined how captive primates move when confronted with the simplest version of the problem: a spatial array of equally valuable goals. These studies have all concluded that the subjects remember many food source locations and show very efficient travel paths; some authors also inferred that the subjects may plan their movements based on considering combinations of three or more future goals at a time. This analysis re-examines critically the claims of planned movement sequences from the evidence presented. The efficiency of observed travel paths is largely consistent with use of the simplest of foraging rules, such as visiting the nearest unused "known" resource. Detailed movement sequences by test subjects are most consistent with a rule that mentally sums spatial information from all unused resources in a given trial into a single "gravity" measure that guides movements to one destination at a time.

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Approximative graph pyramid solution of the E-TSP

Cited by 15 publications

References 40 publications

Initial Result of Clustering Strategy to Euclidean TSP

Initial Result of Clustering Strategy to Euclidean TSP

Fast and Efficient Discrimination of Traveling Salesperson Problem Stimulus Difficulty.

Death of the (traveling) salesman: Primates do not show clear evidence of multi‐step route planning

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