A man-machine approach toward solving the traveling salesman problem

Krolak, Patrick D.; Felts, Wayne; Marble, George

doi:10.1145/362588.362593

Cited by 130 publications

(25 citation statements)

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“…The following test used previously unpublished data from 8 undergraduate students who produced solutions to a single randomly generated 100-node TSP described in Krolak et al (1971). The subjects were tested in a group setting and instructed to choose a starting point and to draw the shortest path from that point, passing through each point and returning to the start.…”

Section: Comparisons With Data From a Too-node Traveling Salesperson mentioning

confidence: 99%

“…To achieve "reasonable" approximations to an optimal solution to within a few percentage points above the shortest path, such procedures generally need to perform on the order of n 3 calculations (Golden, Bodin, Doyle, & Stewart, 1980). One approach to improving heuristic procedures has been to enlist the assistance of human operators (Krolak, Felts, & Marble, 1971;Michie, Fleming, & Oldfield, 1968). Krolak et al compared computer-generated solutions with solutions produced by a human-computer interactive approach.…”

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A model of human performance on the traveling salesperson problem

2000

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A computational model is proposed of how humans solve the traveling salesperson problem (TSP), Tests of the model are reported, using human performance measures from a variety of 10-,20-,40-, and 60-node problems, a single 48-node problem, and a single 100-node problem. The model provided a range of solutions that approximated the range of human solutions and conformed closely to quantitative and qualitative characteristics of human performance. The minimum path lengths of subjects and model deviated by average absolute values of O,OO!6, 0,9%, 2.4%, 1.4%,3.5%, and 0.02%for the 10-,20-, 40-, 48-, 60-, and 100-node problems, respectively. Because the model produces a range of solutions, rather than a single solution, it may find better solutions than some conventional heuristic algorithms for solving TSPs, and comparative results are reported that support this suggestion.The Euclidean form of the traveling salesperson problem (TSP) consists offinding the shortest path (tour) that passes through a set of points and returns to the origin. Any particular instance of a TSP obviously has a finite set of solutions, so there is a guaranteed method of solving any problem by exhaustive search of the solution space. However, exhaustive search becomes increasingly impractical as the number of points (n) increases. This is because the number ofpossible solutions increases as (n -I )!/2 (ignoring direction of travel), Thus, although a computer generating 1,000 solutions per second would require only 3 min to find all the solutions to a I O-node problem, a 20-node problem would occupy it for almost 4 million years. The increased capacity of computers over the past 10 years has made it possible to find guaranteed optimal solutions to fairly large TSPs within reasonable time periods. In 1986, a new record was set (since broken) when a 2,392-city problem was solved, breaking the previous record of 532 cities and requiring 27 h (Sangalli, 1992). There has been a long-term interest in the field of operations reseatch in devising economical procedures for finding solutions that approximate the optimal, and many such heuristic techniques have been developed and compared. To achieve "reasonable" approximations to an optimal solution to within a few percentage points above the shortest path, such procedures generally need to perform on the order of n 3 calculations (Golden, Bodin, Doyle, & Stewart, 1980). One approach to improving heuristic procedures has been to enlist the assistance of human operators (Krolak, Felts, & Marble, 1971;Michie, Fleming, & Oldfield, 1968). Krolak et al. compared computer-generated solutions with solutions produced by a human-computer interactive approach. A number of comparisons were reported that indicated that human-computer solutions were at least as short, and often shorter, than those generated by computer alone. The results imply that human operators respond to TSPs in a manner that is not only different from, but more effective than, the heuristics used by Krolak et al. Otherwise, the human-computer...

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Section: Comparisons With Data From a Too-node Traveling Salesperson mentioning

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A model of human performance on the traveling salesperson problem

2000

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“…The TSP is one of a class of problems of profound theoretical significance in mathematics and computer science (Garey & Johnson, 1979;Lawler, Shmoys, Rinnooy Kan, & Lenstra, 1985). It is also of considerable practical relevance in many scientific and industrial applications, including X-ray diffraction (Bland & Shallcross, 1987), warehousing (Dallari, Marchet, & Ruggeri, 2000), circuit board drilling (Sangalli, 1992), and the laying of ducting (Krolak, Felts, & Marble, 1971). Because no general analytical procedure is guaranteed to find the optimal path, there has been longstanding interest in developing heuristic procedures for generating good approximate solutions.…”

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Effects of cluster location and cluster distribution on performance on the traveling salesman problem

MacGregor

2015

Atten Percept Psychophys

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Research on human performance in solving traveling salesman problems typically uses point sets as stimuli, and most models have proposed a processing stage at which stimulus dots are clustered. However, few empirical studies have investigated the effects of clustering on performance. In one recent study, researchers compared the effects of clustered, random, and regular stimuli, and concluded that clustering facilitates performance (Dry, Preiss, & Wagemans, 2012). Another study suggested that these results may have been influenced by the location rather than the degree of clustering (MacGregor, 2013). Two experiments are reported that mark an attempt to disentangle these factors. The first experiment tested several combinations of degree of clustering and cluster location, and revealed mixed evidence that clustering influences performance. In a second experiment, both factors were varied independently, showing that they interact. The results are discussed in terms of the importance of clustering effects, in particular, and perceptual factors, in general, during performance of the traveling salesman problem.Keywords Visual perception . Spatial cognition . Perceptual organization Dot arrays have been used as stimuli for the study of grouping and clustering effects in perception at least since Wertheimer's (1923Wertheimer's ( /1950 pioneering analysis. Since then, dot arrays have been used to investigate a wide variety of perceptual phenomena, including perceptual organization (Trick & Enns, 1997), clustering (O'Callaghan, 1974, depth perception (Julesz, 1965), texture perception (Pickett, 1964), apparent motion (Ramachandran & Anstis, 1986), and the perception of biological movement (Johansson, 1973). Recently, random and patterned point sets have been used to study human performance in combinatorial optimization problems such as the traveling salesman (TSP), minimum spanning tree, and generalized Steiner tree problems (Vickers, Mayo, Heitmann, Lee, & Hughes, 2004). Although the names may imply that such research falls in the domain of problem solving, theoretical developments and empirical research in the area have frequently cited perceptual mechanisms, and the initial studies were often published in perception journals (Lee & Vickers, 2000;MacGregor & Ormerod, 1996;MacGregor, Ormerod, & Chronicle 1999;Vickers, Butavicius, Lee, & Medvedev, 2001). More recently, this new area of research has captured the interest of cognitive scientists working in clinical neuroscience, comparative psychology, decision making, memory, and vision (MacGregor, 2012), but often from a perception perspective. The present article continues this vein of exploring perceptual influences on TSP performance, by investigating the effects of dot clusters and their locations on human performance of the TSP. Before describing the experiments, however, a brief background summary of relevant TSP research is provided.The TSP is one of a class of combinatorial optimization problems whose problem space typically increases exponentially w...

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“…In addition to its theoretical interest, the TSP has practical implications for problems as apparently diverse as circuit-board drilling, X-ray crystallography, and the laying of ducting (Krolak, Felts, & Marble, 1971;Sangalli, 1992). Some practical problems that involve circuitboard drilling, or laser movements in chip manufacture, translate into TSPs of up to a million nodes (Sangalli, 1992).…”

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Human performance on the traveling salesman problem

MacGregor

Ormerod

1996

Perception & Psychophysics

174

293

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Two experiments on performance on the traveling salesman problem (TSP) are reported. The TSP consists of finding the shortest path through a set of points, returning to the origin. It appears to be an intransigent mathematical problem, and heuristics have been developed to find approximate solutions. The first experiment used lO-point, the second, 20-point problems. The experiments tested the hypothesis that complexity of TSPs is a function of number of nonboundary points, not total number of points. Both experiments supported the hypothesis. The experiments provided information on the quality of subjects' solutions. Their solutions clustered close to the best known solutions, were an order of magnitude better than solutions produced by three well-known heuristics, and on average fell beyond the 99.9th percentile in the distribution of random solutions. The solution process appeared to be perceptually based.

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A man-machine approach toward solving the traveling salesman problem

Cited by 130 publications

References 2 publications

A model of human performance on the traveling salesperson problem

A model of human performance on the traveling salesperson problem

Effects of cluster location and cluster distribution on performance on the traveling salesman problem

Human performance on the traveling salesman problem

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