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Traveling Salesman Problem: A Foveating Pyramid Model 旅行推销员问题:一个浮动金字塔模型
The journal of problem solving Pub Date : 2006-12-05 DOI: 10.7771/1932-6246.1009
Z. Pizlo, Emil Stefanov, John Saalweachter, Zheng Li, Y. Haxhimusa, W. Kropatsch
{"title":"Traveling Salesman Problem: A Foveating Pyramid Model","authors":"Z. Pizlo, Emil Stefanov, John Saalweachter, Zheng Li, Y. Haxhimusa, W. Kropatsch","doi":"10.7771/1932-6246.1009","DOIUrl":"https://doi.org/10.7771/1932-6246.1009","url":null,"abstract":"We tested human performance on the Euclidean Traveling Salesman Problem using problems with 6–50 cities. Results confirmed our earlier findings that: (a) the time of solving a problem is proportional to the number of cities, and (b) the solution error grows very slowly with the number of cities. We formulated a new version of a pyramid model. The new model has an adaptive spatial structure, and it simulates visual acuity and visual attention. Specifically, the model solves the E-TSP problem sequentially by moving attention from city to city, the same way human subjects do. The model includes a parameter representing the magnitude of local search. This parameter allows modeling individual differences among the subjects. The computational complexity of the current implementation of the model is O(n 2 ), but this can most likely be improved to O[nlog(n)]. Simulation experiments demonstrated psychological plausibility of the new model.","PeriodicalId":90070,"journal":{"name":"The journal of problem solving","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2006-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83932429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 85
A Comparison of Heuristic and Human Performance on Open Versions of the Traveling Salesperson Problem 启发式算法与人工算法在开放式旅行销售员问题上的比较
The journal of problem solving Pub Date : 2006-12-05 DOI: 10.7771/1932-6246.1005
J. MacGregor, E. Chronicle, T. Ormerod
{"title":"A Comparison of Heuristic and Human Performance on Open Versions of the Traveling Salesperson Problem","authors":"J. MacGregor, E. Chronicle, T. Ormerod","doi":"10.7771/1932-6246.1005","DOIUrl":"https://doi.org/10.7771/1932-6246.1005","url":null,"abstract":"We compared the performance of three heuristics with that of subjects on variants of a well-known combinatorial optimization task, the Traveling Salesperson Problem (TSP). The present task consisted of finding the shortest path through an array of points from one side of the array to the other. Like the standard TSP, the task is computationally intractable and, as with the standard TSP, people appear to be able to find good solutions with relative ease. The three heuristics used mechanisms that have been cited as potentially relevant in human performance in the standard task. These were: convex hull, nearest neighbor, and crossing avoidance. We compared heuristic and human performance in terms of lengths of paths, overlap between solutions, and number of crossings. Of the three heuristics, the convex hull appeared to result in the best overall fit with human solutions.","PeriodicalId":90070,"journal":{"name":"The journal of problem solving","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2006-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72960766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
Human Performance on Visually Presented Traveling Salesperson Problems with Varying Numbers of Nodes 人类在具有不同节点数的视觉呈现的旅行销售人员问题上的表现
The journal of problem solving Pub Date : 2006-12-05 DOI: 10.7771/1932-6246.1004
M. Dry, M. Lee, D. Vickers, Peter Hughes
{"title":"Human Performance on Visually Presented Traveling Salesperson Problems with Varying Numbers of Nodes","authors":"M. Dry, M. Lee, D. Vickers, Peter Hughes","doi":"10.7771/1932-6246.1004","DOIUrl":"https://doi.org/10.7771/1932-6246.1004","url":null,"abstract":"We investigated the properties of the distribution of human solution times for Traveling Salesperson Problems (TSPs) with increasing numbers of nodes. New experimental data are presented that measure solution times for carefully chosen representative problems with 10, 20, . . . 120 nodes. We compared the solution times predicted by the convex hull procedure proposed by MacGregor and Ormerod (1996), the hierarchical approach of Graham, Joshi, and Pizlo (2000), and by five algorithms drawn from the artificial intelligence and operations research literature. The most likely polynomial model for describing the relationship between mean solution time and the size of a TSP is linear or near-linear over the range of problem sizes tested, supporting the earlier finding of Graham et al. (2000). We argue the properties of the solution time distributions place strong constraints on the development of detailed models of human performance for TSPs, and provide some evaluation of previously proposed models in light of our findings.","PeriodicalId":90070,"journal":{"name":"The journal of problem solving","volume":"53 36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2006-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90987359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 110
Perceptual or Analytical Processing? Evidence from Children's and Adult's Performance on the Euclidean Traveling Salesperson Problem 知觉处理还是分析处理?儿童与成人在欧氏旅行推销员问题上的表现证据
The journal of problem solving Pub Date : 2006-12-05 DOI: 10.7771/1932-6246.1006
I. Rooij, Alissa Schactman, H. Kadlec, U. Stege
{"title":"Perceptual or Analytical Processing? Evidence from Children's and Adult's Performance on the Euclidean Traveling Salesperson Problem","authors":"I. Rooij, Alissa Schactman, H. Kadlec, U. Stege","doi":"10.7771/1932-6246.1006","DOIUrl":"https://doi.org/10.7771/1932-6246.1006","url":null,"abstract":"The Euclidean Traveling Salesperson Problem (E-TSP) is a useful task to study how humans optimize when faced with computational intractability. It has been found that humans are capable of finding high-quality solutions for E-TSP in a relatively short time and with seemingly little cognitive effort. This observation has led to two general proposals: The high quality of performance on E-TSP reflects (a) the output of automatic and innate perceptual processes or (b) a fundamentally intelligent approach to the task by humans. An experiment was performed to compare performance of three age groups (7- year-olds, 12-year-olds, and adults). Our findings provide corroborating evidence that high-level performance on E-TSP is attainable with perceptual processing alone. At the same time, the exceptionally high performance of adult participants suggests that they additionally exploit their cognitive-analytic skills to improve upon what their visual systems provide.","PeriodicalId":90070,"journal":{"name":"The journal of problem solving","volume":"105 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2006-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82233761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 26
Optimizing and “Pessimizing”: Human Performance with Instructional Variants of the Traveling Salesperson Problem 优化与“悲观化”:旅行销售人员问题的教学变体的人的表现
The journal of problem solving Pub Date : 2006-12-05 DOI: 10.7771/1932-6246.1000
E. Chronicle, J. MacGregor, T. Ormerod
{"title":"Optimizing and “Pessimizing”: Human Performance with Instructional Variants of the Traveling Salesperson Problem","authors":"E. Chronicle, J. MacGregor, T. Ormerod","doi":"10.7771/1932-6246.1000","DOIUrl":"https://doi.org/10.7771/1932-6246.1000","url":null,"abstract":"The two-dimensional Traveling Salesperson Problem (TSP) requires finding the shortest tour through n locations. Untrained adults are adept at the task and reliably outperform simple construction algorithms for n ≤ 60. Performance may stem from a specific inherent ability. Alternatively, it may reflect general spatial intelligence, whether inherent or acquired. If the latter holds, then people should be equally adept at finding longest tours. Two experiments comparing ability in the two tasks found participants significantly better at finding short tours than long tours (in the first, with N = 30, F[1,28] = 14.14; ηp 2 = .34; p < 0.01, and in the second, with N = 112, F[1,108] = 48.76; ηp 2 = .31; p < 0.01). Furthermore, human performance was significantly worse than a simple construction algorithm (farthest-neighbor) for the task of finding long tours. The result is consistent with the hypothesis of a specific, inherent ability to find short routes.","PeriodicalId":90070,"journal":{"name":"The journal of problem solving","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2006-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84439917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Are Individual Differences in Performance on Perceptual and Cognitive Optimization Problems Determined by General Intelligence? 个体在感知和认知优化问题上的表现差异是由一般智力决定的吗?
The journal of problem solving Pub Date : 2006-12-05 DOI: 10.7771/1932-6246.1003
N. Burns, M. Lee, D. Vickers
{"title":"Are Individual Differences in Performance on Perceptual and Cognitive Optimization Problems Determined by General Intelligence?","authors":"N. Burns, M. Lee, D. Vickers","doi":"10.7771/1932-6246.1003","DOIUrl":"https://doi.org/10.7771/1932-6246.1003","url":null,"abstract":"Studies of human problem solving have traditionally used deterministic tasks that require the execution of a systematic series of steps to reach a rational and optimal solution. Most real-world problems, however, are characterized by uncertainty, the need to consider an enormous number of variables and possible courses of action at each stage in solving the problem, and the need to optimize the solution subject to multiple interacting constraints. There are reliable individual differences in people’s abilities to solve such realistic problems. It also seems likely that people’s ability to solve these difficult problems reflects, or depends on, their intelligence. We report on a study of N = 101 adults who completed a series of visual optimization problems (Traveling Salesperson, Minimum Spanning Tree, and Generalized Steiner Tree Problems), as well as a cognitive optimization problem (a version of the Secretary Problem). We also characterized these individuals along three relevant and important cognitive abilities dimensions—fluid ability, visuo-spatial ability, and cognitive processing speed. Modeling of covariance structures indicated that performance on both types of optimization problems relies on general intelligence and raises the possibility that they can be used to assess intelligence.","PeriodicalId":90070,"journal":{"name":"The journal of problem solving","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2006-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81915450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 35
Editor's Introduction 编辑器的介绍
The journal of problem solving Pub Date : 2006-01-01 DOI: 10.7771/1932-6246.1008
Z. Pizlo
{"title":"Editor's Introduction","authors":"Z. Pizlo","doi":"10.7771/1932-6246.1008","DOIUrl":"https://doi.org/10.7771/1932-6246.1008","url":null,"abstract":"","PeriodicalId":90070,"journal":{"name":"The journal of problem solving","volume":"13 38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83075339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Editor's Introduction 编辑器的介绍
The journal of problem solving Pub Date : 1900-01-01 DOI: 10.7771/1932-6246.1158
Z. Pizlo
{"title":"Editor's Introduction","authors":"Z. Pizlo","doi":"10.7771/1932-6246.1158","DOIUrl":"https://doi.org/10.7771/1932-6246.1158","url":null,"abstract":"","PeriodicalId":90070,"journal":{"name":"The journal of problem solving","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88088283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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