A comparison of heuristic and human performance on open versions of the traveling salesperson problem.

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

Theory Driven Hints in the Cheap Necklace Problem: A Preliminary Investigation

Three experiments investigated the effects of two hints derived from the Criterion for Satisfactory Progress theory (CSP) and Representational Change Theory (RCT) on the cheap necklace problem (insight problem). In Experiment 1, fewer participants given the CSP hint used an incorrect (maximizing) first move than participants given the RCT hint or control participants given no hint on a single attempt at the problem. Experiment 2 found the number of trials to solution was fewer in the CSP condition than in the control over ten trials, and there were fewer incorrect first moves in the CSP. The results appear to support the CSP theory. However, in Experiment 3, the CSP and RCT hints were combined yielding a 75% solution rate over 34.88% in the control. Perhaps aspects from both theories are employed during the problem solving process

Global perceptual processing in problem solving: The case of the traveling salesperson.

The traveling salesperson problem (TSP) consists of finding the shortest tour around a set of locations and is an important task in computer science and operations research. In four experiments, the relationship between processes implicated in the recognition of good figures and the identification of TSP solutions was investigated. In Experiment 1, a linear relationship was found between participants’ judgments of good figure and the optimality of solutions to TSPs. In Experiment 2, identification performance was shown to be a function of solution optimality and problem orientation. Experiment 3 replicated these findings with a forced-pace method, suggesting that global processing, rather than a local processing strategy involving point-by-point analysis of TSP solutions, is the primary process involved in the derivation of best figures for the presented TSPs. In Experiment 4, the role of global precedence was confirmed using a priming method, in which it was found that short (100 msec) primes facilitated solution identification, relative to no prime or longer primes. Effects of problem type were found in all the experiments, suggesting that local features of some problems may disrupt global processing. The results are discussed in terms of Sanocki’s (1993) global-to-local contingency model. We argue that global perceptual processing may contribute more generally to problem solving and that human performance can complement computational TSP methods

Are PASAT scores related to mathematical ability?

The Paced Auditory Serial Addition Task (PASAT) is employed in neuropsychological practice as a test of divided attention. The influence of mathematical ability on PASAT performance was examined in 40 healthy subjects, 20 male and 20 female. An unpaced computerised task was developed to measure response times for the verification of visually-presented additions, subtractions, divisions, and multiplications. Response times were always strongly negatively correlated with PASAT scores, suggesting that high mental arithmetic ability may give rise to good PASAT performance. Furthermore, a significant percentage of the variability in PASAT scores was predicted by (1) recent attainment in school mathematics examinations, and (2) self-ratings of current mental arithmetic skills. It is suggested that mathematical attainment and ability should be taken into account when interpreting PASAT performance as a measure of divided attention

Cognitive processing in migraine: a failure to find facilitation in patients with aura.

Recent interest in cognitive processing in migraine has been based on the assumption that cortical hyperexcitability in migraine with aura may manifest itself in the form of response time advantages in migraine as compared to controls. The study reported here attempted to replicate and extend the findings of Wray and colleagues (Brain 1995;118:25–35). Using identical cognitive tasks, three experiments failed to find differences between migraine with aura patients and controls: furthermore, an additional group of patients without aura were also statistically indistinguishable from controls with respect to response times. Error rates were consistently high across experiments, indicating that subjects were responding at or near chance levels. These findings cast doubt on the utility of straightforward cognitive psychological methods for the study of cortical hyperexcitability in migraine. Some theoretical difficulties concerning the interpretation of response times in the context of migraine pathophysiology are discussed

Individual Differences in Optimization Problem Solving: Reconciling Conflicting Results

Results on human performance on the Traveling Salesman Problem (TSP) from different laboratories show high consistency. However, one exception is in the area of individual differences. While one research group has consistently failed to find systematic individual differences across instances of TSPs (Chronicle, MacGregor and Ormerod), another group (Vickers, Lee and associates) has found individual differences both within TSP performance and between TSP performance and other cognitive tasks. Among possible reasons for the conflicting results are differences in procedure and differences in the problem instances used. To try to resolve the discrepancy, we collected data on TSP performance by combining the procedure used by one group with problem instances used by the other. The comparison involved nine 30-node and nine 40-node TSP problems previously used by the Vickers group, using computer presentation. Here, we had the same problems completed by 112 participants using a paper-and-pencil mode of presentation. We examined the results in the form of distributions of correlations across individuals for each pair of problems of the same size. The distributions for the computer and paper forms of presentation were very similar, and centered between correlations of 0.20 and 0.30. The results indicated the presence of individual differences at a level that fell between those previously reported by the two laboratories. The pattern of results indicated that previous discrepancies did not arise because of differences in procedure. Instead, individual differences appeared to become more prevalent as the difficulty of problems increased. The results are consistent with an explanation that performance on simpler instances is dominated by lower-level processes, but that as instance difficulty increases, higher-level functions become increasingly involved