Factor Analytic Studies of CSP Heuristics

Factor analysis is a statistical technique for reducing the number of factors responsible for a matrix of correlations to a smaller number of factors that may reflect underlying variables. In this study factor analysis was used to determine if variation in search efficiency due to different variable ordering heuristics could be analyzed by this method to reveal basic sources of variation. It was found that the variation could be ascribed to two major factors, which appear to be related to contention (immediate failure) and to forward propagation (future failure). This was most clearcut with homogeneous random problems, but similar factor patterns were demonstrated for problems with small-world characteristics. Heuristics can be classified in terms of whether they tend to support one or the other strategy, or whether they balance the two; these differences are reflected in the pattern of loadings on the two major factors. Moreover, improvements in efficiency can be obtained by heuristic combinations (“heuristic synergy”) only if the combination includes heuristics that are highly correlated with each factor; therefore, two such heuristics are sufficient. This work represents a step toward understanding the action of heuristics as well as suggesting limits to heuristic performance.