Point pattern reconstruction with incomplete information: computational methods

Abstract

Point patterns can be represented by interpoint distance information. Reconstruction of the pattern is generally carried out by measuring the error between test configurations and the actual measured distances and then successively modifying the configurations to reduce the error. This paper describes efforts at reconstructing 10-point patterns with stress minimization using both the traditional steepest descent algorithm of multidimensional scaling (MDS) and genetic algorithms (GA). Both techniques proved effective when all or most of the possible measurements were used. However, as the number of measurements in the description was reduced and the response surface increased in complexity, successful reconstruction with either method depended on embedding them into more complex computational strategies. These strategies emphasized the exploration aspect of the search, while still retaining an adequate exploitation component. Elements of MDS and GAs were effectively combined into hybrid or mixed strategies.