Optimal Network Analysis

Abstract

Following implementation of optimal regression and interdependence analysis, the authors noted that the general algorithm could also be used to solve the optimal network problem which may be stated simply as follows: given n transportation nodes (cities, stations, or points to be served) and the set of n(n − 1)/2 direct, non-directional links joining all pairs of nodes, select the subset of links that minimizes the sum of shortest path distances between all pairs of nodes, subject to a budget constraint on the total link length. This application extended the original algorithm of Beale et al. (1967) in two ways. First, the size constraint (number of variables) is generalized to a linear constraint (total length of network). Second, the algorithm is applied to a potentially larger tree-search problem outside the field of statistics; however, Beale (1970) also described the application of the algorithm to a plant location problem.