Spatial analysis using unsupervised neural networks

Site selection case studies are often used in training exercises or demonstrations to illustrate the advantages of using a geographical information system (GIS). A typical site selection case study might answer the question “where should I locate a new convenience store?” Current GIS can solve spatialanalysis problems that are well defined efficiently. Unfortunately many “real world” problems are poorly defined, for example combinatorial spatial optimisation problems. In these problems the value of any solution depends on a number of factors, each of which must be changed and tested to generate an optimum solution. The large number of possible combinations that must be examined can render such problems insoluble using conventional analysis techniques. In this paper an example of a combinatorial spatial optimisation problem, which is nonpolynomial complete in nature, is examined. The problem can be defined as finding the optimum location for multiple retail sites, where the chosen retail sites will compete with each other for customers. It is shown that a solution can be determined using a relatively unsophisticated unsupervised Hopfield neuralnetwork algorithm. The neuralnetwork solution is generated within an efficient time-frame and it is shown that counter-intuitively, the algorithm becomes more efficient as the complexity of the problem increases.