Neural Spatial Interaction Models and Genetic Algorithms

Spatial interaction is a broad term encompassing any movement over space such as, for example, journey-to-work, migration, commodity and information flows. Single hidden layer neural networks with three inputs and a single output unit have recently been established as a powerful class of approximators for modelling unconstrained spatial interactions. The project addresses two fundamental issues that are of crucial importance for the successful applications: the model choice problem and the parameter choice problem. The model choice problem has been either completely neglected in spatial application domains or tackled by search heuristics. We viewed this problem as a global optimization problem and propose a novel approach that embeds backpropagation learning into the evolutionary paradigm of genetic algorithms. This has been accomplished by interweaving a genetic search for finding an optimal network topology with gradient-based backpropagation learning for determining the network parameters. Thus, the model builder will be relieved from the burden of identifying appropriate network topologies that will allow a real world problem to be solved with simple, but powerful learning [training] mechanisms. The approach has been applied using interregional telecommunication traffic data for Austria, to illustrate its performance and to evaluate its robustness. Parameter estimation [training, learning] is another central issue in neural spatial interaction modelling. Current practice is dominated by gradient based local minimization techniques. They find local minima efficiently, but can get trapped in multimodal problems. Probabilistic global search procedures provide an alternative optimization scheme that allows to escape from local minima. The project adopted differential evolution as an efficient search procedure for optimizing real-valued multi-modal objective functions and attempted to assess its robustness, measured in terms of in-sample and out-of-sample performance, utilizing an interregional telecommunication traffic data set and backpropagation of conjugate gradients as benchmark. The results illustrate that this search procedure slightly outperforms the benchmark but at a very high price of computational costs, especially in the case of high dimensional problems. This is essentially caused by the fact that our implementation was done as a serial platform even though the multipoint stochastic approach developed is inherently parallelizeable. In terms of value, the project not only provides novel solutions to two central issues in neural spatial interaction modelling, but also identifies several interesting issues deserving further attention.