A variational approach to optimal route location

Abstract

This thesis describes the methods and results of an investigation into the applicability and usefulness of a variational approach to the determination of an optimal route location. The utilization of extremal field (dynamic programming) and variational calculus procedures for optimising staged systems, described by non-linear difference equations, is discussed. The route location problem is then formulated in such a manner that these two methods can be employed during the process of solving this problem, and a complex cost function for a road is derived, a present worth approach being used. A variational approach involving the utilization of the extremal field procedure (to search a broad region and produce bands of interest) and the variational calculus procedure (to explore a band of interest and generate location bands) is formulated. The application of this variational approach to a real road re-alignment problem is described and the results are compared with those obtained independently via a traditional computer-aided approach. The worth of the proposed variational approach is then assessed.

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