Some Problems of Rational Route Choice for a City Road Network

The paper treats some problems of rational route choice for a city road network with changing traffic load. Determination of the optimum route in the strict sense as a program acting from the start time of a certain trip is impossible, the cause consisting in its dependence on future behavior of other drivers. Two approaches to the problem setup and solution are proposed. The first consists in definition of the entire set of suboptimum acyclic routes between start and destination points. For the problem solution the generalization of method by Shier for determining the K shortest paths in a network is proposed. On this basis the most reasonable route may be chosen as the suboptimum route with the minimum prognosis duration. The problem in question is that of the optimum route choice for a network with a known traffic dynamics: its implementation may be based on regularity of traffic dynamics trends taking place for a certain day of a week. The problem setup and Dijkstra algorithm modification is proposed. Some aspects of its computational complexity are studied both theoretically and by means of computational experiments. The latter are fulfilled with our computer program aimed for routes optimization and analysis of route method efficiency that may be studied on real networks as well as randomly generated ones. In addition, as an alternative to dynamic programming methods variants of branch-and-bound method are proposed for both problems.