Geometric Models of Local Optimization of Highway Networks that Improve the Configuration of Tracing in Functional Zones

Abstract. The article discusses the improvement of methods for discrete local optimization of highway tracing in the context of planning urban transport networks. Tracing and building the optimal configuration of the highway network is one of the key tasks in city planning. The main goal is to determine the shortest route for moving vehicles. Delivery of people to their destination and goods to consumers in a short time. The discretely local optimization of the network for three given points is considered. Network tracing for these points is achieved by building a polar Steiner network. Along with the orthogonal and Euclidean distance, as the research results have shown, the polar distance is important in practice. To introduce the polar distance, let us consider a certain plane with a fixed polar coordinate system. For some practical reasons, on a plane with a polar coordinate system, we leave only two directions of movement free. Movements are allowed along concentric circles drawn from the center coinciding with the pole, and along rays emanating from the pole. A bundle of straight lines with a support at the pole and the set of all concentric circles drawn from the center form an orthogonal polar grid. To solve this problem, various variants of geometric network models with a polar metric for three points are systematized and generalized, taking into account the weight of the specified points. The synthesis of an optimal highway route connecting specified points is a necessary component of optimizing the city's transport networks. To solve the problem, a network configuration with a polar metric consisting of radial segments and circular arcs is considered. The total length of the segment of arcs and circles should be minimal. The optimal network configuration is achieved by adding an additional Steiner point. The network constructed in the polar coordinate system will be called the "Steiner Polar Network". Geometric models of local optimization are an effective and visual means of developing various network tracing options within functional zones. From several network tracing options, a network is selected that meets the pre-defined planning requirements. It allows you to analyze and make the right decision in determining the promising directions for the development of the city's transport network.