Differential Evolution Algorithm for Route Optimization Problems of Engineering Networks

Nauka i Obrazovanie

G. Y. Toktoshov¹  O. G. Monahov¹  E. A. Monakhova¹ 

[1] Institute of Computational Mathematics and Mathematical Geophysics SB RAS;

关键词: hypernetwork;    differential evolution algorithm;    minimum cost of engineering networks;   

DOI  :  10.7463/0915.0800020

来源: DOAJ

【 摘 要 】

The paper considers problems of structure optimization of engineering networks to provide a minimum total cost of engineering networks in construction and operation. The mathematical statement of the problem in terms of the hyper-network theory takes into account the interdependence of indicators of hyper-network elements, a layout area and a projected network. A digital model of terrain presents the placement area of engineering networks (a territory). In our case, it will be a weighted mesh (graph of primary network) of dedicated vertices-consumers and a vertex-source for the utilities. The edges weights will be determined by the costs of construction and operation of the route between the given vertices of the network. The initial solution of the problem of minimizing the total cost will be using the minimum spanning tree, obtained on a weighted complete graph the vertices of which are defined by vertices-consumers and the vertexsource for the utilities, and the weights of edges are the distance between the vertices on the given weighted graph of the primary network. The work offers a method of differential evolution to solve the problem in hyper-network formulation that improves the initial solution by the mapping the edges of the secondary network in the primary network using additional Steiner points. As numerical experiments have shown, a differential evolution algorithm allows us to reduce the average total cost for a given engineering network compared to the initial solution by 5% - 15%, depending on the configuration, parameters, and layout area.

【 授权许可】

Unknown