Optimization Model of Pipeline Laying Based on Immune Genetics and Improved Second-order Prim Algorithm

Abstract

The optimization of the water supply pipeline route is of great significance to the design of rural water supply projects and the reform of the rural water supply management system. In this paper, a Minimum Spanning Tree Model based on classic graph theory is established, and the Improved second-order Prim Algorithm and Immune Genetic Algorithm are used to solve the model. Aiming at the minimum spanning tree problem with special constraints, the distance relationship between water supply stations is converted into a weight matrix, and a second-order Prim algorithm is designed to solve the laying plan with the smallest total pipeline mileage. Taking the Euclidean distance between nodes as the cost of the edge, by constraining the generation order of the minimum spanning tree, the total mileage is minimized under the premise of optimizing the mileage of the I-level pipeline. It is calculated that the laying mileage of type II pipeline is 403.40km, and the minimum laying sum of type I pipeline and type II pipeline is 524.34km. At the same time, considering the pipeline laying plan under the power limit of the water supply station, this article puts forward the concept of isolated points under the premise of analyzing the power constraints, and deeply explores the impact of isolated points on rural water supply. Based on the previous analysis, it is concluded that To achieve comprehensive water supply, all isolated points that cannot be connected to other water supply stations must be eliminated. The group coded the level II water supply station, designed an immune genetic algorithm, and achieved comprehensive water supply by optimizing the minimum number of level II water supply stations that need to be upgraded. It is determined that at least one secondary water supply station needs to be upgraded, and the total mileage of pipeline laying in this configuration is at least 415.09km. Finally, the sensitivity analysis of the solution results is carried out. The advantages of this paper are: 1. Based on the classical graph theory algorithm Prim algorithm, the solution obtained can be proved to be the global optimal solution. 2. The optimization calculation based on the immune genetic algorithm makes the algorithm very robust, and takes into account both the local search ability and the global search ability. The algorithm complexity is much lower than the traversal solution.