街道小區(qū)服務設施的優(yōu)化布局

摘  要

本文解決了1個帶權值的網(wǎng)絡最優(yōu)化問題。結合圖論相關知識對問題進行綜合分析，分別采用1維數(shù)組和鄰接矩陣來存儲小區(qū)內居民數(shù)量和小區(qū)間的距離信息。通過對問題1的定量分析，把線路鋪設方案的求解問題轉化為構造連通網(wǎng)的最小代價生成樹，運用普里姆算法對此問題進行求解；通過對問題2的定性分析，把服務設施點選址問題轉化為求源點到其余各頂點的最短路徑問題，選用迪杰斯特拉算法對其進行求解。
  根據(jù)普里姆算法和迪杰斯特拉算法，編寫C++程序對該街道居民的路徑選取過程進行模擬。所得結論顯示問題解答結果與分析的結論相吻合，從而得出最佳線路鋪設方案，并成功解決服務設施點選址問題。
關鍵詞：鄰接矩陣；普里姆算法；迪杰斯特拉算法；最短路徑；最小生成樹。

Abstract

This article has resolved a network optimization problem which has an weight. Uniting the knowledge in the diagram theory, we analyze the problem comprehensively, and adopt one dimension array and adjacency matrix to store the number of the residents resided in this section and the distance between two different sections. By quantitatively analyzing question one, we change the problem of the paving connection scheme into constructing the Minimum Cost Spanning Tree for connected network, and make Prim algorithm to answer the question; By quantitatively analyzing question two, we change the choosing address issue of service establishment into answering the shortest path for other verticals, we make Dijkstra algorithm to answer this question.
Based on Prim algorithm and Dijkstra algorithm, we simulate the choosing path process of this street by C++ program. The result shows that: the result of trouble shooting same to the analyzing result, and we succeed to answer the choosing address issue of service establishment.

Keywords: adjacency matrix; Prim algorithm; Dijkstra algorithm; The most short-circuit path; Minimal spanning tree.

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