基于遗传算法的多辆洒水车最优路径求解(其中包含MATLAB的一些关键语句说明和Floyd,Dijkstra,Euler算法)

摘要

车辆路径问题可以分为以点为服务和以边为服务两种，洒水车问题是以边为服务的一个子问题。作为容量限制弦路径车辆行驶问题(CARP)的一种实际应用，洒水车路线规划涉及带有一定容量限制的总行程最小，以及多辆洒水车工作的合理分配问题，属于复杂的N-P难车辆路径优化问题。因此，在容量限制下实现作业车的总行驶路径最小，节约成本，提高效率，成为我们研究的中心环节。

本文采用了遗传算法，对多辆洒水车线路优化问题进行了容量均衡性方面的研究。首先在矩阵计算过程中采用了Floyd和Dijkstra算法求解了作业区域上任意两点之间的距离，以及指定两点之间的具体路径，为车辆的部分路段行驶获得了指向。接着对洒水车作业图的奇数度点进行随机匹配，从而把洒水车的作业图补成了每个顶点都是偶数，这样就可以获得一条Euler回路，即对应一个花费数值。然后通过遗传算法，初始化，编码，解码，适应度函数的计算以及选择，交叉，变异等一系列操作，最终获得一条花费最小的Euler回路。最后对这条回路进行分割，从而实现多辆车之间的作业分配。本文通过引用柳州市区的一部分区域地图进行实验，获得了比较理想的结果，并服合一定的现实意义。

关键词:路线优化 遗传算法 匹配 Euler算法

Abstract

Vehicle routing problem can be divided into the service for points and the service for sides， while sprinkler service is a subset of the side problem. As a practical application of CARP(Capacitated ARC Routing Problem) ，the sprinkler route planning demanks the total trip Minimum with a certain capacity and shares alike the work .So it is the complexity of VRP(Vehicle routing problem).In order to achieve the total trip minimum， to increase the least cost and increase the efficiency that becomes the central link of our research.

In this paper， we use the genetic algorithm to research how to finishes the sprinkler’s work equal. First of all， we apply the the Floyd and Dijkstra to achieve the distance between any two points and the specific path between two cettain points， which provide a method for the car to some setions road.

Then the point of odd-degree random match in the routing graph，

in this way， we can change the degree of every vertex into even.

This can be an Euler circuit， which corresponds to a cost value.

What’s more， through the genetic algorithm， initialization， encoding， decoding， the calculation of fitness function， as well as selection， crossover， mutation， such as a series of operations, eventually we get the answer.In the paper,we use Part of the liuzhou mapto experiment,and obtain a more satisfactory results,in the same time show the algorithm has practical significance. Key words: path optimization ， Genetic Algori