CN107423838A - Vehicle path planning method based on the search of chaos gravitation - Google Patents

Abstract

The invention discloses a kind of vehicle path planning method based on the search of chaos gravitation.The present invention is searched for using chaos gravitation to plan the path of vehicle.In the search of chaos gravitation, each individual stores the order weights of each transportation point.In evolution process, the search of chaos gravitation first carries out the basic operation operator of gravitation search, then randomly chooses an individual, and the individual to choosing performs the operation of chaos Local Search, strengthens algorithm search performance with this.The present invention can improve the efficiency of vehicle path planning.

Description

Translated fromChinese

基于混沌引力搜索的车辆路径规划方法Vehicle path planning method based on chaotic gravity search

技术领域technical field

本发明涉及车辆路径规划领域，尤其是涉及一种基于混沌引力搜索的车辆路径规划方法。The invention relates to the field of vehicle route planning, in particular to a vehicle route planning method based on chaotic gravity search.

背景技术Background technique

车辆路径规划是现代运输业中的重要课题。在现代运输业中，人们常常会遇到如下车辆路径规划问题：给定了若干个运输点的坐标位置，要求为一运输车辆规划一条路径，使得该车辆需要从源运输点出发然后经过每个运输点一次且仅一次再回到源运输点，并且要求使得该运输车辆所经过路径的耗费最小化。为了解决这个问题，人们往往通过设计启发式的智能优化算法来求解。Vehicle routing planning is an important topic in modern transportation industry. In the modern transportation industry, people often encounter the following vehicle route planning problem: given the coordinates of several transportation points, it is required to plan a route for a transportation vehicle, so that the vehicle needs to start from the source transportation point and then pass through each The transport point returns to the source transport point once and only once, and it is required to minimize the cost of the path traveled by the transport vehicle. In order to solve this problem, people often solve it by designing a heuristic intelligent optimization algorithm.

引力搜索算法是一种新近涌现出来的智能优化算法，它已经成功地应用到了许多工程领域中。例如，高淑萍等发明了一种基于改进万有引力算法的多时间窗车辆路径选择方法(专利号:201310470013.0)；王宇等提出了一种利用引力搜索算法来优化船舶舱室布置的方法(王宇,黄胜,廖全蜜,杨放青.基于引力搜索算法的船舶舱室布置方法[J].上海交通大学学报,2016,50(01):131-139)；李超顺等提出了利用改进引力搜索算法来优化励磁控制PID的参数(李超顺,周建中,肖剑.基于改进引力搜索算法的励磁控制PID参数优化[J].华中科技大学学报(自然科学版),2012,40(10):119-122)；蒋建国等提出了利用改进万有引力搜索算法来分析边坡稳定性的方法(蒋建国,谭雅,董立明,汪翠.改进的万有引力搜索算法在边坡稳定分析中的应用[J].岩土工程学报,2016,38(03):419-425)；李海涛等提出了利用量子万有引力搜索来优化SVM的参数，并利用优化好的SVM对自动驾驶仪进行故障诊断(李海涛,何玉珠,宋平.基于量子万有引力搜索的SVM自驾故障诊断[J].北京航空航天大学学报,2016,42(06):1093-1098)；巢渊等提出了利用广义反向粒子群与引力搜索混合算法来优化多阈值图像分割的方法(巢渊,戴敏,陈恺,陈平,张志胜.基于广义反向粒子群与引力搜索混合算法的多阈值图像分割[J].光学精密工程,2015,03:879-886)。The gravitational search algorithm is a newly emerged intelligent optimization algorithm, which has been successfully applied to many engineering fields. For example, Gao Shuping et al. invented a multi-time-window vehicle routing method based on the improved gravitational algorithm (Patent No.: 201310470013.0); Wang Yu et al. proposed a method for optimizing ship cabin layout using the gravitational search algorithm (Wang Yu, Huang Sheng, Liao Quanmi, Yang Fangqing. Ship cabin layout method based on gravitational search algorithm[J]. Journal of Shanghai Jiao Tong University, 2016, 50(01):131-139); Optimizing the parameters of excitation control PID (Li Chaoshun, Zhou Jianzhong, Xiao Jian. Optimization of excitation control PID parameters based on improved gravitational search algorithm[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2012,40(10):119-122) ; Jiang Jianguo et al proposed a method to analyze slope stability by using improved gravitational search algorithm (Jiang Jianguo, Tan Ya, Dong Liming, Wang Cui. Application of improved gravitational search algorithm in slope stability analysis[J]. Geotechnical Engineering Journal ,2016,38(03):419-425); Li Haitao et al proposed to use quantum gravitational search to optimize the parameters of SVM, and use the optimized SVM to perform fault diagnosis on autopilot (Li Haitao, He Yuzhu, Song Ping. Based on SVM self-driving fault diagnosis based on quantum gravitational search[J].Journal of Beihang University, 2016,42(06):1093-1098); Chao Yuan et al. proposed a hybrid algorithm of generalized inverse particle swarm optimization and gravitational search to optimize multiple thresholds Image Segmentation Method (Chao Yuan, Dai Min, Chen Kai, Chen Ping, Zhang Zhisheng. Multi-Threshold Image Segmentation Based on Generalized Inverse Particle Swarm and Gravity Search Hybrid Algorithm[J]. Optical Precision Engineering, 2015,03:879-886 ).

从现有的研究成果中可知，引力搜索算法在求解工程优化问题中表现出非常有潜力的性能。但传统引力搜索算法在求解较大规模的车辆路径规划问题时容易出现收敛速度慢，规划效率不高的缺点。From the existing research results, it can be seen that the gravitational search algorithm shows very promising performance in solving engineering optimization problems. However, the traditional gravity search algorithm tends to have the disadvantages of slow convergence speed and low planning efficiency when solving large-scale vehicle route planning problems.

发明内容Contents of the invention

本发明的目的是提供一种基于混沌引力搜索的车辆路径规划方法，它能够在一定程度上克服传统引力搜索算法在求解规模较大的车辆路径规划问题时容易出现收敛速度慢，规划效率不高的缺点，本发明能够提高车辆路径规划的效率。The purpose of the present invention is to provide a vehicle path planning method based on chaotic gravity search, which can overcome the slow convergence speed and low planning efficiency of traditional gravity search algorithms to a certain extent when solving large-scale vehicle path planning problems However, the present invention can improve the efficiency of vehicle route planning.

本发明的技术方案：一种基于混沌引力搜索的车辆路径规划方法，包括以下步骤：Technical solution of the present invention: a vehicle path planning method based on chaotic gravity search, comprising the following steps:

步骤1，输入各运输点的坐标位置，并得到运输点的数量D；Step 1, input the coordinate position of each transportation point, and obtain the quantity D of the transportation point;

步骤2，用户初始化种群大小Popsize，最大评价次数MAX_FEs；Step 2, the user initializes the population size Popsize, the maximum number of evaluations MAX_FEs;

步骤3，令当前演化代数t＝0，当前评价次数FEs＝0；Step 3, let the current evolution algebra t=0, the current evaluation times FEs=0;

步骤4，随机产生初始种群其中个体下标i＝1,2,...,Popsize，并且为种群P_t中的第i个个体，其随机初始化公式为：Step 4, randomly generate the initial population where individual subscripts i=1,2,...,Popsize, and is the i-th individual in the population P_t , and its random initialization formula is:

其中维度下标j＝1,2,...,D，且存储了D个运输点的顺序权值，表示第i个个体在每一维度上的速度大小，rand(0,1)为在[0,1]之间服从均匀分布的随机实数产生函数；where dimension subscript j=1,2,...,D, and The sequence weights of D transportation points are stored, Indicates the speed of the i-th individual in each dimension, and rand(0,1) is a random real number generation function that obeys a uniform distribution between [0,1];

步骤5，计算种群P_t中每个个体的适应值，然后保存种群P_t中的最优个体Best^t，并令当前评价次数FEs＝FEs+Popsize；Step 5, calculate the fitness value of each individual in the population P_t , then save the best individual Best^t in the population P_t , and make the current evaluation times FEs=FEs+Popsize;

步骤6，执行引力搜索的基本操作算子，然后计算种群P_t中所有个体的适应值；Step 6, execute the basic operation operator of gravitational search, and then calculate the fitness value of all individuals in the population_Pt ;

步骤7，令当前评价次数FEs＝FEs+Popsize；Step 7, make the current evaluation times FEs=FEs+Popsize;

步骤8，随机选择一个个体，并对选择出来的个体执行混沌局部搜索操作，具体步骤如下：Step 8, randomly select an individual, and perform a chaotic local search operation on the selected individual, the specific steps are as follows:

步骤8.1，令混杂次数NL＝300+200×rand(0,1)；Step 8.1, make the mixing number NL=300+200×rand(0,1);

步骤8.2，在[0,1]之间随机产生一个不等于0.25，0.5和0.75的实数itk；Step 8.2, randomly generate a real number itk not equal to 0.25, 0.5 and 0.75 between [0,1];

步骤8.3，令计数器kj＝0，并令迭代因子tp＝itk；Step 8.3, make the counter kj=0, and let the iteration factor tp=itk;

步骤8.4，令混沌因子tk＝4.0×tp×(1-tp)；Step 8.4, make chaos factor tk=4.0×tp×(1-tp);

步骤8.5，令迭代因子tp＝tk，并令计数器kj＝kj+1；Step 8.5, make iteration factor tp=tk, and let counter kj=kj+1;

步骤8.6，如果计数器kj大于NL，则转到步骤8.7，否则转到步骤8.4；Step 8.6, if the counter kj is greater than NL, then go to step 8.7, otherwise go to step 8.4;

步骤8.7，在[1，Popsize]之间随机产生一个的整数RM1；Step 8.7, randomly generate an integer RM1 between [1, Popsize];

步骤8.8，在[1，Popsize]之间随机产生一个不等于RM1的整数RM2，并令迭代因子tp＝tk；Step 8.8, randomly generate an integer RM2 not equal to RM1 between [1, Popsize], and make the iteration factor tp=tk;

步骤8.9，令混沌因子tk＝4.0×tp×(1-tp)；Step 8.9, make chaos factor tk=4.0×tp×(1-tp);

步骤8.10，按以下公式生成个体VU^t：Step 8.10, generate individual VU^t according to the following formula:

其中VMu表示均值因子，VStd表示标准差因子；杂交因子VK的值为[0,1]之间的随机实数；Norm(VMu,VStd)表示以VMu为均值，VStd为标准差的正态分布随机实数产生函数；Among them, VMu represents the mean factor, VStd represents the standard deviation factor; the value of the hybridization factor VK is a random real number between [0,1]; Norm(VMu, VStd) represents a normal distribution random with VMu as the mean and VStd as the standard deviation. real number generating function;

步骤8.11，计算个体VU^t的适应值，令当前评价次数FEs＝FEs+1；Step 8.11, calculate the fitness value of the individual VU^t , make the current evaluation times FEs=FEs+1;

步骤8.12，如果个体VU^t的适应值优于的适应值，则转到步骤8.13，否则转到步骤9；Step 8.12, if the fitness value of individual VU^t is better than , then go to step 8.13, otherwise go to step 9;

步骤8.13，令个体然后转到步骤8.8；In step 8.13, let the individual Then go to step 8.8;

步骤9，令当前演化代数t＝t+1，然后保存种群P_t中的最优个体Best^t；Step 9, make the current evolution algebra t=t+1, and then save the best individual Best^{t in the population P t}_;

步骤10，重复步骤6至步骤9直至当前评价次数FEs达到MAX_FEs后结束，将执行过程中得到的最优个体Best^t解码为车辆路径，即可实现车辆路径规划。Step 10, repeat step 6 to step 9 until the current evaluation times FEs reaches MAX_FEs and end, and decode the optimal individual Best^t obtained during the execution process into a vehicle route to realize vehicle route planning.

本发明采用混沌引力搜索来规划车辆的路径。在混沌引力搜索中，每个个体存储了各个运输点的顺序权值。在演化进程中，混沌引力搜索先执行引力搜索的基本操作算子，然后随机选择一个个体，并对选择出来的个体执行混沌局部搜索操作，以此增强算法搜索性能。本发明能够提高车辆路径规划的效率。The present invention uses chaotic gravitational search to plan the path of the vehicle. In the chaotic gravity search, each individual stores the order weights of each transportation point. In the evolution process, the chaotic gravitational search first executes the basic operation operator of the gravitational search, then randomly selects an individual, and performs the chaotic local search operation on the selected individual, so as to enhance the search performance of the algorithm. The invention can improve the efficiency of vehicle path planning.

附图说明Description of drawings

图1为待路径规划的运输点示意图，图中每个小黑点表示一个运输点。Figure 1 is a schematic diagram of a transportation point to be route planned, and each small black dot in the figure represents a transportation point.

具体实施方式detailed description

下面通过实施例，并结合附图，对本发明的技术方案作进一步具体的说明。The technical solutions of the present invention will be further specifically described below through the embodiments and in conjunction with the accompanying drawings.

实施例：Example:

步骤1，输入如图1所示的运输点的坐标位置，并得到运输点的数量D＝30；Step 1, input the coordinate position of transportation point as shown in Figure 1, and obtain the quantity D=30 of transportation point;

步骤2，用户初始化种群大小Popsize＝50，最大评价次数MAX_FEs＝200000；Step 2, the user initializes the population size Popsize=50, the maximum number of evaluations MAX_FEs=200000;

步骤3，令当前演化代数t＝0，当前评价次数FEs＝0；Step 3, let the current evolution algebra t=0, the current evaluation times FEs=0;

步骤4，随机产生初始种群其中个体下标i＝1,2,...,Popsize，并且为种群P_t中的第i个个体，其随机初始化公式为：Step 4, randomly generate the initial population where individual subscripts i=1,2,...,Popsize, and is the i-th individual in the population P_t , and its random initialization formula is:

其中维度下标j＝1,2,...,D，且存储了D个运输点的顺序权值，表示第i个个体在每一维度上的速度大小，rand(0,1)为在[0,1]之间服从均匀分布的随机实数产生函数；where dimension subscript j=1,2,...,D, and The sequence weights of D transportation points are stored, Indicates the speed of the i-th individual in each dimension, and rand(0,1) is a random real number generation function that obeys a uniform distribution between [0,1];

步骤5，计算种群P_t中每个个体的适应值，然后保存种群P_t中的最优个体Best^t，并令当前评价次数FEs＝FEs+Popsize；Step 5, calculate the fitness value of each individual in the population P_t , then save the best individual Best^t in the population P_t , and make the current evaluation times FEs=FEs+Popsize;

步骤6，执行引力搜索的基本操作算子，然后计算种群P_t中所有个体的适应值；Step 6, execute the basic operation operator of gravitational search, and then calculate the fitness value of all individuals in the population_Pt ;

步骤7，令当前评价次数FEs＝FEs+Popsize；Step 7, make the current evaluation times FEs=FEs+Popsize;

步骤8，随机选择一个个体，并对选择出来的个体执行混沌局部搜索操作，具体步骤如下：Step 8, randomly select an individual, and perform a chaotic local search operation on the selected individual, the specific steps are as follows:

步骤8.1，令混杂次数NL＝300+200×rand(0,1)；Step 8.1, make the mixing number NL=300+200×rand(0,1);

步骤8.2，在[0,1]之间随机产生一个不等于0.25，0.5和0.75的实数itk；Step 8.2, randomly generate a real number itk not equal to 0.25, 0.5 and 0.75 between [0,1];

步骤8.3，令计数器kj＝0，并令迭代因子tp＝itk；Step 8.3, make the counter kj=0, and let the iteration factor tp=itk;

步骤8.4，令混沌因子tk＝4.0×tp×(1-tp)；Step 8.4, make chaos factor tk=4.0×tp×(1-tp);

步骤8.5，令迭代因子tp＝tk，并令计数器kj＝kj+1；Step 8.5, make iteration factor tp=tk, and let counter kj=kj+1;

步骤8.6，如果计数器kj大于NL，则转到步骤8.7，否则转到步骤8.4；Step 8.6, if the counter kj is greater than NL, then go to step 8.7, otherwise go to step 8.4;

步骤8.7，在[1，Popsize]之间随机产生一个的整数RM1；Step 8.7, randomly generate an integer RM1 between [1, Popsize];

步骤8.8，在[1，Popsize]之间随机产生一个不等于RM1的整数RM2，并令迭代因子tp＝tk；Step 8.8, randomly generate an integer RM2 not equal to RM1 between [1, Popsize], and make the iteration factor tp=tk;

步骤8.9，令混沌因子tk＝4.0×tp×(1-tp)；Step 8.9, make chaos factor tk=4.0×tp×(1-tp);

步骤8.10，按以下公式生成个体VU^t：Step 8.10, generate individual VU^t according to the following formula:

其中VMu表示均值因子，VStd表示标准差因子；杂交因子VK的值为[0,1]之间的随机实数；Norm(VMu,VStd)表示以VMu为均值，VStd为标准差的正态分布随机实数产生函数；Among them, VMu represents the mean factor, VStd represents the standard deviation factor; the value of the hybridization factor VK is a random real number between [0,1]; Norm(VMu, VStd) represents a normal distribution random with VMu as the mean and VStd as the standard deviation. real number generating function;

步骤8.11，计算个体VU^t的适应值，令当前评价次数FEs＝FEs+1；Step 8.11, calculate the fitness value of the individual VU^t , make the current evaluation times FEs=FEs+1;

步骤8.12，如果个体VU^t的适应值优于的适应值，则转到步骤8.13，否则转到步骤9；Step 8.12, if the fitness value of individual VU^t is better than , then go to step 8.13, otherwise go to step 9;

步骤8.13，令个体然后转到步骤8.8；In step 8.13, let the individual Then go to step 8.8;

步骤9，令当前演化代数t＝t+1，然后保存种群P_t中的最优个体Best^t；Step 9, make the current evolution algebra t=t+1, and then save the best individual Best^{t in the population P t}_;

步骤10，重复步骤6至步骤9直至当前评价次数FEs达到MAX_FEs后结束，将执行过程中得到的最优个体Best^t解码为车辆路径，即可实现车辆路径规划。Step 10, repeat step 6 to step 9 until the current evaluation times FEs reaches MAX_FEs and end, and decode the optimal individual Best^t obtained during the execution process into a vehicle route to realize vehicle route planning.

本文中所描述的具体实施例仅仅是对本发明精神作举例说明。本发明所属技术领域的技术人员可以对所描述的具体实施例做各种各样的修改或补充或采用类似的方式替代，但并不会偏离本发明的精神或者超越所附权利要求书所定义的范围。The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which the present invention belongs can make various modifications or supplements to the described specific embodiments or adopt similar methods to replace them, but they will not deviate from the spirit of the present invention or go beyond the definition of the appended claims range.

Claims (1)

1. A kind of 1. vehicle path planning method based on the search of chaos gravitation, it is characterised in that comprise the following steps：

   Step 1, the coordinate position of each transportation point is inputted, and obtains the quantity D of transportation point；

   Step 2, user initializes Population Size Popsize, maximum evaluation number MAX_FEs；

   Step 3, current evolution algebraically t=0, Evaluation: Current number FEs=0 are made；

   Step 4, initial population is randomly generatedWherein individual subscript i=1,2 ...,Popsize, andFor population P_tIn i-th of individual, its random initializtion formula is：

   <mrow> <msubsup> <mi>A</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>t</mi> </msubsup> <mo>=</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow>

   <mrow> <msubsup> <mi>A</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>t</mi> </msubsup> <mo>=</mo> <mn>0</mn> </mrow>

   Wherein dimension subscript j=1,2 ..., D, andThe order weights of D transportation point are stored,Represent that i-th of individual existsVelocity magnitude on per dimension, rand (0,1) produce function to obey equally distributed random real number between [0,1]；

   Step 5, population P is calculated_tIn each individual adaptive value, then preserve population P_tIn optimum individual Best^t, and make and working asPreceding evaluation number FEs=FEs+Popsize；

   Step 6, the basic operation operator of gravitation search is performed, then calculates population P_tIn all individual adaptive values；

   Step 7, Evaluation: Current number FEs=FEs+Popsize is made；

   Step 8, an individual is randomly choosed, and the individual to choosing performs the operation of chaos Local Search, specific steps are such asUnder：

   Step 8.1, order mixes times N L=300+200 × rand (0,1)；

   Step 8.2, a real number itk not equal to 0.25,0.5 and 0.75 is randomly generated between [0,1]；

   Step 8.3, counter kj=0 is made, and makes iteration factor tp=itk；

   Step 8.4, chaos factor t k=4.0 × tp × (1-tp) is made；

   Step 8.5, iteration factor tp=tk is made, and makes counter kj=kj+1；

   Step 8.6, if counter kj is more than NL, step 8.7 is gone to, otherwise goes to step 8.4；

   Step 8.7, the integer RM1 of one is randomly generated between [1, Popsize]；

   Step 8.8, one is randomly generated between [1, Popsize] and is not equal to RM1 integer RM2, and makes iteration factor tp=tk；

   Step 8.9, chaos factor t k=4.0 × tp × (1-tp) is made；

   Step 8.10, individual VU is generated as follows^t：

   <mrow> <mi>V</mi> <mi>M</mi> <mi>u</mi> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>A</mi> <mrow> <mi>R</mi> <mi>M</mi> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> <mi>t</mi> </msubsup> <mo>+</mo> <msubsup> <mi>Best</mi> <mn>1</mn> <mi>t</mi> </msubsup> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mn>0.5</mn> <mo>,</mo> </mrow>

   <mrow> <mi>V</mi> <mi>S</mi> <mi>t</mi> <mi>d</mi> <mo>=</mo> <mo>|</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>R</mi> <mi>M</mi> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> <mi>t</mi> </msubsup> <mo>-</mo> <msubsup> <mi>Best</mi> <mn>1</mn> <mi>t</mi> </msubsup> </mrow> <mo>|</mo> <mo>&amp;times;</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow>

   <mrow> <msubsup> <mi>VU</mi> <mn>1</mn> <mi>t</mi> </msubsup> <mo>=</mo> <mo>&amp;lsqb;</mo> <msubsup> <mi>A</mi> <mrow> <mi>R</mi> <mi>M</mi> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> <mi>t</mi> </msubsup> <mo>+</mo> <mi>t</mi> <mi>k</mi> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <msubsup> <mi>Best</mi> <mn>1</mn> <mi>t</mi> </msubsup> <mo>-</mo> <msubsup> <mi>A</mi> <mrow> <mi>R</mi> <mi>M</mi> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> <mi>t</mi> </msubsup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>&amp;times;</mo> <mi>V</mi> <mi>K</mi> <mo>+</mo> <mi>N</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> <mrow> <mo>(</mo> <mi>V</mi> <mi>M</mi> <mi>u</mi> <mo>,</mo> <mi>V</mi> <mi>S</mi> <mi>t</mi> <mi>d</mi> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>V</mi> <mi>K</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow>

   <mrow> <msubsup> <mi>VU</mi> <mn>2</mn> <mi>t</mi> </msubsup> <mo>=</mo> <msubsup> <mi>A</mi> <mrow> <mi>R</mi> <mi>M</mi> <mn>2</mn> <mo>,</mo> <mn>2</mn> </mrow> <mi>t</mi> </msubsup> </mrow>

   Wherein VMu represents the average factor, and VStd represents standard deviation factor；Random reality of the Hybridization Factor VK value between [0,1]Number；Norm (VMu, VStd) represents that using VMu as average VStd is that the random real number of normal distribution of standard deviation produces function；

   Step 8.11, individual VU is calculated^tAdaptive value, make Evaluation: Current number FEs=FEs+1；

   Step 8.12, if individual VU^tAdaptive value be better thanAdaptive value, then go to step 8.13, otherwise go to step 9；

   Step 8.13, order individualThen go to step 8.8；

   Step 9, current evolution algebraically t=t+1 is made, then preserves population P_tIn optimum individual Best^t；

   Step 10, repeat step 6 is to step 9 until Evaluation: Current number FEs terminates after reaching MAX_FEs, by implementation procedureObtained optimum individual Best^tIt is decoded as vehicle route, you can realize vehicle path planning.