遗传算法求解TSP问题.doc

人工智能实验实验六 遗传算法求解TSP问题一、实验目的w 熟悉和掌握遗传算法的原理、流程和编码策略，并利用遗传求解函数优化问题，理解求解TSP问题的流程并测试主要参数对结果的影响。二、实验内容1、参考实验系统给出的遗传算法核心代码，用遗传算法求解TSP的优化问题，分析遗传算法求解不同规模TSP问题的算法性能。2、对于同一个TSP问题，分析种群规模、交叉概率和变异概率对算法结果的影响。3、增加1种变异策略和1种个体选择概率分配策略，比较求解同一TSP问题时不同变异策略及不同个体选择分配策略对算法结果的影响。4、上交源代码。三、遗传算法求解TSP问题的流程图四、遗传算法求解不同规模的TSP问题的算法性能（1） 遗传算法执行方式说明：l 适应度值计算方法：当前路线的路径长度l 个体选择概率分配方法：适应度比例方法l 选择个体方法：轮盘赌选择l 交叉类型：PMX交叉l 变异类型: 两点互换变异（2）实验模拟结果：城市个数时间（ms）51692510166301518833202259625241593030289353523940386084540032504375755477466058143655994270643617571417图1-1（3）分析由图1-1可知，遗传算法执行时间随着TSP问题规模的增大而增大，并且大致为线性增长。五、不同参数下的计算结果对比（1）种群规模对算法结果的影响实验次数：10最大迭代步数:100交叉概率：0.85变异概率：0.15表1-1种群规模适应度值最优路径1025.2644-5-8-7-6-3-1-0-9-22026.34282-9-1-0-3-6-7-5-8-43025.16521-3-6-7-5-8-4-2-9-05025.16520-1-3-6-7-5-8-4-2-98025.16529-0-1-3-6-7-5-8-4-210025.16521-0-9-2-4-8-5-7-6-315025.16525-8-4-2-9-0-1-3-6-720025.16521-3-6-7-5-8-4-2-9-025025.16523-1-0-9-2-4-8-5-7-630025.16525-8-4-2-9-0-1-3-6-7如表1-1所示，显然最短路径为25.1652m,最优路径为1-0-9-1-3-6-7-5-8-4-2或3-1-0-9-2-4-8-5-7-6，注意到这是一圈，顺时针或者逆时针都可以。当种群规模为10，20时，并没有找到最优解。（2）交叉概率对算法结果的影响实验次数：15种群规模：25最大迭代步数:100变异概率：0.15实验结果：表1-2交叉概率最好适应度最差适应度平均适应度最优解运行时间0.00128.044736.656732.60029-2-6-0-5-4-8-7-3-13100.0127.093534.994332.14957-8-3-1-9-2-6-0-5-42600.128.044735.303331.93727-3-1-9-2-6-0-5-4-83000.1528.044734.117531.21830-5-4-8-7-3-1-9-2-62700.228.710833.951230.90353-1-9-2-6-5-0-4-7-82800.2528.044735.162330.74561-3-7-8-4-5-0-6-2-92600.327.093531.994129.94288-3-1-9-2-6-0-5-4-72900.3527.093532.808530.99459-1-3-8-7-4-5-0-6-22700.427.093532.531330.15341-3-8-7-4-5-0-6-2-92790.4527.093533.201430.17578-3-1-9-2-6-0-5-4-74560.528.093433.630730.90265-0-2-6-9-1-3-8-7-46630.5527.093533.523329.13041-9-2-6-0-5-4-7-8-35200.627.093533.251230.78363-1-9-2-6-0-5-4-7-85460.6528.044733.700330.93715-4-8-7-3-1-9-2-6-05960.727.093532.092729.95029-1-3-8-7-4-5-0-6-25710.7528.044732.448830.36990-5-4-8-7-3-1-9-2-65590.827.093532.155129.93827-4-5-0-6-2-9-1-3-83580.8527.093534.539930.35945-0-6-2-9-1-3-8-7-43600.927.093532.627330.696-0-5-4-7-8-3-1-9-23750.9527.093532.467229.9196-2-9-1-3-8-7-4-5-0476（注:红色表示非最优解）在该情况下，交叉概率过低将使搜索陷入迟钝状态，得不到最优解。（3）变异概率对算法结果的影响实验次数：10种群规模：25最大迭代步数:100交叉概率：0.85实验结果：表1-3变异概率最好适应度最差适应度平均适应度最优解运行时间0.00129.471734.73232.49110-6-2-1-9-3-8-7-4-52450.0129.044634.659132.37148-4-5-0-2-6-9-1-3-72740.128.093434.01130.94175-0-2-6-9-1-3-8-7-42500.1527.093532.09330.25686-0-5-4-7-8-3-1-9-22460.227.093532.234930.31448-7-4-5-0-6-2-9-1-32820.2527.093532.71830.15724-5-0-6-2-9-1-3-8-72450.327.093532.448830.28540-5-4-7-8-3-1-9-2-62520.3527.093533.316730.77481-3-8-7-4-5-0-6-2-92660.429.044634.370531.30412-0-5-4-8-7-3-1-9-63620.4527.093531.37429.68162-6-0-5-4-7-8-3-1-94380.527.093532.375230.22112-9-1-3-8-7-4-5-0-64310.5527.093533.381930.66231-3-8-7-4-5-0-6-2-94920.628.093433.251230.361-3-8-7-4-5-0-2-6-94170.6527.093532.749130.02013-1-9-2-6-0-5-4-7-84340.728.710832.423830.7851-3-8-7-4-0-5-6-2-94320.7527.093531.892830.24511-9-2-6-0-5-4-7-8-34750.828.093431.613530.34719-1-3-8-7-4-5-0-2-63270.8529.66233.239231.15852-9-1-3-7-8-4-0-5-63140.928.044732.038730.41520-5-4-8-7-3-1-9-2-63960.9528.044731.303630.00679-1-3-7-8-4-5-0-6-2436又表1-3可知，当变异概率过大或过低都将导致无法得到最优解。注：（2）（3）的实验数据与（1）的实验数据不同，详见附录。六、不同变异策略和个体选择概率分配策略对算法结果的影响（1）两点互换变异与插入变异的比较：l 试验次数（CASNUM）：10l 城市数(POINTCNT):10l 种群规模(POPSIZE)：100l 最大迭代步数(GENERATIONS):100l 交叉概率(PC)：0.85l 变异概率(PM):0.15l 选择个体方法：轮盘赌选择l 交叉类型：PMX交叉l 个体选择概率分配方法：适应度比例方法a. 变异类型: 两点互换变异表1-4两点互换变异程序结果序号最好适应度最差适应度平均适应度最优解运行时间128.093430.422929.08916-2-0-5-4-7-8-3-1-91199227.093531.141728.98414-5-0-6-2-9-1-3-8-71678327.093530.422829.06040-5-4-7-8-3-1-9-2-61940427.093530.370328.87871-3-8-7-4-5-0-6-2-91756527.093531.061929.07553-1-9-2-6-0-5-4-7-81885627.093531.158929.39422-6-0-5-4-7-8-3-1-91936728.044731.061929.76486-2-9-1-3-7-8-4-5-01772829.044631.347529.84154-5-0-2-6-9-1-3-7-81980927.093530.614329.0590-6-2-9-1-3-8-7-4-519401027.093530.558529.08119-2-6-0-5-4-7-8-3-118721127.093531.017129.42640-5-4-7-8-3-1-9-2-615171227.093531.303629.24141-9-2-6-0-5-4-7-8-315411327.093532.025529.07890-6-2-9-1-3-8-7-4-515171427.093531.51628.89060-6-2-9-1-3-8-7-4-513451527.093530.422829.02266-0-5-4-7-8-3-1-9-213771627.093530.408128.90810-6-2-9-1-3-8-7-4-518531727.093530.408129.33167-8-3-1-9-2-6-0-5-415221827.093530.020328.52431-3-8-7-4-5-0-6-2-916011928.044731.140429.5672-9-1-3-7-8-4-5-0-616092027.093531.141729.53597-4-5-0-6-2-9-1-3-81311平均值27.336130.878229.18771657b. 变异类型: 插入变异表1-5插入变异程序结果序号最好适应度最差适应度平均适应度最优解运行时间127.093531.475328.84532-6-0-5-4-7-8-3-1-91388227.093529.66228.91685-0-6-2-9-1-3-8-7-41355327.093529.663128.9021-9-2-6-0-5-4-7-8-31637428.044730.524129.51194-5-0-6-2-9-1-3-7-81164527.093531.057529.46822-6-0-5-4-7-8-3-1-91245627.093529.66228.55462-6-0-5-4-7-8-3-1-91222728.044730.820529.7483-1-9-2-6-0-5-4-8-71148827.093530.524129.39071-9-2-6-0-5-4-7-8-31742927.093530.42328.68780-6-2-9-1-3-8-7-4-520641027.093530.408128.725-0-6-2-9-1-3-8-7-415181127.093531.37429.32824-5-0-6-2-9-1-3-8-712401227.093530.52328.55441-3-8-7-4-5-0-6-2-912041327.093530.820529.05080-6-2-9-1-3-8-7-4-517341427.093531.117729.59050-5-4-7-8-3-1-9-2-615321527.093530.52329.19044-5-0-6-2-9-1-3-8-714831627.093530.408128.80615-0-6-2-9-1-3-8-7-412821727.093531.763929.45916-0-5-4-7-8-3-1-9-214851827.093531.158929.16144-5-0-6-2-9-1-3-8-716011927.093530.408128.59742-6-0-5-4-7-8-3-1-915072027.093530.614328.80363-1-9-2-6-0-5-4-7-81234平均值27.1886230.646529.06431439分析：两点互换变异20次模拟中，4次得到非最优解；而插入变异只有2次；插入变异的最好适应度平均值比两点互换变异小0.14755，最差适应度平均值和总的适应度平均值都比两点互换下，并且在Release下，运行时间前者比后者快218.3ms。可见在该条件下（交叉概率，变异概率，种群规模等），插入变异比两点互换变异的算法效果要好。（2）个体选择分配策略l 试验次数（CASNUM）：10l 城市数(POINTCNT):10l 种群规模(POPSIZE)：100l 最大迭代步数(GENERATIONS):100l 交叉概率(PC)：0.85l 变异概率(PM):0.15l 选择个体方法：轮盘赌选择l 交叉类型：PMX交叉l 变异类型: 两点互换变异a. 个体选择概率分配方法：适应度比例方法同表1-4b. 个体选择概率分配方法：非线性排序方式表1-6非线性排序方式程序结果序号最好适应度最差适应度平均适应度最优解运行时间127.093532.172130.09041-9-2-6-0-5-4-7-8-3824228.044731.29729.99794-5-0-6-2-9-1-3-7-8865328.093432.168330.56012-0-5-4-7-8-3-1-9-6895427.093532.097330.34723-1-9-2-6-0-5-4-7-81067527.093531.51629.85314-5-0-6-2-9-1-3-8-7887627.093531.40829.46375-0-6-2-9-1-3-8-7-4727727.093531.374229.94763-1-9-2-6-0-5-4-7-8651829.523131.800930.55430-5-4-7-8-1-3-9-2-6901927.093532.714730.3910-5-4-7-8-3-1-9-2-67491029.523131.568830.23859-3-1-8-7-4-5-0-6-28401128.044731.763930.26173-7-8-4-5-0-6-2-9-110441228.044731.630830.32671-3-7-8-4-5-0-6-2-97321327.093531.568829.43320-5-4-7-8-3-1-9-2-67371428.093431.157629.96464-5-0-2-6-9-1-3-8-76721528.044731.662629.77615-0-6-2-9-1-3-7-8-48231628.093431.559130.34732-0-5-4-7-8-3-1-9-67321727.093531.61829.59887-8-3-1-9-2-6-0-5-46971827.093532.71829.70331-3-8-7-4-5-0-6-2-967