遺傳算法求解TSP問題.doc

人工智能實驗實驗六 遺傳算法求解TSP問題一、實驗?zāi)康膚 熟悉和掌握遺傳算法的原理、流程和編碼策略，并利用遺傳求解函數(shù)優(yōu)化問題，理解求解TSP問題的流程并測試主要參數(shù)對結(jié)果的影響。二、實驗內(nèi)容1、參考實驗系統(tǒng)給出的遺傳算法核心代碼，用遺傳算法求解TSP的優(yōu)化問題，分析遺傳算法求解不同規(guī)模TSP問題的算法性能。2、對于同一個TSP問題，分析種群規(guī)模、交叉概率和變異概率對算法結(jié)果的影響。3、增加1種變異策略和1種個體選擇概率分配策略，比較求解同一TSP問題時不同變異策略及不同個體選擇分配策略對算法結(jié)果的影響。4、上交源代碼。三、遺傳算法求解TSP問題的流程圖四、遺傳算法求解不同規(guī)模的TSP問題的算法性能（1） 遺傳算法執(zhí)行方式說明：l 適應(yīng)度值計算方法：當前路線的路徑長度l 個體選擇概率分配方法：適應(yīng)度比例方法l 選擇個體方法：輪盤賭選擇l 交叉類型：PMX交叉l 變異類型: 兩點互換變異（2）實驗?zāi)M結(jié)果：城市個數(shù)時間（ms）51692510166301518833202259625241593030289353523940386084540032504375755477466058143655994270643617571417圖1-1（3）分析由圖1-1可知，遺傳算法執(zhí)行時間隨著TSP問題規(guī)模的增大而增大，并且大致為線性增長。五、不同參數(shù)下的計算結(jié)果對比（1）種群規(guī)模對算法結(jié)果的影響實驗次數(shù)：10最大迭代步數(shù):100交叉概率：0.85變異概率：0.15表1-1種群規(guī)模適應(yīng)度值最優(yōu)路徑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，顯然最短路徑為25.1652m,最優(yōu)路徑為1-0-9-1-3-6-7-5-8-4-2或3-1-0-9-2-4-8-5-7-6，注意到這是一圈，順時針或者逆時針都可以。當種群規(guī)模為10，20時，并沒有找到最優(yōu)解。（2）交叉概率對算法結(jié)果的影響實驗次數(shù)：15種群規(guī)模：25最大迭代步數(shù):100變異概率：0.15實驗結(jié)果：表1-2交叉概率最好適應(yīng)度最差適應(yīng)度平均適應(yīng)度最優(yōu)解運行時間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:紅色表示非最優(yōu)解）在該情況下，交叉概率過低將使搜索陷入遲鈍狀態(tài)，得不到最優(yōu)解。（3）變異概率對算法結(jié)果的影響實驗次數(shù)：10種群規(guī)模：25最大迭代步數(shù):100交叉概率：0.85實驗結(jié)果：表1-3變異概率最好適應(yīng)度最差適應(yīng)度平均適應(yīng)度最優(yōu)解運行時間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，當變異概率過大或過低都將導(dǎo)致無法得到最優(yōu)解。注：（2）（3）的實驗數(shù)據(jù)與（1）的實驗數(shù)據(jù)不同，詳見附錄。六、不同變異策略和個體選擇概率分配策略對算法結(jié)果的影響（1）兩點互換變異與插入變異的比較：l 試驗次數(shù)（CASNUM）：10l 城市數(shù)(POINTCNT):10l 種群規(guī)模(POPSIZE)：100l 最大迭代步數(shù)(GENERATIONS):100l 交叉概率(PC)：0.85l 變異概率(PM):0.15l 選擇個體方法：輪盤賭選擇l 交叉類型：PMX交叉l 個體選擇概率分配方法：適應(yīng)度比例方法a. 變異類型: 兩點互換變異表1-4兩點互換變異程序結(jié)果序號最好適應(yīng)度最差適應(yīng)度平均適應(yīng)度最優(yōu)解運行時間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. 變異類型: 插入變異表1-5插入變異程序結(jié)果序號最好適應(yīng)度最差適應(yīng)度平均適應(yīng)度最優(yōu)解運行時間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：兩點互換變異20次模擬中，4次得到非最優(yōu)解；而插入變異只有2次；插入變異的最好適應(yīng)度平均值比兩點互換變異小0.14755，最差適應(yīng)度平均值和總的適應(yīng)度平均值都比兩點互換下，并且在Release下，運行時間前者比后者快218.3ms?？梢娫谠摋l件下（交叉概率，變異概率，種群規(guī)模等），插入變異比兩點互換變異的算法效果要好。（2）個體選擇分配策略l 試驗次數(shù)（CASNUM）：10l 城市數(shù)(POINTCNT):10l 種群規(guī)模(POPSIZE)：100l 最大迭代步數(shù)(GENERATIONS):100l 交叉概率(PC)：0.85l 變異概率(PM):0.15l 選擇個體方法：輪盤賭選擇l 交叉類型：PMX交叉l 變異類型: 兩點互換變異a. 個體選擇概率分配方法：適應(yīng)度比例方法同表1-4b. 個體選擇概率分配方法：非線性排序方式表1-6非線性排序方式程序結(jié)果序號最好適應(yīng)度最差適應(yīng)度平均適應(yīng)度最優(yōu)解運行時間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