无所事事，就想找个题目练一下遗传算法。然后想到可以用遗传算法找遍历给定城市的最短路径。从网上搜了一些中国的城市，各城市之间的距离取它们之间的直线距离，每个城市一个编号，然后每个所有编号构成的排列就是一个解，每个解会得到一个相应的总距离。问题就变成寻找最优排列的问题。
用遗传算法处理这个问题，先随机生成一群初始解作为初始种群。每个解作为一个个体可以进行增殖和变异，然后种群的数量增加，再通过筛选函数以更高的概率挑选一部分更加满足要求的个体进行增殖，通过数代的进化，以期得到总距离尽可能短的解。写好程序测试后发现效果还不错。
下面是对程序中一些问题的说明。遗传算法中的一步是要求两个个体通过交叉和变异产生一个新个体，模仿生物的有性生殖。但是对于两个12345或者31452的排列，实在不知道该怎么进行交叉。所以程序只对原始排列进行变异，但是不进行两个排列之间的交叉。
变异的方法可以有很多，这里为了提高程序的运行速度，把变异分为两点之间交换和两个序列之间的交换，其中序列交换时可以进行翻转。
在程序运行过程中发现种群的进化速度较慢，一些优秀的个体会因为随机性被淘汰，所以程序里加上了保留最优个体的规则。尽管这样做可能会降低种群的多样性，降低算法对所有解的“遍历性”，但是实践发现确实能够得到更好的解，而且解优化的速度快很多。不保留最优个体的时候优化速度在越接近极值的时候速度越慢，甚至不会进一步优化。也许是因为这时候选择压力太小了，可能一个更好的办法是提供一个可变的选择压力而不是保留最优个体。
至于筛选函数，不知道该怎么做到尽可能好，就简单的选择了距离平均值乘一个系数作为筛选标准。为了防止出现大小年的现象，进行了二次筛选。
为了提高序列的质量，对序列的子序列进行了优化，重新排列相邻的四个值，使新的子序列对应的长度最小。
为了图简单，程序需要的各城市之间距离的矩阵和城市名直接写在程序里了，改成从文件里读取也是很容易的。
代码如下：
1 #include <iostream>
2 #include <algorithm>
3 #include <list>
4 #include <random>
5 #define NUM 37
6
7 double dis_mat[NUM][NUM] = {{0.00,101.26,543.55,624.38,270.58,408.52,421.60,618.75,457.61,855.97,1052.50,1066.24,897.04,1050.24,1341.21,1884.46,2287.62,2051.23,1522.09,1462.87,1024.61,1124.39,1206.52,1377.53,898.06,1564.50,1726.42,1248.46,362.94,1718.93,2417.35,1328.53,1185.95,917.73,2090.88,2575.17,1735.43}
8 ,{101.26,0.00,442.45,581.22,268.00,427.52,505.13,601.62,386.93,857.93,1065.92,966.74,804.46,985.11,1280.91,1816.36,2229.02,2003.83,1521.70,1444.72,926.52,1028.59,1107.84,1282.31,813.68,1474.14,1640.55,1171.72,278.25,1623.61,2502.20,1374.80,1223.32,915.77,2073.10,2608.50,1704.83}
9 ,{543.55,442.45,0.00,617.67,566.63,717.80,920.76,690.41,335.80,970.23,1199.59,550.96,468.91,821.97,1117.58,1585.54,2037.59,1874.12,1622.44,1474.56,527.26,646.97,697.39,897.52,546.73,1119.76,1311.45,920.28,301.46,1232.26,2897.35,1655.67,1480.03,1055.27,2079.11,2815.16,1665.86}
10 ,{624.38,581.22,617.67,0.00,374.61,361.57,698.60,1152.84,844.16,1425.05,1640.78,821.18,556.95,461.60,730.30,1286.82,1669.30,1426.87,1008.78,885.79,749.88,784.81,914.64,996.41,461.14,1106.84,1220.35,703.70,369.87,1314.75,2448.23,1092.94,905.93,441.65,1509.29,2201.37,1126.66}
11 ,{270.58,268.00,566.63,374.61,0.00,166.63,389.01,869.08,633.73,1119.95,1321.31,994.58,774.86,826.65,1104.36,1658.56,2043.48,1793.95,1256.65,1192.29,938.06,1014.70,1120.55,1257.41,736.12,1412.72,1552.72,1050.21,276.53,1594.22,2331.46,1125.98,966.09,650.88,1820.34,2345.77,1467.15}
12 ,{408.52,427.52,717.80,361.57,166.63,0.00,337.38,1023.15,800.08,1264.37,1457.52,1098.63,858.07,820.85,1073.64,1634.38,1992.72,1722.71,1116.61,1076.41,1035.97,1097.63,1214.46,1328.76,793.72,1459.84,1580.80,1065.20,418.00,1657.76,2190.94,959.58,799.73,516.59,1700.25,2181.53,1368.71}
13 ,{421.60,505.13,920.76,698.60,389.01,337.38,0.00,987.11,878.93,1173.66,1330.62,1382.60,1162.70,1158.18,1406.02,1967.04,2311.62,2026.95,1318.04,1332.96,1326.93,1402.90,1509.54,1643.36,1115.27,1788.37,1915.69,1401.75,656.00,1977.98,1997.27,969.74,860.07,766.65,1937.12,2235.80,1646.09}
14 ,{618.75,601.62,690.41,1152.84,869.08,1023.15,987.11,0.00,354.93,282.49,510.81,1191.46,1158.81,1483.23,1784.60,2273.73,2719.84,2534.78,2122.56,2034.63,1189.05,1316.28,1335.14,1554.70,1232.31,1792.40,1992.59,1608.16,790.12,1872.38,2905.84,1939.59,1803.11,1516.90,2661.05,3192.79,2276.35}
15 ,{457.61,386.93,335.80,844.16,633.73,800.08,878.93,354.93,0.00,636.02,865.14,856.45,804.63,1136.29,1436.51,1919.09,2367.11,2190.09,1843.57,1729.35,846.15,971.18,1002.69,1215.62,877.98,1447.06,1643.36,1253.51,474.37,1542.04,2871.80,1757.05,1599.79,1246.32,2349.41,2977.03,1951.37}
16 ,{855.97,857.93,970.23,1425.05,1119.95,1264.37,1173.66,282.49,636.02,0.00,229.38,1454.15,1437.28,1765.40,2066.86,2555.06,3002.22,2816.23,2376.46,2301.38,1457.33,1585.66,1594.98,1818.31,1513.98,2060.56,2264.18,1889.49,1067.34,2127.68,2997.08,2142.22,2019.46,1770.83,2929.28,3405.84,2551.05}
17 ,{1052.50,1065.92,1199.59,1640.78,1321.31,1457.52,1330.62,510.81,865.14,229.38,0.00,1679.15,1666.61,1991.71,2293.36,2784.24,3230.47,3040.85,2573.83,2510.29,1684.25,1812.82,1818.68,2043.19,1742.99,2286.99,2491.73,2118.66,1288.47,2348.69,3059.36,2299.04,2187.82,1970.20,3138.77,3565.77,2767.42}
18 ,{1066.24,966.74,550.96,821.18,994.58,1098.63,1382.60,1191.46,856.45,1454.15,1679.15,0.00,269.60,680.39,887.38,1201.33,1675.07,1596.81,1656.10,1438.49,75.92,160.69,146.97,364.15,401.49,610.52,821.95,603.48,730.77,685.79,3266.39,1903.85,1713.65,1218.13,1957.10,2910.99,1521.19}
19 ,{897.04,804.46,468.91,556.95,774.86,858.07,1162.70,1158.81,804.63,1437.28,1666.61,269.60,0.00,450.20,706.81,1124.68,1585.55,1454.09,1403.56,1198.82,195.21,240.44,359.60,484.87,143.27,671.19,849.75,465.45,537.44,825.11,3005.10,1634.55,1444.21,948.68,1749.11,2653.79,1316.76}
20 ,{1050.24,985.11,821.97,461.60,826.65,820.85,1158.18,1483.23,1136.29,1765.40,1991.71,680.39,450.20,0.00,301.74,834.75,1247.09,1054.07,982.01,758.10,607.41,560.72,699.48,676.50,310.79,705.30,779.80,262.02,717.61,940.04,2764.34,1335.73,1146.42,649.19,1299.62,2239.44,869.08}
21 ,{1341.21,1280.91,1117.58,730.30,1104.36,1073.64,1406.02,1784.60,1436.51,2066.86,2293.36,887.38,706.81,301.74,0.00,561.03,948.18,756.74,899.12,637.78,823.51,739.42,861.29,757.16,583.10,677.61,662.39,295.01,1017.40,924.34,2841.44,1398.80,1221.00,772.66,1073.88,2132.83,638.48}
22 ,{1884.46,1816.36,1585.54,1286.82,1658.56,1634.38,1967.04,2273.73,1919.09,2555.06,2784.24,1201.33,1124.68,834.75,561.03,0.00,474.36,508.55,1236.25,977.40,1162.31,1041.42,1110.31,910.61,1041.59,686.67,504.99,665.58,1543.36,859.33,3280.12,1857.52,1697.86,1304.10,1095.79,2327.33,764.08}
23 ,{2287.62,2229.02,2037.59,1669.30,2043.48,1992.72,2311.62,2719.84,2367.11,3002.22,3230.47,1675.07,1585.55,1247.09,948.18,474.36,0.00,357.42,1327.91,1117.50,1634.41,1514.88,1584.40,1381.40,1490.85,1147.99,947.70,1120.69,1964.64,1289.97,3366.79,2013.16,1883.41,1583.86,946.83,2201.49,805.65}
24 ,{2051.23,2003.83,1874.12,1426.87,1793.95,1722.71,2026.95,2534.78,2190.09,2816.23,3040.85,1596.81,1454.09,1054.07,756.74,508.55,357.42,0.00,972.50,773.57,1543.23,1437.89,1533.95,1362.49,1337.68,1167.34,1006.69,999.46,1754.84,1361.10,3009.60,1661.52,1538.23,1276.31,627.13,1885.96,451.91}
25 ,{1522.09,1521.70,1622.44,1008.78,1256.65,1116.61,1318.04,2122.56,1843.57,2376.46,2573.83,1656.10,1403.56,982.01,899.12,1236.25,1327.91,972.50,0.00,268.40,1581.17,1542.73,1681.23,1631.38,1261.18,1576.72,1542.06,1161.95,1372.27,1823.43,2055.13,695.37,600.88,605.98,637.04,1257.47,522.55}
26 ,{1462.87,1444.72,1474.56,885.79,1192.29,1076.41,1332.96,2034.63,1729.35,2301.38,2510.29,1438.49,1198.82,758.10,637.78,977.40,1117.50,773.57,268.40,0.00,1365.29,1314.17,1449.71,1382.61,1055.62,1314.50,1274.19,911.58,1255.48,1560.51,2304.01,900.79,766.02,568.35,628.49,1499.21,332.15}
27 ,{1024.61,926.52,527.26,749.88,938.06,1035.97,1326.93,1189.05,846.15,1457.33,1684.25,75.92,195.21,607.41,823.51,1162.31,1634.41,1543.23,1581.17,1365.29,0.00,129.01,183.56,370.68,325.57,603.53,808.13,545.36,680.23,705.69,3196.88,1829.74,1639.36,1143.00,1889.92,2835.64,1454.30}
28 ,{1124.39,1028.59,646.97,784.81,1014.70,1097.63,1402.90,1316.28,971.18,1585.66,1812.82,160.69,240.44,560.72,739.42,1041.42,1514.88,1437.89,1542.73,1314.17,129.01,0.00,140.77,254.28,328.59,476.24,679.22,449.76,770.35,595.13,3230.17,1840.28,1649.01,1146.84,1812.69,2800.15,1376.78}
29 ,{1206.52,1107.84,697.39,914.64,1120.55,1214.46,1509.54,1335.14,1002.69,1594.98,1818.68,146.97,359.60,699.48,861.29,1110.31,1584.40,1533.95,1681.23,1449.71,183.56,140.77,0.00,228.27,465.01,481.77,697.89,567.09,863.78,539.35,3362.50,1978.64,1787.46,1285.97,1934.86,2938.69,1499.76}
30 ,{1377.53,1282.31,897.52,996.41,1257.41,1328.76,1643.36,1554.70,1215.62,1818.31,2043.19,364.15,484.87,676.50,757.16,910.61,1381.40,1362.49,1631.38,1382.61,370.68,254.28,228.27,0.00,537.11,254.64,472.05,471.03,1021.15,341.40,3420.71,2006.15,1815.48,1312.74,1812.43,2881.79,1383.82}
31 ,{898.06,813.68,546.73,461.14,736.12,793.72,1115.27,1232.31,877.98,1513.98,1742.99,401.49,143.27,310.79,583.10,1041.59,1490.85,1337.68,1261.18,1055.62,325.57,328.59,465.01,537.11,0.00,676.84,828.46,376.36,536.05,864.23,2902.18,1513.90,1322.80,822.46,1610.35,2512.86,1179.67}
32 ,{1564.50,1474.14,1119.76,1106.84,1412.72,1459.84,1788.37,1792.40,1447.06,2060.56,2286.99,610.52,671.19,705.30,677.61,686.67,1147.99,1167.34,1576.72,1314.50,603.53,476.24,481.77,254.64,676.84,0.00,217.86,449.20,1202.04,247.17,3466.87,2031.26,1844.40,1353.13,1669.68,2802.95,1257.00}
33 ,{1726.42,1640.55,1311.45,1220.35,1552.72,1580.80,1915.69,1992.59,1643.36,2264.18,2491.73,821.95,849.75,779.80,662.39,504.99,947.70,1006.69,1542.06,1274.19,808.13,679.22,697.89,472.05,828.46,217.86,0.00,520.08,1363.94,354.77,3500.60,2058.04,1876.97,1405.06,1552.62,2732.91,1163.18}
34 ,{1248.46,1171.72,920.28,703.70,1050.21,1065.20,1401.75,1608.16,1253.51,1889.49,2118.66,603.48,465.45,262.02,295.01,665.58,1120.69,999.46,1161.95,911.58,545.36,449.76,567.09,471.03,376.36,449.20,520.08,0.00,894.24,690.53,3017.76,1582.46,1395.27,904.96,1367.82,2410.77,933.02}
35 ,{362.94,278.25,301.46,369.87,276.53,418.00,656.00,790.12,474.37,1067.34,1288.47,730.77,537.44,717.61,1017.40,1543.36,1964.64,1754.84,1372.27,1255.48,680.23,770.35,863.78,1021.15,536.05,1202.04,1363.94,894.24,0.00,1362.13,2605.16,1356.31,1183.16,782.44,1877.49,2533.80,1486.56}
36 ,{1718.93,1623.61,1232.26,1314.75,1594.22,1657.76,1977.98,1872.38,1542.04,2127.68,2348.69,685.79,825.11,940.04,924.34,859.33,1289.97,1361.10,1823.43,1560.51,705.69,595.13,539.35,341.40,864.23,247.17,354.77,690.53,1362.13,0.00,3704.38,2272.42,2084.47,1589.23,1894.22,3045.55,1490.66}
37 ,{2417.35,2502.20,2897.35,2448.23,2331.46,2190.94,1997.27,2905.84,2871.80,2997.08,3059.36,3266.39,3005.10,2764.34,2841.44,3280.12,3366.79,3009.60,2055.13,2304.01,3196.88,3230.17,3362.50,3420.71,2902.18,3466.87,3500.60,3017.76,2605.16,3704.38,0.00,1442.74,1624.64,2115.18,2491.22,1598.96,2571.40}
38 ,{1328.53,1374.80,1655.67,1092.94,1125.98,959.58,969.74,1939.59,1757.05,2142.22,2299.04,1903.85,1634.55,1335.73,1398.80,1857.52,2013.16,1661.52,695.37,900.79,1829.74,1840.28,1978.64,2006.15,1513.90,2031.26,2058.04,1582.46,1356.31,2272.42,1442.74,0.00,191.33,694.82,1288.98,1266.79,1209.62}
39 ,{1185.95,1223.32,1480.03,905.93,966.09,799.73,860.07,1803.11,1599.79,2019.46,2187.82,1713.65,1444.21,1146.42,1221.00,1697.86,1883.41,1538.23,600.88,766.02,1639.36,1649.01,1787.46,1815.48,1322.80,1844.40,1876.97,1395.27,1183.16,2084.47,1624.64,191.33,0.00,503.59,1228.00,1389.70,1089.40}
40 ,{917.73,915.77,1055.27,441.65,650.88,516.59,766.65,1516.90,1246.32,1770.83,1970.20,1218.13,948.68,649.19,772.66,1304.10,1583.86,1276.31,605.98,568.35,1143.00,1146.84,1285.97,1312.74,822.46,1353.13,1405.06,904.96,782.44,1589.23,2115.18,694.82,503.59,0.00,1185.74,1760.44,879.99}
41 ,{2090.88,2073.10,2079.11,1509.29,1820.34,1700.25,1937.12,2661.05,2349.41,2929.28,3138.77,1957.10,1749.11,1299.62,1073.88,1095.79,946.83,627.13,637.04,628.49,1889.92,1812.69,1934.86,1812.43,1610.35,1669.68,1552.62,1367.82,1877.49,1894.22,2491.22,1288.98,1228.00,1185.74,0.00,1259.87,436.01}
42 ,{2575.17,2608.50,2815.16,2201.37,2345.77,2181.53,2235.80,3192.79,2977.03,3405.84,3565.77,2910.99,2653.79,2239.44,2132.83,2327.33,2201.49,1885.96,1257.47,1499.21,2835.64,2800.15,2938.69,2881.79,2512.86,2802.95,2732.91,2410.77,2533.80,3045.55,1598.96,1266.79,1389.70,1760.44,1259.87,0.00,1574.69}
43 ,{1735.43,1704.83,1665.86,1126.66,1467.15,1368.71,1646.09,2276.35,1951.37,2551.05,2767.42,1521.19,1316.76,869.08,638.48,764.08,805.65,451.91,522.55,332.15,1454.30,1376.78,1499.76,1383.82,1179.67,1257.00,1163.18,933.02,1486.56,1490.66,2571.40,1209.62,1089.40,879.99,436.01,1574.69,0.00}
44 };
45
46 unsigned int order[24][4] = {
47 {0,1,2,3},{0,1,3,2},{0,2,1,3}
48 ,{0,2,3,1},{0,3,1,2},{0,3,2,1}
49 ,{1,0,2,3},{1,0,3,2},{1,2,0,3}
50 ,{1,2,3,0},{1,3,0,2},{1,3,2,0}
51 ,{2,0,1,3},{2,0,3,1},{2,1,0,3}
52 ,{2,1,3,0},{2,3,0,1},{2,3,1,0}
53 ,{3,0,1,2},{3,0,2,1},{3,1,0,2}
54 ,{3,1,2,0},{3,2,0,1},{3,2,1,0}};
55 //个体,随机生成一个初始序列
56 struct unit{
57 unsigned int path[NUM];
58 inline unit(){
59 for( unsigned int i = 0; i < NUM; ++i)
60 path[i] = i;
61 std::random_shuffle(path, path+NUM);
62 }
63 inline unit(const unit & val){
64 for( unsigned int i = 0; i < NUM; ++i)
65 path[i] = val.path[i];
67 }
68 inline unit operator = (const unit & val){
69 for(unsigned int i = 0; i < NUM; ++i)
70 path[i] = val.path[i];
71 return *this;
72 }
76 inline double distance(){
77 double dis = 0.0;
78 for(unsigned int i = 1; i < NUM; ++i)
79 dis += dis_mat[path[i-1]][path[i]];
80 return dis;
81 }
82 };
83 //序列左端点处的优化，返回重新的排列顺序对应的编号（order）
84 unsigned int shortest_path4l(unit & theone){
85 unsigned int reti = 0;
86 double shortdis = 0.0;
87 for(unsigned int j = 0; j < 3; ++j)
88 shortdis += dis_mat[theone.path[order[0][j]]][theone.path[order[0][j+1]]];
89 shortdis += dis_mat[theone.path[order[0][3]]][theone.path[4]];
90 for( unsigned int i = 1; i < 24; ++i){
91 double dis = 0.0;
92 for(unsigned int j = 0; j < 3; ++j){
93 dis += dis_mat[theone.path[order[i][j]]][theone.path[order[i][j+1]]];
94 }
95 dis += dis_mat[theone.path[order[i][3]]][theone.path[4]];
96 if(dis < shortdis){
97 shortdis = dis;
98 reti = i;
99 }
100 }
101 return reti;
102 }
103 //右端点对应的优化函数
104 unsigned int shortest_path4r(unit & theone, unsigned int o){
105 unsigned int reti = 0;
106 double shortdis = 0.0;
107 shortdis += dis_mat[theone.path[o-1]][theone.path[o+order[0][0]]];
108 for( unsigned int j = 0; j < 3; ++j)
109 shortdis += dis_mat[theone.path[o+order[0][j]]][theone.path[o+order[0][j+1]]];
110 for(unsigned int i = 1; i < 24; ++i){
111 double dis = dis_mat[theone.path[o-1]][theone.path[o+order[i][0]]];
112 for(unsigned int j = 0; j < 3; ++j)
113 dis += dis_mat[theone.path[o+order[i][j]]][theone.path[o+order[i][j+1]]];
114 if(dis < shortdis){
115 shortdis = dis;
116 reti = i;
117 }
118 }
119 return reti;
120 }
121 //一般情况下的优化函数
122 unsigned int shortest_path4(unit & theone, unsigned int o){
123 unsigned int reti = 0;
124 double shortdis = dis_mat[theone.path[o-1]][theone.path[o+order[0][0]]];
125 for(unsigned int j = 0; j < 3; ++j)
126 shortdis += dis_mat[theone.path[o+order[0][j]]][theone.path[o+order[0][j+1]]];
127 shortdis += dis_mat[theone.path[o+order[0][3]]][theone.path[o+4]];
128 for(unsigned int i = 1; i < 24; ++i){
129 double dis = dis_mat[theone.path[o-1]][theone.path[o+order[i][0]]];
130 for( unsigned int j = 0; j < 3; ++j)
131 dis += dis_mat[theone.path[o+order[i][j]]][theone.path[o+order[i][j+1]]];
132 dis += dis_mat[theone.path[o+order[i][3]]][theone.path[o+4]];
133 if(dis < shortdis){
134 shortdis = dis;
135 reti = i;
136 }
137 }
138 return reti;
139 }
140 //对子序列重新排序
141 void ch_order( unit & theone, unsigned int o, unsigned int i){
142 unsigned int ach[4];
143 for(unsigned int j = 0; j < 4; ++j)
144 ach[j] = theone.path[o+order[i][j]];
145 for(unsigned int j = 0; j < 4; ++j)
146 theone.path[o+j] = ach[j];
147 }
148 //优化函数，调用上面的四个函数，实现对整个序列的优化
149 void optimize(unit & theone){
150 ch_order(theone, 0, shortest_path4l(theone));
151 for( unsigned int i = 1; i < NUM - 5; ++i)
152 ch_order(theone, i, shortest_path4(theone, i));
153 ch_order(theone, NUM-4, shortest_path4r(theone,NUM-4));
154 }
155
156 std::random_device rd;
157 std::mt19937 mt(rd());
158 std::bernoulli_distribution witera(0.5); //是否迭代
159 std::bernoulli_distribution wch(0.5); //是否变异
160 std::bernoulli_distribution porl(0.5);//选择点或序列变异
161 std::bernoulli_distribution wrev(0.5);//是否翻转
162 std::uniform_int_distribution<> startpoint(0, NUM-1);//点或序列变异起始点或结束点
163 //变异函数，以一定的概率选择各个变异方向
164 unit ch_unit( const unit & theone){
165 unit ret(theone);
166 if(wch(mt)){
167 if(porl(mt)){
168 auto start1 = startpoint(mt);
169 auto start2 = startpoint(mt);
170 if( start1 != start2){
171 auto temp = ret.path[start1];
172 ret.path[start1] = ret.path[start2];
173 ret.path[start2] = temp;
174 }
175 }
176 else {//选择序列变异
177 decltype(startpoint(mt)) cutpoint[4];
178 do{//选择两个变异序列开始和结束的位置
179 for(unsigned int i1 = 0; i1 < 4; ++i1)
180 cutpoint[i1] = startpoint(mt);
181 for(unsigned int i1 = 0; i1 < 3; ++i1)
182 for( unsigned int i2 = i1+1; i2 < 4; ++i2)
183 if(cutpoint[i1] > cutpoint[i2])
184 std::swap(cutpoint[i1], cutpoint[i2]);
185 }
186 while(cutpoint[1] == cutpoint[2]);
188 unsigned int tmp[NUM];
189 unsigned int pos = 0;
190 for(unsigned int i3 = 0; i3 < cutpoint[0]; ++i3)
191 tmp[pos++] = ret.path[i3];
192 if(wrev(mt)){
193 for(unsigned int i3 = cutpoint[3]; i3 >= cutpoint[2]; --i3)
194 tmp[pos++] = ret.path[i3];
195 }
196 else{
197 for(unsigned int i3 = cutpoint[2]; i3 <= cutpoint[3]; ++i3)
198 tmp[pos++] = ret.path[i3];
199 }
200 for(unsigned int i3 = cutpoint[1]+1; i3 < cutpoint[2]; ++i3)
201 tmp[pos++] = ret.path[i3];
202 if(wrev(mt)){
203 for(int i3 = cutpoint[1]; i3 >= cutpoint[0]; --i3)
204 tmp[pos++] = ret.path[i3];
205 }
206 else{
207 for(unsigned int i3 = cutpoint[0]; i3 <= cutpoint[1]; ++i3)
208 tmp[pos++] = ret.path[i3];
209 }
210 for(unsigned int i3 = cutpoint[3]+1; i3 < NUM; ++i3)
211 tmp[pos++] = ret.path[i3];
212 for(unsigned int i3 = 0; i3 < NUM; ++i3)
213 ret.path[i3] = tmp[i3];
214 }
215 }
216 if(witera(mt))
217 return ch_unit(ret);
218 else
219 return ret;
220 }
221 //增殖函数
222 void add_unit( std::list<unit> & conti){
223 const unsigned int SIZE = conti.size();
224 unsigned int i = 0;
225 auto itr = conti.begin();
227 while(i < SIZE){
228 conti.push_back(ch_unit(*itr));
229 ++itr;
230 ++i;
232 }
233 }
234 //筛选函数使用的满足正态分布的相乘系数，使优秀或不好的个体都有一定概率被选择和淘汰，目的是增加随机性、遍历性，减少取得局部极小值的可能
235 std::normal_distribution<double> normald(1., 0.25);
236
237 void select(std::list<unit> & conti )
238 auto thekeep = *(conti.begin());//保留最优个体
239 for(auto itk = conti.begin(); itk != conti.end(); ++itk)
240 if(thekeep.distance() > itk->distance())
241 thekeep = *itk;
242 double av_dis = 0.0;
243 auto SIZE = conti.size();
244 for(auto itr = conti.begin(); itr != conti.end(); ++itr)
245 av_dis += itr->distance();
246 av_dis /= conti.size();
247 std::list<unit> tmp_conti;
248 auto itr = conti.begin();
249 while(itr != conti.end()){
250 if(normald(mt) * itr->distance() > av_dis*2000./SIZE){
251 tmp_conti.push_back(*itr);
252 itr = conti.erase(itr);
253 }
254 else{
255 ++itr;
256 }
257 }
258 conti.push_back(thekeep);
259 unsigned int looplimit = 0;
260 while(conti.size() < 2000*0.5){//二次筛选，避免出现大小年现象
261 auto back_num = 2000 - conti.size();
262 auto itb = tmp_conti.begin();
263 auto TMPSIZE = tmp_conti.size();
264 while(itb != tmp_conti.end()){
265 if(normald(mt) * itb->distance() < av_dis*back_num/TMPSIZE){
266 conti.push_back(*itb);
267 itb = tmp_conti.erase(itb);
268 }
269 else{
270 ++itb;
271 }
272 }
273 if(++looplimit < 10)
274 break;
275 }
276 }
277
278 void print_city(unsigned int order[NUM]){
279 std::vector<std::string> cityname = {
280 "北京","天津", "青岛", "郑州", "石家庄","太原","呼和浩特","沈阳", "大连", "长春", "哈尔滨","上海","南京","武汉", "长沙", "广州", "海口", "南宁", "成都", "重庆", "苏州", "杭州", "宁波","温州", "合肥", "福州", "厦门", "南昌", "济南", "台北", "乌鲁木齐","西宁", "兰州", "西安", "昆明", "拉萨", "贵阳"};
281 for(unsigned int i = 0; i < NUM; ++i)
282 std::cout << cityname[order[i]] << std::endl;
283 }
284
285 int main(){
286 std::list<unit> conti;
287 for( unsigned int i = 0; i < 10000; ++i){
288 conti.push_back(unit());
289 }
290 // std::cout << "biaozhi 1" << std::endl;
291 //繁殖的代数
292 for(unsigned int i = 0; i < 100000; ++i){
293 add_unit(conti);
294 std::cout << "种群数量:" << conti.size() << std::endl;
295 for(auto itr = conti.begin(); itr != conti.end(); ++itr)
296 optimize(*itr);
297 select(conti);
298 auto itr = conti.begin();
299 auto dis = itr->distance();
300 while(itr != conti.end()){
301 if(dis > itr->distance())
302 dis = itr->distance();
303 ++itr;
304 }
305 std::cout << "distance = " << dis << std::endl;
306 }
307 auto itr = conti.begin();
308 auto dis = itr->distance();
309 auto theone = *itr;
310 while(itr != conti.end()){
311 if(dis > itr->distance()){
312 dis = itr->distance();
313 theone = *itr;
314 }
315 ++itr;
316 }
317 std::cout << "short distance " << dis << std::endl;
318 print_city(theone.path);
319 return 0;
320 }最终得到的路径如图所示，似乎不错的样子。
后来使用了88个城市，得到的路径如下所示，分别是保留最优个体得到的更好路径和不保留最优个体得到的路径：
来源：oschina
链接：https://my.oschina.net/u/4364212/blog/3228784