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模拟退火算法--求解货郎担问题(C#实现)

王朝c#·作者佚名  2006-01-09
窄屏简体版  字體: |||超大  

具体原理已在前面已经介绍过了。下面是实现过程

退火过程由冷却进度表(Cooling Schedule)控制,包括控制参数的初值t及其衰减因子Δt、每个t值时的迭代次数L和停止条件S。本试验分别使用Temperature、DiminishedRate、MarkovLength、AIM来表示。其参数值经过多次试验反复测试得到最好的组合,当

Temperature=300、DiminishedRate=0.9

MarkovLength=130000、AIM=100

的时候最好。

--------------------------------------------

1 初始化:初始温度T(充分大),初始解状态So(是算法迭代的起点), 每个T值的迭代次数L

2 while(true)

2.1对k=1,……,L做第2.1.1至第2.1.5步:

2.1.1 先预算新解和当前解的差值distinct

2.1.2 if(distinct<0||random(0..1)<exp(distinct/temperature))则产生新解S′并将新解作为当前解

2.1.3 如果 currentPath < bestPath 则 bestPath=currentPath

2.1.4 如果 连续退火了 AIM 次仍没有新的最好解产生则就假设找到了最好路径,跳出循环,结束程序,返回最优解。

2.1.5 如果连续Diminish_T_num此循环都没有更好的解产生则aim+1表明此次退火没有产生新的最好解,并退出此次循环,进行退火,即跳到第2.2步

2.2 降温

2.3 currentPath = bestPath

3 输出最佳路径

----------------------------------------------

初始路径为1,2,…,144,对进度表中的每个参数进行了10次的测试。

² Temperature

测试条件:

DiminishedRate:0.9 MarkovLength:130000 AIM:100 Diminish_ T _num:20000

Temperature

>=31000

31000-30600

30600-30400

30300-30400

<30300

200

0

5

4

1

0

250

1

7

1

0

1

300

1

4

2

2

1

350

0

7

2

2

0

400

2

3

4

1

0

根据初始温度测试,温度<300的时候效果不好出现大的数值的情况比较多,当在300-400的时候各个数据段的数据都会有,单中间的比例比较大,而温度>=400的时候出现的值趋于中间段,也就是温度越大效果越稳定,但是需要花费的时间更多了,因此综合起来,取300的温度比较适合,而且出现小值的情况也不少,在测试过程中曾经得到30159.07的数值。

² DiminishedRate

测试条件:

Temperature:300 MarkovLength:130000 AIM:100 Diminish_ T _num:20000

DiminishedRate

>=31000

31000-30600

30600-30400

30300-30400

<30300

0.70

3

5

1

1

0

0.80

1

5

4

0

0

0.90

0

4

4

1

1

0.95

1

3

4

2

0

温度的降低率,当在0.9的时候从时间和效果上考虑最好,当<=0.7的时候效果明显变差。在0.95的时候速度慢了一倍,而且效果也不是很好。

² MarkovLength

测试条件:

Temperature:300 DiminishedRate:0.9 AIM:100 Diminish_ T _num:20000

当MarkovLength取150000的时候得到的最佳路径大部分都在30300以下,曾经得到30086.52的解,不过需要12秒的时间来完成。当取200000的时候需要17秒时间,当然效果更好、更稳定。

² Diminish_ T _num

测试条件:

MarkovLength:130000 Temperature:300 DiminishedRate:0.9 AIM:100

当Diminish_ T _num取<20000的时候出现大值的几率加大,当>20000的时候产生的值效果好,数值稳定,当时间增加。

-----------------------------------------------

代码如下:

using System;

using System.Collections;

namespace SAA

{

/// <summary>

/// SAA 的摘要说明。

/// </summary>

public class SAA

{

public static double[,] city = {

{0,1073.54,111.29,141.52,174.09,408.02,266.27,266.84,153.88,162.86,509.36,263.15,602.66,395.03,723.71,553.71,555.32,1068.43,410.12,1081.02,454.46,565.85,455.72,665.11,418.44,619.43,493.88,826.23,853.55,750.51,818.26,1152.97,1055,1436.61,1320.27,1355.71,1194.55,1026.9,1550.18,1016.54,1125.84,910.19,705.87,588.4,1814.04,1163.79,1105.81,1578.46,1350.87,920.91,869.01,1644.17,1885.82,1308.77,2997.32,2401.71,1909.44,3121.66,3387.76,2773.73,2388.86,370.87,505.38,549.66,600.7,427,504.05,475.64,907.93,998.98,639.88,885.96,1136.27,1343.93,1245.63,1219.25,1392.84,1056.66,792.11,908.01,1156.91,978.22,1585.64,1194.36,1148.66,1263.54,1399.29,1313.59,1572.14,1662.82,1540.23,1738.19,1963.33,1732.29,1806.79,465.84,604.16,679.48,848.7,897.38,629.09,1103.23,1139.16,954.77,1069.18,965.01,1129.07,1291.64,1350.41,1614.49,1503.12,1505.42,1218.28,1896.57,1847.35,1711.56,1951.27,2163.85,1917.99,2171.49,1734.37,1863.54,2049.69,2188.13,2297.84,2493.83,1510.83,1463.64,2012.5,1406.55,1858.56,1647.1,1732.07,1739.09,1833.37,1618.79,2188.32,2225.18,2089.49,2451.64,2538.94,2743,1985.57,1996.17},

{1073.54,0,964.49,1009.6,1137.39,876.45,993.25,988.64,983.88,1223.43,942.79,1233.47,1055.46,1094.32,1053.51,1473.02,1619.09,2015.95,1382.73,2078.96,1502.41,1119.01,861.51,1032.99,1113.13,1200.15,1058.76,1620.08,1460.25,1364.06,1242.72,1502.48,1687,2178.78,1772.24,1898.09,1654.37,1818.16,2065.22,1362.87,1353.79,1201.66,1243.5,1311.59,2566.51,1687.12,1495.63,2326.49,2065.01,1581.99,1579.98,2272.9,2476.35,1883.68,3772.08,3345.61,2754.62,3791.35,4127.41,3678.64,3239.36,730.62,648.53,552.96,670.01,651.69,703.78,605.15,267.03,117.48,520.46,231.71,171.27,290.55,293.97,154.87,372.94,428.16,426.85,398.29,344.33,289.5,877.62,458.46,544.94,602.13,837.33,540.3,612.16,812.6,673.24,823.54,962.05,692.36,793.05,846.52,766.08,915.76,854.06,699.51,820,614.84,874.52,1005.4,682.88,881.41,955.95,963.23,878.8,1023.16,983.76,1176.99,819.38,1208.51,989.93,1049.65,1209.2,1567.34,1269.28,1636.99,1275.79,1408.64,1592.04,1775.86,1673.91,1870.4,1635.91,1429.67,1973.81,1566.31,1873.95,1633.68,1454.79,1515.23,1686.42,1449.59,2152.14,2000.14,1949.26,2419.27,2873.8,3093.77,1232.57,1274.15},

{111.29,964.49,0,148.22,216.72,369.01,221.28,262.05,99.2,272.25,487.28,348.63,599.04,416.71,711.97,640.34,666.53,1142.56,503.56,1166.87,550.33,535.42,377.19,612.36,401.14,600.23,456.25,862.68,854.92,747.59,787.15,1127.16,1068.42,1476.31,1313.4,1362.64,1185.37,1068.27,1556.86,1026.97,1125.24,907.23,727.79,636.84,1893.46,1204.14,1125.9,1655.5,1421.01,974.23,928.57,1706.87,1946.28,1359.52,3083.89,2504.43,2000.32,3197.43,3471.52,2873.17,2481.94,279.02,419.69,438.49,500.59,316.08,402.78,364.61,806.74,892.49,547.39,781.52,1031.81,1237.33,1143.81,1111.36,1288.79,966.51,699.03,815.84,1060.09,879.78,1505.63,1103.2,1064.54,1179.55,1326.8,1223.43,1473.5,1573.06,1447.79,1644.25,1863.4,1628.07,1705.2,421.68,548.09,647.6,802.59,832.28,582.38,1025.65,1083.2,922.66,998.28,917.7,1081.81,1236.05,1284,1544.43,1436.79,1456.37,1153.44,1822.56,1758.82,1637.28,1873.26,2100.81,1847.62,2114.24,1678.15,1809.79,1998.25,2142.64,2233.49,2431.02,1509.85,1443.57,2002.6,1406.97,1852.16,1633.66,1693.01,1705.49,1809.32,1588.24,2180.92,2198.62,2069.96,2447.37,2575.27,2782.41,1906.95,1920.31},

{141.52,1009.6,148.22,0,313.6,268.96,366.64,126.37,243.07,225.96,367.93,233.82,465.3,270.14,584.3,515.14,611.92,1202.23,391.46,1206.46,574.17,679.4,522.49,760.52,539.46,740.52,601.84,967.48,985.88,880.7,931.99,1270.87,1192.02,1578.13,1449.47,1490.85,1322.45,1168.42,1685.36,886.51,990.74,773.87,582.42,489.26,1755.87,1056.02,981.74,1516.57,1278.48,826.9,782.8,1561.17,1799.85,1211.61,2951.36,2396.56,1873.33,3056.73,3336.31,2758.03,2357.16,280.92,398.2,525.87,626.93,393.01,529.14,440.59,819.07,924.43,538.68,805.99,1053.89,1267.31,1155.51,1148.52,1307.76,946.72,689.14,802.24,1056.86,882.66,1462.21,1085.01,1030.78,1145.01,1270.26,1202.3,1473.63,1549.85,1431.31,1631,1866.39,1646.42,1713.91,327.69,469.36,538.05,709.07,765.31,490.41,979.17,1001.95,813.26,940.05,825.45,989.26,1154.03,1217.64,1483.43,1370.04,1365.69,1084.93,1767.79,1732.41,1583.22,1825.51,2028.45,1786.74,2033.76,1596.54,1724.84,1910.28,2047.46,2162.97,2358.15,1375.91,1323.22,1874.69,1272.14,1721.81,1508.16,1590.74,1597.57,1692.47,1477.32,2051.34,2084.06,1949.35,2315.83,2427.78,2634.55,1860.26,1868.62},

{174.09,1137.39,216.72,313.6,0,573.39,178.92,439.85,155.76,253.29,680.92,399.15,776.74,567.38,897.44,671.06,570.24,927.75,520.7,959.44,366.89,419.61,387.59,540.89,266.82,461.7,359,654.95,682.37,581.42,666.74,994.3,881.1,1267.21,1150.77,1182.41,1026.26,857.87,1376.81,1188.96,1299.7,1084.25,876.21,747.32,1929.14,1323.55,1275.48,1698.39,1481.83,1072.58,1015.57,1782.76,2026.13,1460.31,3096.23,2457.69,2001.86,3239.63,3491.65,2840.36,2474.41,492.79,634.76,588.1,574.06,489.16,487.63,533.49,1004.98,1077.09,758.02,973.05,1221.44,1419.23,1338.92,1288.89,1478.21,1177.03,908.22,1025.26,1263.67,1081.96,1720.74,1312.58,1278.44,1393.36,1543.43,1433.36,1673.26,1782.79,1655.33,1849.92,2060.21,1815.92,1899.09,629.34,761.59,848.92,1012.59,1048.53,792.1,1241.69,1297.52,1124.69,1215,1128.46,1292.74,1450.36,1500.57,1761.15,1653.37,1668.38,1369.8,2038.95,1969.31,1853.67,2088.81,2317.11,2064.32,2329.35,1892.86,2023.76,2211.45,2353.3,2449.97,2647.32,1684.59,1636.82,2186.59,1580.21,2032.61,1821.04,1900.06,1909.13,2005.97,1789.72,2362.38,2397.35,2262.9,2625.53,2698.67,2900.48,2122.33,2136.37},

{408.02,876.45,369.01,268.96,573.39,0,578.42,161.08,465.03,475.18,130.68,407.17,264.88,217.92,356.72,601.03,819.42,1470.46,532.08,1469.98,836.85,887.18,671.34,935.36,764.62,958.81,804.49,1227.72,1221.31,1112.96,1132.42,1473.37,1437.12,1840.53,1674.17,1729.67,1545.2,1431.26,1923.58,695.44,775.02,557.92,439.22,445.03,1734.48,932.93,809.76,1492.04,1237.2,754.54,734.2,1487.98,1715.43,1112.18,2942.85,2470.28,1895.01,3008.1,3314.49,2809.59,2381.58,222.73,230.02,523.35,698.73,404.98,612.65,436.02,643.36,773.52,358.56,650.42,881.42,1100.17,964.62,996.33,1123.33,721.63,489.75,590.44,848.77,689.38,1208.23,858.26,789,900.78,1009.11,970.25,1261.53,1311.88,1201.09,1402.18,1653.59,1455.38,1509.48,59.41,205,278.64,440.68,502.2,221.45,727.1,733.19,553.72,680.14,557,721.07,885.14,952.16,1219.4,1104.04,1097.4,819.07,1505.97,1490.3,1322.24,1567.35,1760.35,1522.18,1764.81,1327.59,1455.96,1641.74,1780.62,1895.17,2089.84,1155.69,1076.01,1639.25,1055.07,1491.63,1268.83,1326.74,1337.21,1440.55,1219.38,1818.98,1829.61,1702.05,2087.39,2274.02,2486.76,1602.63,1608.16},

{266.27,993.25,221.28,366.64,178.92,578.42,0,483.29,123.57,403.77,702.44,528.27,818.85,636.69,929.04,815.89,748.47,1031.93,668.7,1086.09,532.6,314.2,209.35,399.36,187.26,381.17,235.26,689.96,644.57,535.49,565.94,905.89,865.61,1299.04,1096.21,1152.97,967.54,898.2,1346.39,1248.04,1344.41,1126.22,948.55,848.91,2077.5,1420.93,1347.06,1843.04,1617.02,1184.19,1134.13,1910.19,2151.56,1571.4,3255.24,2632.48,2163.73,3386.21,3647.89,3012.58,2639.7,432.48,571.4,440.48,397.43,367.09,315.5,403.77,890.11,944.31,673.61,849.73,1092.34,1280.37,1215.44,1147.12,1346.66,1083.82,815.94,931.29,1154.03,972.13,1640.56,1214.81,1195.56,1309.01,1478.69,1335.96,1554.04,1682.63,1550.57,1740.17,1934.96,1680.79,1770.6,626,737.76,855.48,997.01,1003.45,780.25,1171.7,1263.15,1127.52,1157.23,1109.44,1271.89,1415.01,1446.86,1698.86,1598.42,1641.78,1320.17,1967.73,1870.36,1783.13,2009.87,2264.08,1999.56,2286.2,1853.36,1987.68,2178.39,2329.45,2394.17,2593.59,1728.44,1653.91,2217.34,1626.05,2068.55,1847.2,1887.93,1905.32,2016.26,1790.96,2396.61,2403.05,2279.42,2664.16,2794.02,3000.16,2042.07,2061.21},

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