计算智能-群智能算法-蚁群算法matlab实现
2024-05-13 11:28:25
方法一：Main_0
信息素跟随蚂蚁一步一变化(已完成，信息素变化函Pheromones_Change_0)
方法二：Main_1
信息素在蚂蚁走完一圈后一次性变化(Main1已完成，信息素变化函数Pheromones_Change_1)
辅助函数：
Distance_citys_Array()：TSP问题att48的城市距离矩阵
Initial_Map()：根据城市坐标返回城市距离矩阵
Next_City()：根据当前信息素地图给出蚂蚁下一城市编号
Pheromones_Change()：用于方法一的信息素增加
Pheromones_Change_1()：用于方法二的信息素增加
改进方向：
1、根据信息素对路径的选择函数可继续优化
2、信息素增加函数/挥发率可继续优化，使得结果收敛更快且总移动距离更低
3、信息素变化函数可改进为并行运算方式以提高运算速度(目前能力有限，未想到改进方法)
当前最短路程：33522
最优路径如下：
Best_Points=[1,8,38,31,44,18,7,28,6,37,19,27,17,43,30,36,46,33,20,47,21,32,39,48,5,42,24,10,45,35,4,26,2,29,34,41,16,22,3,23,14,25,13,11,12,15,40,9];
当前已达到的最短总路程：35000左右
方法一：
%城市数量初始化
Point_Nums=48;%城市数量
Points=[1:Point_Nums;rand(2,Point_Nums).*Point_Nums]';%城市编号 城市横坐标 城市纵坐标
%Distance_Map= Initial_Map(Point_Nums,Points);%城市距离矩阵形成
Distance_Map=Distance_citys_Array();
%当前最短路程：33522
%最优路径如下：
Best_Points=[1,8,38,31,44,18,7,28,6,37,19,27,17,43,30,36,46,33,20,47,21,32,39,48,5,42,24,10,45,35,4,26,2,29,34,41,16,22,3,23,14,25,13,11,12,15,40,9];%信息素地图初始化
temp=rand(Point_Nums,Point_Nums);
Pheromones_Map=abs(temp-temp');
Pheromones_evaporation_rate=0.1;%信息素挥发率
Ant_Nums=1000;%蚂蚁数量
Frequence=1000;%循环次数
Pop_Ants=zeros(Ant_Nums,3+Point_Nums);%蚂蚁序号 蚂蚁当前位置 蚂蚁已走距离
temp=1:Ant_Nums;
Pop_Ants(:,1)=temp';%序号初始化
temp=round(rand(1,Ant_Nums).*(Point_Nums-1));
Pop_Ants(:,2)=temp+1;%初始位置
Pop_Ants(:,3)=zeros(Ant_Nums,1);%已走距离初始化
Pop_Ants(:,4:3+Point_Nums)=ones(Ant_Nums,Point_Nums);%已走城市flag矩阵
for i=1:Ant_NumsPop_Ants(i,3+Pop_Ants(i,2))=0;%已走城市flag更新
endflag_0=0;
Min_Dis=zeros(Frequence,Point_Nums+2);%初始位置+更新位置+距离
while(flag_0<Frequence)flag_1=0;Start_Point=Pop_Ants(:,2);%记录初始位置?Next_Trace=zeros(Ant_Nums,Point_Nums);%记录已走路线while(flag_1<Point_Nums-1)Next_Point=Next_City(Point_Nums,Ant_Nums,Pop_Ants(:,2),Pop_Ants(:,4:3+Point_Nums),Pheromones_Map);%计算下一城市Next_Trace(:,flag_1+1)=Next_Point;%路线记录Move_Ant=[Pop_Ants(:,2) Next_Point];%蚂蚁本次移动始末城市记录for i=1:Ant_NumsPop_Ants(i,3)=Pop_Ants(i,3)+Distance_Map(Move_Ant(i,1),Move_Ant(i,2));%已走距离更新Pop_Ants(i,3+Move_Ant(i,2))=0;%已走城市flag更新Pheromones_Map=Pheromones_Change(Move_Ant(i,1),Move_Ant(i,2),Pheromones_Map,Distance_Map);%信息素增加end%当前位置更新Pop_Ants(:,2)=Next_Point;flag_1=flag_1+1;endPheromones_Map=Pheromones_Map.*(1-Pheromones_evaporation_rate);%信息素整体挥发Next_Point=Start_Point;%回到起点Next_Trace(:,flag_1+1)=Next_Point;%路线记录Move_Ant=[Pop_Ants(:,2) Next_Point];%蚂蚁本次移动始末城市记录for i=1:Ant_NumsPop_Ants(i,3)=Pop_Ants(i,3)+Distance_Map(Move_Ant(i,1),Move_Ant(i,2));%已走距离更新Pop_Ants(i,3+Move_Ant(i,2))=0;%已走城市flag更新Pheromones_Map=Pheromones_Change(Move_Ant(i,1),Move_Ant(i,2),Pheromones_Map,Distance_Map);%信息素增加endtemp=sortrows(Pop_Ants,3);%根据已走距离对Pop_Ants进行升序行排序Min_Dis(flag_0+1,:)=[Start_Point(temp(1,1),1) Next_Trace(temp(1,1),:) temp(1,3)];%最短距离路线记录%一次循环结束，Pop_Ants初始化temp=round(rand(1,Ant_Nums).*(Point_Nums-1));Pop_Ants(:,2)=temp+1;%初始位置Pop_Ants(:,3)=zeros(Ant_Nums,1);%已走距离Pop_Ants(:,4:3+Point_Nums)=ones(Ant_Nums,Point_Nums);%已走城市flag矩阵for i=1:Ant_NumsPop_Ants(i,3+Pop_Ants(i,2))=0;%已走城市flag更新endflag_0=flag_0+1;
end%disp(Min_Dis);
%plot(Points(:,2),Points(:,3),'*');%城市散点图
%hold on;
%路线图
X_Y=zeros(Point_Nums,2);%横纵坐标记录
for i=1:Frequencefor j=1:Point_Nums+1X_Y(j,:)=Points(Min_Dis(i,j),[2,3]);%从城市位置图获取城市横纵坐标enddisp("该路线总距离为："+Min_Dis(i,Point_Nums+2));plot(X_Y(:,1),X_Y(:,2));%pause();
end
disp("该路线最短距离为："+min(Min_Dis(:,Point_Nums+2)));
方法二：
%城市数量初始化
Point_Nums=48;%城市数量
Points=[1:Point_Nums;rand(2,Point_Nums).*Point_Nums]';%城市编号 城市横坐标 城市纵坐标
%Distance_Map= Initial_Map(Point_Nums,Points);%城市距离矩阵形成
Distance_Map=Distance_citys_Array();
%当前最短路程：33522
%最优路径如下：
Best_Points=[1,8,38,31,44,18,7,28,6,37,19,27,17,43,30,36,46,33,20,47,21,32,39,48,5,42,24,10,45,35,4,26,2,29,34,41,16,22,3,23,14,25,13,11,12,15,40,9];%信息素地图初始化
temp=rand(Point_Nums,Point_Nums);
Pheromones_Map=abs(temp-temp');
Pheromones_evaporation_rate=0.1;%信息素挥发率
Ant_Nums=1000;%蚂蚁数量
Frequence=1000;%循环次数
Pop_Ants=zeros(Ant_Nums,3+Point_Nums);%蚂蚁序号 蚂蚁当前位置 蚂蚁已走距离
temp=1:Ant_Nums;
Pop_Ants(:,1)=temp';%序号初始化
temp=round(rand(1,Ant_Nums).*(Point_Nums-1));
Pop_Ants(:,2)=temp+1;%初始位置
Pop_Ants(:,3)=zeros(Ant_Nums,1);%已走距离初始化
Pop_Ants(:,4:3+Point_Nums)=ones(Ant_Nums,Point_Nums);%已走城市flag矩阵
for i=1:Ant_NumsPop_Ants(i,3+Pop_Ants(i,2))=0;%已走城市flag更新
endflag_0=0;
Min_Dis=zeros(Frequence,Point_Nums+2);%初始位置+更新位置+距离
while(flag_0<Frequence)flag_1=0;Start_Point=Pop_Ants(:,2);%记录初始位置?Next_Trace=zeros(Ant_Nums,Point_Nums);%记录已走路线while(flag_1<Point_Nums-1)Next_Point=Next_City(Point_Nums,Ant_Nums,Pop_Ants(:,2),Pop_Ants(:,4:3+Point_Nums),Pheromones_Map);%计算下一城市Next_Trace(:,flag_1+1)=Next_Point;%路线记录Move_Ant=[Pop_Ants(:,2) Next_Point];%蚂蚁本次移动始末城市记录for i=1:Ant_NumsPop_Ants(i,3)=Pop_Ants(i,3)+Distance_Map(Move_Ant(i,1),Move_Ant(i,2));%已走距离更新Pop_Ants(i,3+Move_Ant(i,2))=0;%已走城市flag更新end%当前位置更新Pop_Ants(:,2)=Next_Point;flag_1=flag_1+1;endNext_Point=Start_Point;%回到起点Next_Trace(:,flag_1+1)=Next_Point;%路线记录Move_Ant=[Pop_Ants(:,2) Next_Point];%蚂蚁本次移动始末城市记录for i=1:Ant_NumsPop_Ants(i,3)=Pop_Ants(i,3)+Distance_Map(Move_Ant(i,1),Move_Ant(i,2));%已走距离更新Pop_Ants(i,3+Move_Ant(i,2))=0;%已走城市flag更新endPheromones_Map=Pheromones_Map.*(1-Pheromones_evaporation_rate);%信息素整体挥发%整体路线Trace=[Start_Point Next_Trace];Pheromones_Map=Pheromones_Change_1(Ant_Nums,Point_Nums,Trace,Pheromones_Map,Distance_Map);%信息素增加temp=sortrows(Pop_Ants,3);%根据已走距离对Pop_Ants进行升序行排序Min_Dis(flag_0+1,:)=[Start_Point(temp(1,1),1) Next_Trace(temp(1,1),:) temp(1,3)];%最短距离路线记录%一次循环结束，Pop_Ants初始化temp=round(rand(1,Ant_Nums).*(Point_Nums-1));Pop_Ants(:,2)=temp+1;%初始位置Pop_Ants(:,3)=zeros(Ant_Nums,1);%已走距离Pop_Ants(:,4:3+Point_Nums)=ones(Ant_Nums,Point_Nums);%已走城市flag矩阵for i=1:Ant_NumsPop_Ants(i,3+Pop_Ants(i,2))=0;%已走城市flag更新endflag_0=flag_0+1;
end%disp(Min_Dis);
%plot(Points(:,2),Points(:,3),'*');%城市散点图
%hold on;
%路线图
X_Y=zeros(Point_Nums,2);%横纵坐标记录
for i=1:Frequencefor j=1:Point_Nums+1X_Y(j,:)=Points(Min_Dis(i,j),[2,3]);%从城市位置图获取城市横纵坐标enddisp("该路线总距离为："+Min_Dis(i,Point_Nums+2));plot(X_Y(:,1),X_Y(:,2));%pause();
end
disp("该路线最短距离为："+min(Min_Dis(:,Point_Nums+2)));
自定义函数：
function [Ret]=Initial_Map(Point_Nums,Points)
%接收参数：城市数量，[城市编号 城市横坐标 城市纵坐标]
%返回：城市距离矩阵
Ret=zeros(Point_Nums,Point_Nums);
for i=1:Point_Numsfor j=1:Point_NumsRet(i,j)=sqrt((Points(i,2)-Points(j,2))^2+(Points(i,3)-Points(j,3))^2);end
end
end
function [Ret]=Distance_citys_Array()
Ret=[0,4727,1205,6363,3657,3130,2414,563,463,5654,1713,1604,2368,2201,1290,1004,3833,2258,3419,2267,2957,720,1700,5279,2578,6076,3465,2654,3625,3115,1574,3951,1748,2142,6755,2383,3306,1029,3530,825,2188,4820,3489,1947,6835,1542,2379,3744;4727,0,3588,2012,1842,6977,6501,5187,5028,2327,4148,4723,3635,3125,4907,3930,7463,6338,7243,5105,4043,4022,3677,2863,3106,1850,7173,6630,1204,6814,6001,3447,5253,2656,3123,6274,7183,5622,3085,4564,2756,1591,7027,6186,3472,5461,4390,2088;1205,3588,0,5163,2458,3678,3071,1742,1444,4462,1184,1520,1498,1103,1501,951,4298,2903,3967,2169,2209,652,828,4136,1518,4873,3954,3254,2446,3581,2441,2960,1966,950,5564,2916,3878,2035,2482,1027,1395,3617,3891,2686,5661,2023,1867,2560;6363,2012,5163,0,2799,8064,7727,6878,6581,1402,5366,5946,4679,4378,6225,5709,8417,7578,8296,6135,4802,5707,4982,2322,4178,320,8186,7800,2778,7859,7408,3763,6461,4223,1427,7451,8263,7131,3669,6011,4638,1681,7987,7502,1877,6758,5360,2844;3657,1842,2458,2799,0,5330,4946,4200,3824,2012,2573,3157,1924,1580,3427,3179,5749,4793,5577,3409,2223,3066,2185,1860,1401,2491,5486,5035,894,5141,4611,1669,3677,1590,3113,4682,5533,4352,1252,3227,2426,1169,5313,4706,3241,3962,2651,304;3130,6977,3678,8064,5330,0,743,3209,2670,6929,2831,2266,3407,3854,2178,4076,727,881,293,1930,3310,3672,3315,6199,3932,7745,365,482,5774,261,1659,4513,1746,4431,7910,769,207,2225,4435,2681,5053,6384,550,1224,7805,1670,2704,5230;2414,6501,3071,7727,4946,743,0,2468,1952,6673,2380,1795,3051,3405,1604,3382,1469,168,1020,1681,3110,2993,2827,6009,3552,7412,1104,267,5300,821,916,4348,1270,3890,7698,332,900,1484,4185,2049,4415,6051,1219,482,7635,1054,2432,4884;563,5187,1742,6878,4200,3209,2468,0,718,6203,2241,2051,2920,2762,1687,1304,3932,2331,3487,2669,3487,1175,2260,5840,3141,6596,3563,2728,4120,3240,1559,4507,2082,2658,7304,2512,3364,985,4091,1319,2544,5358,3632,1987,7391,1785,2879,4296;463,5028,1444,6581,3824,2670,1952,718,0,5789,1602,1343,2330,2291,970,1451,3376,1796,2959,1951,2835,1112,1725,5346,2628,6285,3007,2193,3889,2661,1122,3920,1372,2391,6883,1927,2845,611,3543,676,2590,4993,3039,1486,6934,1112,2196,3876;5654,2327,4462,1402,2012,6929,6673,6203,5789,0,4392,4947,3648,3501,5274,5183,7216,6535,7140,5022,3621,5077,4090,922,3207,1131,7014,6714,2437,6707,6477,2476,5432,3599,1102,6376,7121,6284,2497,5160,4318,937,6795,6507,1268,5773,4249,1914;1713,4148,1184,5366,2573,2831,2380,2241,1602,4392,0,586,766,1029,883,2040,3353,2224,3100,1049,1246,1625,503,3841,1196,5054,3042,2488,2945,2676,2087,2331,1114,1650,5459,2132,3037,1958,1997,931,2513,3701,2923,2137,5459,1394,711,2534;1604,4723,1520,5946,3157,2266,1795,2051,1343,4947,586,0,1299,1612,406,2208,2824,1639,2542,694,1586,1767,1050,4357,1770,5633,2498,1907,3520,2128,1558,2778,531,2171,6003,1552,2472,1538,2506,791,2912,4277,2403,1564,5983,827,892,3109;2368,3635,1498,4679,1924,3407,3051,2920,2330,3648,766,1299,0,646,1642,2446,3840,2905,3655,1488,730,2096,697,3076,533,4363,3567,3122,2453,3219,2842,1592,1791,1480,4706,2772,3610,2721,1232,1656,2550,3001,3403,2860,4697,2126,756,1836;2201,3125,1103,4378,1580,3854,3405,2762,2291,3501,1029,1612,646,0,1853,2026,4349,3247,4119,1997,1341,1753,606,3078,419,4070,4052,3517,1923,3690,3032,1866,2142,838,4593,3161,4060,2788,1380,1663,1932,2736,3915,3138,4647,2395,1351,1592;1290,4907,1501,6225,3427,2178,1604,1687,970,5274,883,406,1642,1853,0,2029,2803,1438,2466,986,1987,1593,1253,4716,2072,5915,2454,1764,3710,2082,1204,3164,497,2287,6342,1419,2379,1134,2867,554,2885,4569,2405,1289,6338,555,1297,3406;1004,3930,951,5709,3179,4076,3382,1304,1451,5183,2040,2208,2446,2026,2029,0,4759,3220,4368,2900,3151,442,1765,4960,2444,5443,4396,3610,2932,4034,2572,3891,2525,1590,6278,3313,4261,2033,3398,1476,1241,4287,4390,2928,6419,2428,2749,3337;3833,7463,4298,8417,5749,727,1469,3932,3376,7216,3353,2824,3840,4349,2803,4759,0,1601,477,2359,3617,4345,3851,6433,4372,8098,370,1206,6267,726,2384,4754,2335,4991,8148,1452,609,2949,4752,3331,5687,6746,437,1948,8005,2334,3098,5618;2258,6338,2903,7578,4793,881,168,2331,1796,6535,2224,1639,2905,3247,1438,3220,1601,0,1165,1563,2988,2829,2666,5882,3401,7263,1233,399,5138,923,794,4227,1117,3724,7565,286,1049,1348,4051,1881,4248,5903,1322,355,7508,887,2302,4736;3419,7243,3967,8296,5577,293,1020,3487,2959,7140,3100,2542,3655,4119,2466,4368,477,1165,0,2170,3520,3965,3588,6393,4183,7977,202,767,6041,438,1932,4706,2027,4711,8107,1061,132,2503,4652,2972,5344,6617,486,1501,7989,1962,2939,5469;2267,5105,2169,6135,3409,1930,1681,2669,1951,5022,1049,694,1488,1997,986,2900,2359,1563,2170,0,1430,2460,1547,4333,2019,5817,2079,1694,3910,1733,1813,2668,654,2694,6029,1366,2130,1991,2525,1474,3542,4455,1923,1641,5957,1071,777,3302;2957,4043,2209,4802,2223,3310,3110,3487,2835,3621,1246,1586,730,1341,1987,3151,3617,2988,3520,1430,0,2779,1387,2905,1062,4482,3398,3119,2922,3087,3115,1240,1953,2175,4607,2796,3501,3119,1136,2173,3268,3136,3189,3029,4527,2355,711,2042;720,4022,652,5707,3066,3672,2993,1175,1112,5077,1625,1767,2096,1753,1593,442,4345,2829,3965,2460,2779,0,1401,4781,2166,5427,3984,3212,2946,3620,2224,3603,2089,1496,6178,2906,3861,1719,3132,1040,1479,4211,3969,2553,6290,2012,2336,3189;1700,3677,828,4982,2185,3315,2827,2260,1725,4090,503,1050,697,606,1253,1765,3851,2666,3588,1547,1387,1401,0,3621,903,4675,3537,2954,2475,3169,2427,2254,1578,1148,5177,2598,3521,2194,1833,1074,2054,3340,3423,2541,5213,1801,1077,2190;5279,2863,4136,2322,1860,6199,6009,5840,5346,922,3841,4357,3076,3078,4716,4960,6433,5882,6393,4333,2905,4781,3621,0,2718,2042,6254,6024,2569,5966,5913,1687,4807,3384,1716,5699,6384,5787,1852,4687,4285,1272,6022,5892,1629,5178,3581,1639;2578,3106,1518,4178,1401,3932,3552,3141,2628,3207,1196,1770,533,419,2072,2444,4372,3401,4183,2019,1062,2166,903,2718,0,3864,4097,3635,1932,3748,3274,1448,2284,1164,4286,3283,4136,3086,967,1973,2285,2507,3935,3331,4312,2589,1284,1340;6076,1850,4873,320,2491,7745,7412,6596,6285,1131,5054,5633,4363,4070,5915,5443,8098,7263,7977,5817,4482,5427,4675,2042,3864,0,7866,7483,2515,7539,7101,3449,6146,3938,1375,7134,7944,6831,3349,5709,4397,1363,7667,7190,1798,6446,5041,2528;3465,7173,3954,8186,5486,365,1104,3563,3007,7014,3042,2498,3567,4052,2454,4396,370,1233,202,2079,3398,3984,3537,6254,4097,7866,0,839,5973,374,2019,4569,1996,4669,7970,1085,305,2581,4532,2976,5339,6509,287,1581,7844,1974,2838,5369;2654,6630,3254,7800,5035,482,267,2728,2193,6714,2488,1907,3122,3517,1764,3610,1206,399,767,1694,3119,3212,2954,6024,3635,7483,839,0,5427,558,1181,4349,1377,4044,7723,356,653,1744,4218,2241,4614,6121,955,743,7644,1231,2465,4957;3625,1204,2446,2778,894,5774,5300,4120,3889,2437,2945,3520,2453,1923,3710,2932,6267,5138,6041,3910,2922,2946,2475,2569,1932,2515,5973,5427,0,5612,4824,2550,4050,1498,3476,5071,5980,4470,2096,3388,1911,1501,5831,4994,3704,4264,3209,1196;3115,6814,3581,7859,5141,261,821,3240,2661,6707,2676,2128,3219,3690,2082,4034,726,923,438,1733,3087,3620,3169,5966,3748,7539,374,558,5612,0,1716,4280,1624,4298,7679,735,420,2263,4216,2606,4967,6179,400,1277,7567,1609,2501,5032;1574,6001,2441,7408,4611,1659,916,1559,1122,6477,2087,1558,2842,3032,1204,2572,2384,794,1932,1813,3115,2224,2427,5913,3274,7101,2019,1181,4824,1716,0,4330,1180,3346,7545,1023,1808,578,4062,1438,3693,5763,2115,440,7537,763,2404,4603;3951,3447,2960,3763,1669,4513,4348,4507,3920,2476,2331,2778,1592,1866,3164,3891,4754,4227,4706,2668,1240,3603,2254,1687,1448,3449,4569,4349,2550,4280,4330,0,3184,2510,3402,4031,4698,4281,533,3245,3612,2187,4339,4265,3296,3576,1941,1381;1748,5253,1966,6461,3677,1746,1270,2082,1372,5432,1114,531,1791,2142,497,2525,2335,1117,2027,654,1953,2089,1578,4807,2284,6146,1996,1377,4050,1624,1180,3184,0,2685,6475,1022,1952,1341,2963,1050,3358,4787,1926,1086,6436,422,1244,3619;2142,2656,950,4223,1590,4431,3890,2658,2391,3599,1650,2171,1480,838,2287,1590,4991,3724,4711,2694,2175,1496,1148,3384,1164,3938,4669,4044,1498,4298,3346,2510,2685,0,4697,3693,4636,2975,1981,1909,1124,2718,4565,3548,4830,2839,2140,1751;6755,3123,5564,1427,3113,7910,7698,7304,6883,1102,5459,6003,4706,4593,6342,6278,8148,7565,8107,6029,4607,6178,5177,1716,4286,1375,7970,7723,3476,7679,7545,3402,6475,4697,0,7393,8097,7370,3515,6249,5379,2001,7738,7556,461,6829,5267,3013;2383,6274,2916,7451,4682,769,332,2512,1927,6376,2132,1552,2772,3161,1419,3313,1452,286,1061,1366,2796,2906,2598,5699,3283,7134,1085,356,5071,735,1023,4031,1022,3693,7393,0,965,1542,3883,1913,4286,5772,1121,600,7322,902,2128,4608;3306,7183,3878,8263,5533,207,900,3364,2845,7121,3037,2472,3610,4060,2379,4261,609,1049,132,2130,3501,3861,3521,6384,4136,7944,305,653,5980,420,1808,4698,1952,4636,8097,965,0,2380,4629,2877,5250,6583,570,1380,7986,1866,2904,5432;1029,5622,2035,7131,4352,2225,1484,985,611,6284,1958,1538,2721,2788,1134,2033,2949,1348,2503,1991,3119,1719,2194,5787,3086,6831,2581,1744,4470,2263,578,4281,1341,2975,7370,1542,2380,0,3952,1127,3197,5518,2658,1002,7395,951,2429,4380;3530,3085,2482,3669,1252,4435,4185,4091,3543,2497,1997,2506,1232,1380,2867,3398,4752,4051,4652,2525,1136,3132,1833,1852,967,3349,4532,4218,2096,4216,4062,533,2963,1981,3515,3883,4629,3952,0,2873,3080,2012,4324,4046,3478,3328,1755,1000;825,4564,1027,6011,3227,2681,2049,1319,676,5160,931,791,1656,1663,554,1476,3331,1881,2972,1474,2173,1040,1074,4687,1973,5709,2976,2241,3388,2606,1438,3245,1050,1909,6249,1913,2877,1127,2873,0,2374,4392,2943,1659,6285,1012,1563,3254;2188,2756,1395,4638,2426,5053,4415,2544,2590,4318,2513,2912,2550,1932,2885,1241,5687,4248,5344,3542,3268,1479,2054,4285,2285,4397,5339,4614,1911,4967,3693,3612,3358,1124,5379,4286,5250,3197,3080,2374,0,3386,5284,3997,5585,3386,3125,2664;4820,1591,3617,1681,1169,6384,6051,5358,4993,937,3701,4277,3001,2736,4569,4287,6746,5903,6617,4455,3136,4211,3340,1272,2507,1363,6509,6121,1501,6179,5763,2187,4787,2718,2001,5772,6583,5518,2012,4392,3386,0,6314,5837,2205,5095,3680,1169;3489,7027,3891,7987,5313,550,1219,3632,3039,6795,2923,2403,3403,3915,2405,4390,437,1322,486,1923,3189,3969,3423,6022,3935,7667,287,955,5831,400,2115,4339,1926,4565,7738,1121,570,2658,4324,2943,5284,6314,0,1676,7603,1964,2662,5184;1947,6186,2686,7502,4706,1224,482,1987,1486,6507,2137,1564,2860,3138,1289,2928,1948,355,1501,1641,3029,2553,2541,5892,3331,7190,1581,743,4994,1277,440,4265,1086,3548,7556,600,1380,1002,4046,1659,3997,5837,1676,0,7521,744,2325,4670;6835,3472,5661,1877,3241,7805,7635,7391,6934,1268,5459,5983,4697,4647,6338,6419,8005,7508,7989,5957,4527,6290,5213,1629,4312,1798,7844,7644,3704,7567,7537,3296,6436,4830,461,7322,7986,7395,3478,6285,5585,2205,7603,7521,0,6805,5208,3102;1542,5461,2023,6758,3962,1670,1054,1785,1112,5773,1394,827,2126,2395,555,2428,2334,887,1962,1071,2355,2012,1801,5178,2589,6446,1974,1231,4264,1609,763,3576,422,2839,6829,902,1866,951,3328,1012,3386,5095,1964,744,6805,0,1644,3928;2379,4390,1867,5360,2651,2704,2432,2879,2196,4249,711,892,756,1351,1297,2749,3098,2302,2939,777,711,2336,1077,3581,1284,5041,2838,2465,3209,2501,2404,1941,1244,2140,5267,2128,2904,2429,1755,1563,3125,3680,2662,2325,5208,1644,0,2532;3744,2088,2560,2844,304,5230,4884,4296,3876,1914,2534,3109,1836,1592,3406,3337,5618,4736,5469,3302,2042,3189,2190,1639,1340,2528,5369,4957,1196,5032,4603,1381,3619,1751,3013,4608,5432,4380,1000,3254,2664,1169,5184,4670,3102,3928,2532,0];
end
function [Ret] = Next_City(Point_Nums,Ant_Nums,Local_Ants,Flag_Map,Pheromones_Map)
%接收参数：城市数量，蚂蚁数量，蚂蚁当前位置，蚂蚁已走过标记地图，信息素地图
%返回蚂蚁下一位置矩阵
%此处使用轮盘赌产生返回结果%第一步构造信息素总量地图Pheromones_Sum_Array
temp=Pheromones_Map(Local_Ants,:).*Flag_Map;%蚂蚁未经过城市的信息素矩阵
P_S_Array=[zeros(Ant_Nums,1) temp];%第一列为0，其余为未走过城市的信息素
for i=2:Point_Nums+1P_S_Array(:,i)=(P_S_Array(:,i)+P_S_Array(:,i-1));
end%第二步构造随机选择数矩阵Rand_Array
R_Array=rand(Ant_Nums,1).*P_S_Array(:,1+Point_Nums);%第三步遍历每一个城市开始生成Ret
Ret=zeros(Ant_Nums,1);
for i=1:Point_Numstemp=(P_S_Array(1:Ant_Nums,i)<=R_Array).*(R_Array<P_S_Array(1:Ant_Nums,i+1));%随机数落在[a,b)，则选中那一列Ret=Ret+temp.*i;%点乘i意为第i个城市
end
end
function [Ret] = Pheromones_Change(Point_x,Point_y,Pheromones_Map,Distance_Map)
%接收参数：源城市、目标城市、挥发率、信息素地图、距离地图
%信息素增加
Pheromones_Map(Point_x,Point_y)=Pheromones_Map(Point_x,Point_y)+5./Distance_Map(Point_x,Point_y);%信息素变动=信息素增加+信息素挥发
Pheromones_Map(Point_y,Point_x)=Pheromones_Map(Point_x,Point_y);%对称位置信息素变动
Ret=Pheromones_Map;
end
function [Ret] = Pheromones_Change_1(Ant_Nums,Point_Nums,Trace,Pheromones_Map,Distance_Map)
%接收参数：蚂蚁总数、城市总数、蚁群轨迹、信息素地图、距离地图
%信息素增加
for i=1:Ant_Numsfor j=1:Point_NumsPheromones_Map(Trace(i,j),Trace(i,j+1))=Pheromones_Map(Trace(i,j),Trace(i,j+1))+5./Distance_Map(Trace(i,j),Trace(i,j+1));Pheromones_Map(Trace(i,j+1),Trace(i,j))=Pheromones_Map(Trace(i,j),Trace(i,j+1));end
end
Ret=Pheromones_Map;
end
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