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蚁群算法

分类： C/C++

2016-01-30 14:29:29

蚁群算法(ant colony optimization, ACO)，又称蚂蚁算法，是一种用来在图中寻找优化路径的机率型算法。它由Marco Dorigo于1992年在他的博士论文中提出，其灵感来源于蚂蚁在寻找食物过程中发现路径的行为。蚁群算法是一种模拟进化算法，初步的研究表明该算法具有许多优良的性质。针对PID控制器参数优化设计问题，将蚁群算法设计的结果与遗传算法设计的结果进行了比较，数值仿真结果表明，蚁群算法具有一种新的模拟进化优化方法的有效性和应用价值。

        各个蚂蚁在没有事先告诉他们食物在什么地方的前提下开始寻找食物。当一只找到食物以后，它会向环境释放一种挥发性分泌物pheromone (称为信息素,该信息素随着时间的推移会逐渐挥发消失，信息素浓 度的大小表征路径的远近)来实现的，吸引其他的蚂蚁过来，这样越来越多的蚂蚁会找到食物。有些蚂蚁并没有象其它蚂蚁一样总重复同样的路，他们会另辟蹊径， 如果另开辟的道路比原来的其他道路更短，那么，渐渐地，更多的蚂蚁被吸引到这条较短的路上来。最后，经过一段时间运行，可能会出现一条最短的路径被大多数蚂蚁重复着。

        下面看一个实际的例子，用蚁群算法解决TSP问题，直接上代码：

JAVA：

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  1. package ant;
  2.       
  3.     import java.util.Random;
  4.       
  5.     /**
  6.      * 蚂蚁类
  7.      * @Time 2014-5-17
  8.      */
  9.     public class Ant {
  10.         private int[] tour; //蚂蚁的路径
  11.          private int[] city; //存储是否访问过某一城市
  12.          private int length; //蚂蚁当前走过的距离
  13.          private int count; //城市个数
  14.            
  15.          public int[] getTour() {
  16.             return tour;
  17.         }
  18.       
  19.         public int getLength() {
  20.             return length;
  21.         }
  22.           
  23.         public void init(int count) {
  24.              this.count = count;
  25.              city = new int[count];
  26.              tour = new int[count+1];
  27.              for(int i=0; i<count; i++) {
  28.                  city[i] = 0;
  29.              }
  30.              int random = new Random(System.currentTimeMillis()).nextInt(count);
  31.              city[random] = 1;
  32.              tour[0] = random;
  33.          }
  34.            
  35.          public void SelectNextCity(int index, double [][]pheromone, int[][] distance) {
  36.              int current = tour[index-1];
  37.              double []p = new double[count];
  38.              double sum = 0.0;
  39.              for(int i=0; i<count; i++) {
  40.                  if(city[i] == 0) {
  41.                      sum += pheromone[current][i]/(Math.pow(distance[current][i], 2));
  42.                  }
  43.              }
  44.              for(int i=0; i<count; i++) {
  45.                  if(city[i] == 1) {
  46.                      p[i] = 0.0;
  47.                  } else {
  48.                      p[i] = pheromone[current][i]/(Math.pow(distance[current][i], 2))/sum;
  49.                  }
  50.              }
  51.              int select = getSelect(p);
  52.              tour[index] = select;
  53.              city[select] = 1;
  54.          }
  55.       
  56.         private int getSelect(double[] p) {
  57.             double selectP = new Random(System.currentTimeMillis()).nextDouble();
  58.             double sumSel = 0.0;
  59.             for(int i=0; i<count; i++) {
  60.                 sumSel += p[i];
  61.                 if(sumSel>selectP) return i;
  62.             }
  63.             return -1;
  64.         }
  65.           
  66.         public void calLength(int [][]distance) {
  67.             length = 0;
  68.             tour[count] = tour[0];
  69.             for(int i=0; i<count; i++) {
  70.                 length += distance[tour[i]][tour[i+1]];
  71.             }
  72.         }
  73.     }


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  1. package ant;
  2. /**
  3.  * 城市类
  4.  * @Time 2014-5-17 
  5.  */
  6. public class Citys {
  7.     private String cityName[] = {"北京", "上海", "天津", "重庆", "哈尔滨", "长春", "沈阳", "呼和浩特",
  8.             "石家庄", "太原", "济南", "郑州", "西安", "杭州", "武汉", "成都", "广州", "昆明", "拉萨"};
  9.     private int[][] distance = new int[34][34];
  10.       
  11.     public void initDis() {
  12.         distance[0][1] = distance[1][0] = 1320;
  13.         distance[0][2] = distance[2][0] = 120;
  14.         distance[0][3] = distance[3][0] = 2080;
  15.         distance[0][4] = distance[4][0] = 1240;
  16.         distance[0][5] = distance[5][0] = 1010;
  17.         distance[0][6] = distance[6][0] = 700;
  18.         distance[0][7] = distance[7][0] = 530;
  19.         distance[0][8] = distance[8][0] = 280;
  20.         distance[0][9] = distance[9][0] = 510;
  21.         distance[0][10] = distance[10][0] = 410;
  22.         distance[0][11] = distance[11][0] = 700;
  23.         distance[0][12] = distance[12][0] = 1220;
  24.         distance[0][13] = distance[13][0] = 1280;
  25.         distance[0][14] = distance[14][0] = 1230;
  26.         distance[0][15] = distance[15][0] = 2130;
  27.         distance[0][16] = distance[16][0] = 2300;
  28.         distance[0][17] = distance[17][0] = 3170;
  29.         distance[0][18] = distance[18][0] = 3760;
  30.         distance[1][2] = distance[2][1] = 1210;
  31.         distance[1][3] = distance[3][1] = 2020;
  32.         distance[1][4] = distance[4][1] = 2420;
  33.         distance[1][5] = distance[5][1] = 2000;
  34.         distance[1][6] = distance[6][1] = 1880;
  35.         distance[1][7] = distance[7][1] = 2380;
  36.         distance[1][8] = distance[8][1] = 1410;
  37.         distance[1][9] = distance[9][1] = 1510;
  38.         distance[1][10] = distance[10][1] = 900;
  39.         distance[1][11] = distance[11][1] = 990;
  40.         distance[1][12] = distance[12][1] = 1500;
  41.         distance[1][13] = distance[13][1] = 170;
  42.         distance[1][14] = distance[14][1] = 810;
  43.         distance[1][15] = distance[15][1] = 2150;
  44.         distance[1][16] = distance[16][1] = 1780;
  45.         distance[1][17] = distance[17][1] = 2660;
  46.         distance[1][18] = distance[18][1] = 4370;
  47.         distance[2][3] = distance[3][2] = 2170;
  48.         distance[2][4] = distance[4][2] = 1240;
  49.         distance[2][5] = distance[5][2] = 990;
  50.         distance[2][6] = distance[6][2] = 690;
  51.         distance[2][7] = distance[7][2] = 750;
  52.         distance[2][8] = distance[8][2] = 420;
  53.         distance[2][9] = distance[9][2] = 660;
  54.         distance[2][10] = distance[10][2] = 320;
  55.         distance[2][11] = distance[11][2] = 830;
  56.         distance[2][12] = distance[12][2] = 1430;
  57.         distance[2][13] = distance[13][2] = 1180;
  58.         distance[2][14] = distance[14][2] = 1350;
  59.         distance[2][15] = distance[15][2] = 2460;
  60.         distance[2][16] = distance[16][2] = 2440;
  61.         distance[2][17] = distance[17][2] = 3120;
  62.         distance[2][18] = distance[18][2] = 3880;
  63.         distance[3][4] = distance[4][3] = 3530;
  64.         distance[3][5] = distance[5][3] = 3190;
  65.         distance[3][6] = distance[6][3] = 2890;
  66.         distance[3][7] = distance[7][3] = 1850;
  67.         distance[3][8] = distance[8][3] = 1800;
  68.         distance[3][9] = distance[9][3] = 1430;
  69.         distance[3][10] = distance[10][3] = 2060;
  70.         distance[3][11] = distance[11][3] = 1390;
  71.         distance[3][12] = distance[12][3] = 780;
  72.         distance[3][13] = distance[13][3] = 1990;
  73.         distance[3][14] = distance[14][3] = 1240;
  74.         distance[3][15] = distance[15][3] = 310;
  75.         distance[3][16] = distance[16][3] = 1700;
  76.         distance[3][17] = distance[17][3] = 1100;
  77.         distance[3][18] = distance[18][3] = 3640;
  78.         distance[4][5] = distance[5][4] = 230;
  79.         distance[4][6] = distance[6][4] = 540;
  80.         distance[4][7] = distance[7][4] = 1720;
  81.         distance[4][8] = distance[8][4] = 1660;
  82.         distance[4][9] = distance[9][4] = 1910;
  83.         distance[4][10] = distance[10][4] = 1590;
  84.         distance[4][11] = distance[11][4] = 2110;
  85.         distance[4][12] = distance[12][4] = 2630;
  86.         distance[4][13] = distance[13][4] = 2730;
  87.         distance[4][14] = distance[14][4] = 2550;
  88.         distance[4][15] = distance[15][4] = 3470;
  89.         distance[4][16] = distance[16][4] = 3650;
  90.         distance[4][17] = distance[17][4] = 4600;
  91.         distance[4][18] = distance[18][4] = 5010;
  92.         distance[5][6] = distance[6][5] = 320;
  93.         distance[5][7] = distance[7][5] = 1480;
  94.         distance[5][8] = distance[8][5] = 1380;
  95.         distance[5][9] = distance[9][5] = 1640;
  96.         distance[5][10] = distance[10][5] = 1280;
  97.         distance[5][11] = distance[11][5] = 1790;
  98.         distance[5][12] = distance[12][5] = 2400;
  99.         distance[5][13] = distance[13][5] = 2790;
  100.         distance[5][14] = distance[14][5] = 2320;
  101.         distance[5][15] = distance[15][5] = 3220;
  102.         distance[5][16] = distance[16][5] = 3390;
  103.         distance[5][17] = distance[17][5] = 4140;
  104.         distance[5][18] = distance[18][5] = 4770;
  105.         distance[6][7] = distance[7][6] = 1450;
  106.         distance[6][8] = distance[8][6] = 1090;
  107.         distance[6][9] = distance[9][6] = 1320;
  108.         distance[6][10] = distance[10][6] = 970;
  109.         distance[6][11] = distance[11][6] = 1400;
  110.         distance[6][12] = distance[12][6] = 2000;
  111.         distance[6][13] = distance[13][6] = 1850;
  112.         distance[6][14] = distance[14][6] = 1930;
  113.         distance[6][15] = distance[15][6] = 2840;
  114.         distance[6][16] = distance[16][6] = 3010;
  115.         distance[6][17] = distance[17][6] = 3840;
  116.         distance[6][18] = distance[18][6] = 4460;
  117.         distance[7][8] = distance[8][7] = 900;
  118.         distance[7][9] = distance[9][7] = 850;
  119.         distance[7][10] = distance[10][7] = 1390;
  120.         distance[7][11] = distance[11][7] = 1330;
  121.         distance[7][12] = distance[12][7] = 1070;
  122.         distance[7][13] = distance[13][7] = 2150;
  123.         distance[7][14] = distance[14][7] = 1870;
  124.         distance[7][15] = distance[15][7] = 2320;
  125.         distance[7][16] = distance[16][7] = 2940;
  126.         distance[7][17] = distance[17][7] = 3010;
  127.         distance[7][18] = distance[18][7] = 4290;
  128.         distance[8][9] = distance[9][8] = 220;
  129.         distance[8][10] = distance[10][8] = 310;
  130.         distance[8][11] = distance[11][8] = 410;
  131.         distance[8][12] = distance[12][8] = 940;
  132.         distance[8][13] = distance[13][8] = 1370;
  133.         distance[8][14] = distance[14][8] = 950;
  134.         distance[8][15] = distance[15][8] = 2080;
  135.         distance[8][16] = distance[16][8] = 2010;
  136.         distance[8][17] = distance[17][8] = 2890;
  137.         distance[8][18] = distance[18][8] = 3470;
  138.         distance[9][10] = distance[10][9] = 540;
  139.         distance[9][11] = distance[11][9] = 640;
  140.         distance[9][12] = distance[12][9] = 690;
  141.         distance[9][13] = distance[13][9] = 1680;
  142.         distance[9][14] = distance[14][9] = 1170;
  143.         distance[9][15] = distance[15][9] = 1490;
  144.         distance[9][16] = distance[16][9] = 2240;
  145.         distance[9][17] = distance[17][9] = 2920;
  146.         distance[9][18] = distance[18][9] = 3250;
  147.         distance[10][11] = distance[11][10] = 650;
  148.         distance[10][12] = distance[12][10] = 1060;
  149.         distance[10][13] = distance[13][10] = 870;
  150.         distance[10][14] = distance[14][10] = 940;
  151.         distance[10][15] = distance[15][10] = 2300;
  152.         distance[10][16] = distance[16][10] = 2010;
  153.         distance[10][17] = distance[17][10] = 2980;
  154.         distance[10][18] = distance[18][10] = 3780;
  155.         distance[11][12] = distance[12][11] = 510;
  156.         distance[11][13] = distance[13][11] = 950;
  157.         distance[11][14] = distance[14][11] = 590;
  158.         distance[11][15] = distance[15][11] = 1350;
  159.         distance[11][16] = distance[16][11] = 1610;
  160.         distance[11][17] = distance[17][11] = 2490;
  161.         distance[11][18] = distance[18][11] = 3380;
  162.         distance[12][13] = distance[13][12] = 1680;
  163.         distance[12][14] = distance[14][12] = 1050;
  164.         distance[12][15] = distance[15][12] = 840;
  165.         distance[12][16] = distance[16][12] = 2120;
  166.         distance[12][17] = distance[17][12] = 1940;
  167.         distance[12][18] = distance[18][12] = 3860;
  168.         distance[13][14] = distance[14][13] = 770;
  169.         distance[13][15] = distance[15][13] = 2280;
  170.         distance[13][16] = distance[16][13] = 1610;
  171.         distance[13][17] = distance[17][13] = 2490;
  172.         distance[13][18] = distance[18][13] = 4530;
  173.         distance[14][15] = distance[15][14] = 1360;
  174.         distance[14][16] = distance[16][14] = 1070;
  175.         distance[14][17] = distance[17][14] = 1950;
  176.         distance[14][18] = distance[18][14] = 3910;
  177.         distance[15][16] = distance[16][15] = 2010;
  178.         distance[15][17] = distance[17][15] = 1100;
  179.         distance[15][18] = distance[18][15] = 3360;
  180.         distance[16][17] = distance[17][16] = 1640;
  181.         distance[16][18] = distance[18][16] = 3980;
  182.         distance[17][18] = distance[18][17] = 4460;
  183.         for(int i=0; i<5; i++) {
  184.             distance[i][i] = 0;
  185.         }
  186.     }
  187.       
  188.     public String[] getCityName() {
  189.         return cityName;
  190.     }
  191.       
  192.     public int[][] getDistance() {
  193.         return distance;
  194.     }
  195. }


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  1. package ant;
  2.       
  3.     /**
  4.      * 蚁群优化算法，用来求解TSP问题
  5.      * @Time 2014-5-17 
  6.      */
  7.     public class ACO {
  8.         Ant []ants;
  9.         int antCount;
  10.         int [][]distance;
  11.         double [][]pheromone;
  12.         int cityCount;
  13.         int []bestTour;
  14.         String []city;
  15.         int bestLength;
  16.           
  17.         public void init(int antCount) {
  18.             this.antCount = antCount;
  19.             ants = new Ant[antCount];
  20.             Citys citys = new Citys();
  21.             citys.initDis();
  22.             distance = citys.getDistance();
  23.             city = citys.getCityName();
  24.             cityCount = city.length;
  25.             pheromone = new double[cityCount][cityCount];
  26.             for(int i=0; i<cityCount; i++) {
  27.                 for(int j=0; j<cityCount; j++) {
  28.                     pheromone[i][j] = 0.1;
  29.                 }
  30.             }
  31.             bestLength = Integer.MAX_VALUE;
  32.             bestTour = new int[cityCount+1];
  33.             for(int i=0;i<antCount;i++){
  34.                 ants[i] = new Ant();
  35.                 ants[i].init(cityCount);
  36.             }
  37.         }
  38.           
  39.          public void run(int maxgen){
  40.              for(int gen=0; gen<maxgen; gen++) {
  41.                  for(int i=0; i<antCount; i++) {
  42.                      for(int j=1;j<cityCount;j++) {
  43.                          ants[i].SelectNextCity(j, pheromone, distance);
  44.                      }
  45.                      ants[i].calLength(distance);
  46.                      if(ants[i].getLength() < bestLength) {
  47.                          bestLength = ants[i].getLength();
  48.                          System.out.println("第" + gen + "代，发现新的解为："+bestLength);
  49.                          for(int j=0; j<cityCount+1; j++) {
  50.                              bestTour[j] = ants[i].getTour()[j];
  51.                              System.out.print(city[bestTour[j]] + " ");
  52.                          }
  53.                          System.out.println();
  54.                      }
  55.                  }
  56.                  update();
  57.                  for(int i=0;i<antCount;i++) {
  58.                      ants[i].init(cityCount);
  59.                  }
  60.              }
  61.          }
  62.       
  63.         private void update() {
  64.             double r = 0.5;
  65.             for(int i=0; i<cityCount; i++) {
  66.                 for(int j=0;j<cityCount;j++) {
  67.                     pheromone[i][j] *= (1-r);
  68.                 }
  69.             }
  70.             for(int i=0; i<antCount; i++) {
  71.                 for(int j=0; j<cityCount; j++) {
  72.                     pheromone[ants[i].getTour()[j]][ants[i].getTour()[j+1]] += 1.0/ants[i].getLength();
  73.                 }
  74.             }
  75.         }
  76.           
  77.         public void ReportResult(){
  78.             System.out.println("最优路径长度是"+bestLength);
  79.             for(int j=0; j<cityCount+1; j++) {
  80.                 System.out.print(city[bestTour[j]] + " ");
  81.             }
  82.         }
  83.     }


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  1. package ant;
  2. /**
  3.  * 主程序 调用ACO求解问题
  4.  * @Time 2014-5-17
  5.  */
  6. public class Main {
  7.     public static void main(String[] args) {
  8.         ACO aco = new ACO();
  9.         aco.init(10000);
  10.         aco.run(20);
  11.         aco.ReportResult();
  12.     }
  13. }
运行结果是： 第0代，发现新的解为：21890
广州 成都 西安 郑州 武汉 杭州 上海 济南 石家庄 太原 呼和浩特 长春 沈阳 哈尔滨 天津 北京 拉萨 昆明 重庆 广州 
第0代，发现新的解为：20500
昆明 成都 西安 郑州 武汉 杭州 上海 济南 石家庄 太原 呼和浩特 长春 沈阳 哈尔滨 天津 北京 拉萨 广州 重庆 昆明 
第1代，发现新的解为：20400
西安 成都 昆明 广州 武汉 杭州 上海 郑州 济南 太原 石家庄 沈阳 长春 哈尔滨 呼和浩特 天津 北京 拉萨 重庆 西安 
第6代，发现新的解为：19440
武汉 杭州 上海 济南 石家庄 天津 北京 沈阳 长春 哈尔滨 呼和浩特 太原 郑州 西安 成都 重庆 昆明 广州 拉萨 武汉 
最优路径长度是19440
武汉 杭州 上海 济南 石家庄 天津 北京 沈阳 长春 哈尔滨 呼和浩特 太原 郑州 西安 成都 重庆 昆明 广州 拉萨 武汉
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