蚁群算法

参考段海滨的代码.. TSP 31cities

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <time.h>

#define DIST_2_CITY(a, b) sqrt((float)((a)[0]-(b)[0])*((a)[0]-(b)[0])+((a)[1]-(b)[1])*((a)[1]-(b)[1]))


const int CityNum = 31;                     /* 城市数量 */
const int AntNum = 50;                      /* 蚂蚁数量 */
const int CityCoor[CityNum][2] =            /* 城市坐标 */
{
    {1304, 2312}, {3639, 1315}, {4177, 2244}, {3712, 1399}, {3488, 1535},
    {3326, 1556}, {3238, 1229}, {4196, 1004}, {4312, 790 }, {4386, 570 },
    {3007, 1970}, {2562, 1756}, {2788, 1491}, {2381, 1676}, {1332, 695 },
    {3715, 1678}, {3918, 2179}, {4061, 2370}, {3780, 2212}, {3676, 2578},
    {4029, 2838}, {4263, 2931}, {3429, 1908}, {3507, 2367}, {3394, 2643},
    {3439, 3201}, {2935, 3240}, {3140, 3550}, {2545, 2357}, {2778, 2826},
    {2370, 2975}
};


const float inittau = 1.0f;                 /* 初始信息量 */
float tau[CityNum][CityNum];                /* τ, 每条路径上的信息量 */
float deltatau[CityNum][CityNum];           /* Δτ, 代表相应路径上的信息素增量 */
float DistMatrix[CityNum][CityNum];         /* 城市距离矩阵 */
float eta[CityNum][CityNum];                /* η, 启发函数，其值eta[i][j] = 1 / DistMatrix[i][j] */
int tabu[AntNum][CityNum];                  /* 禁忌表，tabu[i][j]=1表示蚂蚁i已经走过了j城市 */
int route[AntNum][CityNum];                 /* 保存蚂蚁k的路径的数组为route[k][CityNum] */

/* 最优解 */
float solution[AntNum];
int BestRoute[CityNum];
float BestSolution;


float alpha;                                /* α, 信息启发因子 */
float beta;                                 /* β, 期望启发因子 */
float rho;                                  /* ρ, 信息残留因子 */
float Q;                                    /* 信息素强度 */




int MaxIter;                                /* 最大迭代次数 */


/* 计算适应度(长度) */
float GetFitness( int citypos[] )
{
    register int i;
    register float sum;

    sum = 0.0f;
    for ( i = CityNum - 1; i > 0; i -- )
    {
        sum += DistMatrix[citypos[i]][citypos[i - 1]];
    }
    sum += DistMatrix[citypos[0]][citypos[CityNum - 1]];

    return sum;
}

int main( )
{
    register int i, j, k;
    int iter, step;
    float drand;
    float sum, partsum[CityNum];
    float tmpq;

    srand( ( unsigned int )time( NULL ) );

    /* 初始化全局参数 */
    alpha = 1.0f;
    beta = 5.0f;
    rho = 0.95f;
    Q = 100.0f;
    MaxIter = 200;

    /* 获取距离矩阵 */
    for ( i = 0; i < CityNum; i ++ )
    {
        DistMatrix[i][i] = 0.0f;
        for ( j = i + 1; j < CityNum; j ++ )
        {
            DistMatrix[j][i] = DistMatrix[i][j] = DIST_2_CITY( CityCoor[i], CityCoor[j] );
        }
    }

    /* 初始化启发因子 */
    for ( i = 0; i < CityNum; i++ )
    {
        for ( j = 0; j < CityNum; j++ )
        {
            tau[i][j] = inittau;
            if ( j > i )
            {
                eta[j][i] = eta[i][j] = 1.0f / DistMatrix[i][j];
            }
        }
    }

    for ( iter = 0; iter < MaxIter; iter ++ )
    {
        /* 初始化蚂蚁 */
        memset( tabu, 0, sizeof( tabu ) );
        for ( k = 0; k < AntNum; k++ )
        {
            route[k][0] = rand() % CityNum;     /* 设置第k个蚂蚁的起始城市 */
            tabu[k][route[k][0]] = 1;           /* 填充禁忌表 */
        }

        /* 为每只蚂蚁生成完整路径 */
        for ( k = 0; k < AntNum; k++ )
        {
            /* 步进 */
            for ( step = 1; step < CityNum; step ++ )
            {
                /* 轮盘赌 */
                i = 0;
                sum = 0.0f;

                for ( j = 0; j < CityNum; j ++ )
                {
                    if ( tabu[k][j] == 0 )
                    {
                        partsum[i] = pow( tau[route[k][step - 1]][j], alpha ) * pow( eta[route[k][step - 1]][j], beta );
                        sum += partsum[i];
                        i ++;
                    }
                }

                partsum[0] /= sum;
                for ( j = 1; j < i; j ++ )
                {
                    partsum[j] = partsum[j] / sum + partsum[j - 1];
                }
                partsum[i - 1] = 1.1f;

                drand = rand() / ( RAND_MAX + 1.0f );
                i = 0;
                for ( j = 0; j < CityNum; j ++ )
                {
                    if ( tabu[k][j] == 0 && drand < partsum[i ++] )
                    {
                        break;
                    }
                }

                tabu[k][j] = 1;         /* 禁忌表置访问标志 */
                route[k][step] = j;     /* 保存蚂蚁k的第step步经过的城市 */
            }
        }


        /* 查询最优,并保存 */
        j = 0;
        BestSolution = solution[0] = GetFitness( route[0] );
        for ( k = 1; k < AntNum; k ++ )
        {
            solution[k] = GetFitness( route[k] );
            if ( solution[k] < BestSolution )
            {
                j = k;
                BestSolution = solution[k];
            }
        }
        memcpy( BestRoute, route[j], sizeof( BestRoute ) );

        /* 计算各个路径上的信息素增量 */
        memset( deltatau, 0, sizeof( deltatau ) );
        for ( k = 0; k < AntNum; k ++ )
        {
            tmpq = Q / solution[k];

            for ( step = 1; step < CityNum; step ++ )
            {
                deltatau[route[k][step - 1]][route[k][step]] += tmpq;
                deltatau[route[k][step]][route[k][step - 1]] += tmpq;
            }
            deltatau[route[k][CityNum - 1]][route[k][0]] += tmpq;
            deltatau[route[k][0]][route[k][CityNum - 1]] += tmpq;
        }

        /* 更新路径上的信息素 */
        for ( i = 0; i < CityNum; i ++ )
        {
            for ( j = i + 1; j < CityNum; j ++ )
            {
                tau[i][j] = rho * tau[i][j] + deltatau[i][j];

                /* 避免启发信息被路径信息淹没 */
                if ( tau[i][j] < 0.00001f ) tau[i][j] = 0.00001f;
                else if ( tau[i][j] > 20.0f ) tau[i][j] = 20.0f;

                tau[j][i] = tau[i][j];
            }
        }
    }


    printf( "*-------------------------------------------------------------------------*
" );
    printf( "the initialized parameters of ACA are as follows:
" );
    printf( "alpha = %f, beta = %f, rho = %f, Q = %f
", alpha, beta, rho, Q );
    printf( "the maximum iteration number of ACA is: %d
", MaxIter );
    printf( "the shortest length of the path is: %f
", BestSolution );
    printf( "the best route is:
" );
    for ( i = 0; i < CityNum; i ++ )
    {
        printf( "%d ", BestRoute[i] );
    }
    printf( "
" );
    printf( "*-------------------------------------------------------------------------*
" );


    return 0;
}