蟻羣算法matlab實現

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如下用matlab實現蟻羣算法：

 

%螞蟻算法test  
%用產生的一個圓上的十個點來檢驗螞蟻算法
 
clc
clear
 
%參數
alpha = 1 ;                               %信息素指數
beta = 5  ;                                %啓發指數
rho = 0.5 ;                                %揮發係數 
n = 16 ;                                   %城市個數
k = 20 ;                                    %迭代次數
m = n - 1 ;                                %螞蟻只數，這裏取比城市數目少一的螞蟻只數
Q = 100 ;
bestr = inf ;
%產生一個圓上的十個點
x = zeros(1,n) ;
y = x ;
for i = 1 : (n/2)                          
    x(i) = rand * 20 ;
    y(i) = sqrt(100 - (x(i) - 10) ^ 2) + 10;
end
for i = (n/2 + 1) : n
    x(i) = rand * 20 ;
    y(i) = - sqrt(100 - (x(i) - 10) ^ 2) + 10;
end
plot(x,y,'.') ;
%計算距離
d = zeros(n,n) ;
for i = 1 : n 
    for j = 1 : n
        d(i,j) = sqrt( ( x(i) - x(j) ) ^ 2 + ( y(i) - y(j) ) ^ 2) ;
    end
end
temp = min(d) ;
dmin = temp(1) ;
tau = ones(n,n) ;
%tau = tau ./ (n * dmin) ;                   %初始化tau信息素矩陣
 
%開始迭代
for i = 1 : k   
    %初始化
    visited = zeros(m,n) ;                  %用visited 來儲存全部螞蟻走過的城市 m×n 其中未到達的城市爲0
    visited(:,1) = (randperm(n,m))';        %將m只螞蟻隨機放在n座城市 即產生一列1到n的隨機數進行第一列數據的更新
    for b = 2 : n                           %全部螞蟻都走到第b個城市時
        current = visited(:,(b-1)) ;         %全部螞蟻如今所在城市 m×1
        allow = zeros(m,(n - b + 1)) ; 
        
        for a = 1 : m
            j = 1 ;
            for s = 1 : n
                if length(find(visited(a,:) == s)) == 0
                   allow(a,j) = s ;
                   j = j + 1 ;
                end
            end
        end
        
        l = n-b+1 ;
        for a = 1 : m                       %分析第a只螞蟻
            p = zeros(1,l) ;
            for j = 1 : l                   %根據下式來選擇下一個城市
                p(j) = ( ( tau( current(a,1) , allow(a,j) ) ) ^ alpha ) * ( ( 1 / d( current(a,1) , allow(a,j) ) ) ^ beta ) ;
            end
            p = p ./ sum(p) ;               %採用輪盤賭的方式
            p = cumsum(p) ;
            pick = rand ;
            for c = 1 : l
                if pick < p(c)
                    visited(a,b) = allow(a,c) ;          %找到符合要求的城市 並 記入螞蟻a的路徑中
                    break ;
                end
            end
        end
    end
    %計算每隻螞蟻所走的路徑總長
    L = zeros(1,m) ;
    for a = 1 : m
        t = d(visited(a,n),visited(a,1)) ;
        for b = 1 : (n - 1)
            t = t + d(visited(a,b),visited(a,(b + 1)));
        end
        L(a) = t ;
    end
    [newbestr,newbestant] = min(L) ;          %尋本次迭代最短路徑及其相應螞蟻
    if newbestr < bestr                       %到目前爲止最優值的保存
        bestr = newbestr ;
        bestroad = visited(newbestant,:) ;
    end
    %離線更新信息素矩陣
    %揮發
    for a = 1 : m
        tau(visited(a,n),visited(a,1)) = tau(visited(a,n),visited(a,1)) * (1 - rho) ;
        for b = 1 : (n - 1)
            tau(visited(a,b),visited(a,(b + 1))) = tau(visited(a,b),visited(a,(b + 1))) * (1 - rho) ;
        end
    end
    %增強
    tau(visited(newbestant,n),visited(newbestant,1)) = tau(visited(newbestant,n),visited(newbestant,1)) + Q / L(newbestant) ;
    for b = 1 : (n - 1)
        tau(visited(newbestant,b),visited(newbestant,(b + 1))) = tau(visited(newbestant,b),visited(newbestant,(b + 1))) + Q / L(newbestant) ;
    end
end
bestr 
bestx = zeros(1,n) ;
besty = zeros(1,n) ;
for i = 1 : n
    bestx(i) = x(bestroad(i)) ;
    besty(i) = y(bestroad(i)) ;
end
bestx = [bestx,bestx(1)] ;
besty = [besty,besty(1)] ;
plot(bestx,besty,'-') ;