例による最適化。 シミュレーションアニーリングとantアルゴリズム。 パート1

%   (     ) %-------------------------------------------------------------------------- tic % clearvars -except cities clearvars % ----------------------------------------------------------------- % -  m = 100000; % ---------------------------------------------------------------- %   Tstart = 10000; %   Tend = 0.1; %     T = Tstart; %  S = inf; %   n = 100; % ------------------------------------------------------------------- %   dist = zeros(n,n); % ------------------------------------------------------------------------- %   (x,y) cities = rand(n,2)*100; %    ROUTE = randperm(n); %    for i = 1:n for j = 1:n % dist (  ) dist(i,j) = sqrt((cities(i,1) - cities(j,1))^2 + ... (cities(i,2) - cities(j,2))^2); end end %  ,   -  for k = 1:m %    Sp = 0; %     , ROUTEp - %   %   ROUTEp = ROUTE; %    transp = randperm(n,2); %  ,     transp  %     if transp(1) < transp(2) ROUTEp(transp(1):transp(2)) = fliplr(ROUTEp(transp(1):transp(2))); else ROUTEp(transp(2):transp(1)) = fliplr(ROUTEp(transp(2):transp(1))); end %   ()   for i = 1:n-1 Sp = Sp + dist(ROUTEp(i),ROUTEp(i+1)); end Sp = Sp + dist(ROUTEp(1),ROUTEp(end)); %    ,     ... %  , ,    if Sp < S S = Sp; ROUTE = ROUTEp; else %     0  1 RANDONE = rand(1); %    P = exp((-(Sp - S)) / T); if RANDONE <= P S = Sp; ROUTE = ROUTEp; end end %   T = Tstart / k; %    if T < Tend break; end; end %   citiesOP(:,[1,2]) = cities(ROUTE(:),[1,2]); plot([citiesOP(:,1);citiesOP(1,1)],[citiesOP(:,2);citiesOP(1,2)],'-r.') %   clearvars -except cities ROUTE S %   toc 

 %   (     ) % ------------------------------------------------------------------------- tic % clearvars -except cities clearvars % ----------------------------------------------------------------- % -  (  ) age = 50; % -    countage = 30; % -  n = 30; % ----------------------------------------------------------------- %  -  ,  0     %   a = 1; %  -  ,  0  %      b = 2.5; %   (   ) e = 0.5; %    Q = 1; % -   (     elite  ) elite = 1; %   ph = 0.01; % ------------------------------------------------------------------- %   dist = zeros(n,n); %    returndist = zeros(n,n); %       ROUTEant = zeros(countage,n); %       DISTant = zeros(countage,1); %       bestDistVec = zeros(age,1); %    bestDIST = inf; %   ROUTE = zeros(1,n+1); %     (    ) RANDperm = randperm(n); %   P = zeros(1,n); % ------------------------------------------------------------------------- %   (x,y) cities = rand(n,2)*100; %    tao = ph*(ones(n,n)); %        for i = 1:n for j = 1:n % dist (  ) dist(i,j) = sqrt((cities(i,1) - cities(j,1))^2 + ... (cities(i,2) - cities(j,2))^2); % nn (   ) if i ~= j returndist(i,j) = 1/sqrt((cities(i,1) - cities(j,1))^2 + ... (cities(i,2) - cities(j,2))^2); end end end %  for iterration = 1:age %  (  ) for k = 1:countage % ******************    ****************** %    %     % ROUTEant(k,1) = randi([1 n]); %       (   ), - %   -       ROUTEant(k,1) = RANDperm(k); %           1- % ROUTEant(k,1) = 1; %       ,    %  ,     ,      %   % if iterration == 1 % ROUTEant(k,1) = randi([1 n]); % % ROUTEant(k,1) = RANDperm(k); % % ROUTEant(k,1) = 1; % else % ROUTEant(k,1) = lastROUTEant(k); % end % ********************************************************************* %   ,   ,     for s = 2:n %     ir = ROUTEant(k,s-1); %    (  ) ,     % : tao^a*(1/S)^b % 1/S - returndist. %      (-  *  %  * - ) ,       , %      .    %   .     : % for c = 1:n % P(1,c) = tao(ir,c).^a * returndist(ir,c).^b; % end P = tao(ir,:).^a .* returndist(ir,:).^b; %   (     k- ) %  n ,      ,   %  %     ,   ,  %    0,     %       P(ROUTEant(k,1:s-1)) = 0; %    (     = 1 ) P = P ./ sum(P); %       RANDONE = rand; getcity = find(cumsum(P) >= RANDONE, 1, 'first'); %    -  ,   if isempty(getcity) == 1 disp '  !' end %  s-    k-  ROUTEant(k,s) = getcity; end %   k-  ROUTE = [ROUTEant(k,1:end),ROUTEant(k,1)]; %   S = 0; %   k-  for i = 1:n S = S + dist(ROUTE(i),ROUTE(i+1)); end %  k- ,   k-  DISTant(k) = S; %     S if DISTant(k) < bestDIST bestDIST = DISTant(k); bestROUTE = ROUTEant(k,1:end); end %  ""  k-  (    %      ,    %  ) % lastROUTEant = ROUTEant(1:end,end); end % -----------------------  --------------------- %   ""   -   tao = (1-e)*tao; for u = 1:countage %   u-  ROUTE = [ROUTEant(u,1:end), ROUTEant(u,1)]; %    for t = 1:n x = ROUTE(t); y = ROUTE(t+1); %    if DISTant(u) ~= max(DISTant) %         %  tao(x,y) = tao(x,y) + Q / DISTant(u); else %     tao(x,y) = tao(x,y) + (elite*Q) / DISTant(u); end end end end %   citiesOP(:,[1,2]) = cities(bestROUTE(:),[1,2]); plot([citiesOP(:,1);citiesOP(1,1)],[citiesOP(:,2);citiesOP(1,2)],'.r-') clearvars -except cities ROUTE bestDIST bestROUTE ROUTEant toc