• MATLAB算法实战应用案例精讲-【优化算法】树木生长算法（TGA）（附MATLAB代码实现）

    前言

    Armin Cheraghalipour 根据树木生长的特点于2017 年提出了一种新的元启发式优化算法TGA该算将始定量的群按照解的适应度从高到低排序,分成4组具有不同功能的种群。每次迭代分别进行处理。

    算法原理

    算法流程图

     

    代码实现

    MATLAB

    TGA.m

    1. % "Tree growth algorithm (TGA): A novel approach for solving
    2. % optimization problems"
    3. function [fitG,Xgb,curve] = TGA(N, max_Iter, lb,ub ,dim, fun)
    4. % Parameters
    5. num_tree1  = 3;    % size of first group
    6. num_tree2  = 5;    % size of second group
    7. num_tree4  = 3;    % size of fourth group
    8. theta      = 0.8;  % tree reduction rate of power
    9. lambda     = 0.5;  % control nearest tree
    10. % Limit number of N4 to N1
    11. if num_tree4 > num_tree1 + num_tree2
    12.   num_tree4 = num_tree1 + num_tree2; 
    13. end
    14. % Initial 
    15. X   = zeros(N,dim); 
    16. for i = 1:N
    17. 	for d = 1:dim
    18.     X(i,d) = lb + (ub - lb) * rand();
    19. 	end
    20. end
    21. % Fitness
    22. fit  = zeros(1,N); 
    23. fitG = inf;
    24. for i = 1:N
    25.   fit(i) = fun(X(i,:));
    26.   % Best 
    27.   if fit(i) < fitG
    28.     fitG = fit(i); 
    29.     Xgb  = X(i,:);
    30.   end
    31. end
    32. % Sort tree from best to worst
    33. [fit, idx] = sort(fit,'ascend');
    34. X          = X(idx,:); 
    35. % Initial
    36. dist = zeros(1,num_tree1 + num_tree2);
    37. X1   = zeros(num_tree1,dim);
    38. Xnew = zeros(num_tree4,dim);
    39. Fnew = zeros(1,num_tree4);
    40. curve = zeros(1,max_Iter);
    41. curve(1) = fitG;
    42. t = 2;
    43. % Iterations
    44. while t <= max_Iter
    45. 	% {1} Best trees group
    46.   for i = 1:num_tree1
    47.     r1 = rand();
    48.     for d = 1:dim
    49.       % Local search (1)
    50.       X1(i,d) = (X(i,d) / theta) + r1 * X(i,d);
    51.     end
    52.   	% Boundary
    53.     XB = X1(i,:); XB(XB > ub) = ub; XB(XB < lb) = lb;
    54.     X1(i,:) = XB;
    55.     % Fitness
    56.     fitT = fun(X1(i,:));
    57.     % Greedy selection
    58.     if fitT <= fit(i)
    59.       X(i,:) = X1(i,:);
    60.       fit(i) = fitT;
    61.     end
    62.   end
    63.   % {2} Competitive for light tree group
    64.   X_ori = X;
    65.   for i = num_tree1 + 1 : num_tree1 + num_tree2
    66.     % Neighbor tree
    67.     for j = 1 : num_tree1 + num_tree2           
    68.       if j ~= i
    69.         % Compute Euclidean distance (2)
    70.         dist(j) = sqrt(sum((X_ori(j,:) - X_ori(i,:)) .^ 2));
    71.       else
    72.         % Solve same tree problem
    73.         dist(j) = inf;
    74.       end
    75.     end
    76.     % Find 2 trees with shorter distance
    77.     [~, idx] = sort(dist,'ascend'); 
    78.     T1       = X_ori(idx(1),:);
    79.     T2       = X_ori(idx(2),:); 
    80.     % Alpha in [0,1]
    81.     alpha    = rand();
    82.     for d = 1:dim
    83.       % Compute linear combination between 2 shorter tree (3)
    84.       y = lambda * T1(d) + (1 - lambda) * T2(d);
    85.       % Move tree i between 2 adjacent trees (4)
    86.       X(i,d) = X(i,d) + alpha * y;
    87.     end
    88.     % Boundary
    89.     XB = X(i,:); XB(XB > ub) = ub; XB(XB < lb) = lb;
    90.     X(i,:) = XB;
    91.     % Fitness
    92.     fit(i) = fun(X(i,:));
    93.   end
    94.   % {3} Remove and replace group
    95.   for i = num_tree1 + num_tree2 + 1 : N
    96.     for d = 1:dim
    97.       % Generate new tree by remove worst tree
    98.       X(i,d) = lb + (ub - lb) * rand();
    99.     end
    100.     % Fitness
    101.     fit(i) = fun(X(i,:) );
    102.   end
    103.   % {4} Reproduction group
    104.   for i = 1:num_tree4
    105.     % Random a best tree
    106.     r     = randi([1,num_tree1]);
    107.     Xbest = X(r,:);
    108.     % Mask operator
    109.     mask  = randi([0,1],1,dim);
    110.     % Mask opration between new & best trees
    111.     for d = 1:dim
    112.       % Generate new solution 
    113.       Xn = lb + (ub - lb) * rand();
    114.       if mask(d) == 1
    115.         Xnew(i,d) = Xbest(d);
    116.       elseif mask(d) == 0
    117.         % Generate new tree
    118.         Xnew(i,d) = Xn;
    119.       end
    120.     end
    121.     % Fitness
    122.     Fnew(i) = fun(Xnew(i,:));
    123.   end
    124.   % Sort population get best nPop trees
    125.   XX        = [X; Xnew];
    126.   FF        = [fit, Fnew];
    127.   [FF, idx] = sort(FF,'ascend');
    128.   X         = XX(idx(1:N),:);
    129.   fit       = FF(1:N);
    130.   % Global best
    131.   if fit(1) < fitG
    132.     fitG = fit(1); 
    133.     Xgb  = X(1,:);
    134.   end
    135.   curve(t) = fitG;
    136.     t = t + 1;
    137. end
    138. end

    func_plot.m

    1. % This function draw the benchmark functions
    2.  
    3. function func_plot(func_name)
    4.  
    5. [lb,ub,dim,fobj]=Get_Functions_details(func_name);
    6.  
    7. switch func_name 
    8.     case 'F1' 
    9.         x=-100:2:100; y=x; %[-100,100]
    10.         
    11.     case 'F2' 
    12.         x=-100:2:100; y=x; %[-10,10]
    13.         
    14.     case 'F3' 
    15.         x=-100:2:100; y=x; %[-100,100]
    16.         
    17.     case 'F4' 
    18.         x=-100:2:100; y=x; %[-100,100]
    19.     case 'F5' 
    20.         x=-200:2:200; y=x; %[-5,5]
    21.     case 'F6' 
    22.         x=-100:2:100; y=x; %[-100,100]
    23.     case 'F7' 
    24.         x=-1:0.03:1;  y=x;  %[-1,1]
    25.     case 'F8' 
    26.         x=-500:10:500;y=x; %[-500,500]
    27.     case 'F9' 
    28.         x=-5:0.1:5;   y=x; %[-5,5]    
    29.     case 'F10' 
    30.         x=-20:0.5:20; y=x;%[-500,500]
    31.     case 'F11' 
    32.         x=-500:10:500; y=x;%[-0.5,0.5]
    33.     case 'F12' 
    34.         x=-10:0.1:10; y=x;%[-pi,pi]
    35.     case 'F13' 
    36.         x=-5:0.08:5; y=x;%[-3,1]
    37.     case 'F14' 
    38.         x=-100:2:100; y=x;%[-100,100]
    39.     case 'F15' 
    40.         x=-5:0.1:5; y=x;%[-5,5]
    41.     case 'F16' 
    42.         x=-1:0.01:1; y=x;%[-5,5]
    43.     case 'F17' 
    44.         x=-5:0.1:5; y=x;%[-5,5]
    45.     case 'F18' 
    46.         x=-5:0.06:5; y=x;%[-5,5]
    47.     case 'F19' 
    48.         x=-5:0.1:5; y=x;%[-5,5]
    49.     case 'F20' 
    50.         x=-5:0.1:5; y=x;%[-5,5]        
    51.     case 'F21' 
    52.         x=-5:0.1:5; y=x;%[-5,5]
    53.     case 'F22' 
    54.         x=-5:0.1:5; y=x;%[-5,5]     
    55.     case 'F23' 
    56.         x=-5:0.1:5; y=x;%[-5,5]  
    57. end    
    58.  
    59.     
    60.  
    61. L=length(x);
    62. f=[];
    63.  
    64. for i=1:L
    65.     for j=1:L
    66.         if strcmp(func_name,'F15')==0 && strcmp(func_name,'F19')==0 && strcmp(func_name,'F20')==0 && strcmp(func_name,'F21')==0 && strcmp(func_name,'F22')==0 && strcmp(func_name,'F23')==0
    67.             f(i,j)=fobj([x(i),y(j)]);
    68.         end
    69.         if strcmp(func_name,'F15')==1
    70.             f(i,j)=fobj([x(i),y(j),0,0]);
    71.         end
    72.         if strcmp(func_name,'F19')==1
    73.             f(i,j)=fobj([x(i),y(j),0]);
    74.         end
    75.         if strcmp(func_name,'F20')==1
    76.             f(i,j)=fobj([x(i),y(j),0,0,0,0]);
    77.         end       
    78.         if strcmp(func_name,'F21')==1 || strcmp(func_name,'F22')==1 ||strcmp(func_name,'F23')==1
    79.             f(i,j)=fobj([x(i),y(j),0,0]);
    80.         end          
    81.     end
    82. end
    83.  
    84. surfc(x,y,f,'LineStyle','none');
    85.  
    86. end
    87.

    Get_Functions_details.m

    1. % This function containts full information and implementations of the benchmark 
    2. % functions in Table 1, Table 2, and Table 3 in the paper
    3.  
    4. % lb is the lower bound: lb=[lb_1,lb_2,...,lb_d]
    5. % up is the uppper bound: ub=[ub_1,ub_2,...,ub_d]
    6. % dim is the number of variables (dimension of the problem)
    7.  
    8. function [lb,ub,dim,fobj] = Get_Functions_details(F)
    9.  
    10.  
    11. switch F
    12.     case 'F1'
    13.         fobj = @F1;
    14.         lb=-100;
    15.         ub=100;
    16.         dim=30;
    17.         
    18.     case 'F2'
    19.         fobj = @F2;
    20.         lb=-10;
    21.         ub=10;
    22.         dim=30;
    23.         
    24.     case 'F3'
    25.         fobj = @F3;
    26.         lb=-100;
    27.         ub=100;
    28.         dim=30;
    29.         
    30.     case 'F4'
    31.         fobj = @F4;
    32.         lb=-100;
    33.         ub=100;
    34.         dim=30;
    35.         
    36.     case 'F5'
    37.         fobj = @F5;
    38.         lb=-30;
    39.         ub=30;
    40.         dim=30;
    41.         
    42.     case 'F6'
    43.         fobj = @F6;
    44.         lb=-100;
    45.         ub=100;
    46.         dim=30;
    47.         
    48.     case 'F7'
    49.         fobj = @F7;
    50.         lb=-1.28;
    51.         ub=1.28;
    52.         dim=30;
    53.         
    54.     case 'F8'
    55.         fobj = @F8;
    56.         lb=-500;
    57.         ub=500;
    58.         dim=30;
    59.         
    60.     case 'F9'
    61.         fobj = @F9;
    62.         lb=-5.12;
    63.         ub=5.12;
    64.         dim=30;
    65.         
    66.     case 'F10'
    67.         fobj = @F10;
    68.         lb=-32;
    69.         ub=32;
    70.         dim=30;
    71.         
    72.     case 'F11'
    73.         fobj = @F11;
    74.         lb=-600;
    75.         ub=600;
    76.         dim=30;
    77.         
    78.     case 'F12'
    79.         fobj = @F12;
    80.         lb=-50;
    81.         ub=50;
    82.         dim=30;
    83.         
    84.     case 'F13'
    85.         fobj = @F13;
    86.         lb=-50;
    87.         ub=50;
    88.         dim=30;
    89.         
    90.     case 'F14'
    91.         fobj = @F14;
    92.         lb=-65.536;
    93.         ub=65.536;
    94.         dim=2;
    95.         
    96.     case 'F15'
    97.         fobj = @F15;
    98.         lb=-5;
    99.         ub=5;
    100.         dim=4;
    101.         
    102.     case 'F16'
    103.         fobj = @F16;
    104.         lb=-5;
    105.         ub=5;
    106.         dim=2;
    107.         
    108.     case 'F17'
    109.         fobj = @F17;
    110.         lb=[-5,0];
    111.         ub=[10,15];
    112.         dim=2;
    113.         
    114.     case 'F18'
    115.         fobj = @F18;
    116.         lb=-2;
    117.         ub=2;
    118.         dim=2;
    119.         
    120.     case 'F19'
    121.         fobj = @F19;
    122.         lb=0;
    123.         ub=1;
    124.         dim=3;
    125.         
    126.     case 'F20'
    127.         fobj = @F20;
    128.         lb=0;
    129.         ub=1;
    130.         dim=6;     
    131.         
    132.     case 'F21'
    133.         fobj = @F21;
    134.         lb=0;
    135.         ub=10;
    136.         dim=4;    
    137.         
    138.     case 'F22'
    139.         fobj = @F22;
    140.         lb=0;
    141.         ub=10;
    142.         dim=4;    
    143.         
    144.     case 'F23'
    145.         fobj = @F23;
    146.         lb=0;
    147.         ub=10;
    148.         dim=4;            
    149. end
    150.  
    151. end
    152.  
    153. % F1
    154.  
    155. function o = F1(x)
    156. o=sum(x.^2);
    157. end
    158.  
    159. % F2
    160.  
    161. function o = F2(x)
    162. o=sum(abs(x))+prod(abs(x));
    163. end
    164.  
    165. % F3
    166.  
    167. function o = F3(x)
    168. dim=size(x,2);
    169. o=0;
    170. for i=1:dim
    171.     o=o+sum(x(1:i))^2;
    172. end
    173. end
    174.  
    175. % F4
    176.  
    177. function o = F4(x)
    178. o=max(abs(x));
    179. end
    180.  
    181. % F5
    182.  
    183. function o = F5(x)
    184. dim=size(x,2);
    185. o=sum(100*(x(2:dim)-(x(1:dim-1).^2)).^2+(x(1:dim-1)-1).^2);
    186. end
    187.  
    188. % F6
    189.  
    190. function o = F6(x)
    191. o=sum(abs((x+.5)).^2);
    192. end
    193.  
    194. % F7
    195.  
    196. function o = F7(x)
    197. dim=size(x,2);
    198. o=sum([1:dim].*(x.^4))+rand;
    199. end
    200.  
    201. % F8
    202.  
    203. function o = F8(x)
    204. o=sum(-x.*sin(sqrt(abs(x))));
    205. end
    206.  
    207. % F9
    208.  
    209. function o = F9(x)
    210. dim=size(x,2);
    211. o=sum(x.^2-10*cos(2*pi.*x))+10*dim;
    212. end
    213.  
    214. % F10
    215.  
    216. function o = F10(x)
    217. dim=size(x,2);
    218. o=-20*exp(-.2*sqrt(sum(x.^2)/dim))-exp(sum(cos(2*pi.*x))/dim)+20+exp(1);
    219. end
    220.  
    221. % F11
    222.  
    223. function o = F11(x)
    224. dim=size(x,2);
    225. o=sum(x.^2)/4000-prod(cos(x./sqrt([1:dim])))+1;
    226. end
    227.  
    228. % F12
    229.  
    230. function o = F12(x)
    231. dim=size(x,2);
    232. o=(pi/dim)*(10*((sin(pi*(1+(x(1)+1)/4)))^2)+sum((((x(1:dim-1)+1)./4).^2).*...
    233. (1+10.*((sin(pi.*(1+(x(2:dim)+1)./4)))).^2))+((x(dim)+1)/4)^2)+sum(Ufun(x,10,100,4));
    234. end
    235.  
    236. % F13
    237.  
    238. function o = F13(x)
    239. dim=size(x,2);
    240. o=.1*((sin(3*pi*x(1)))^2+sum((x(1:dim-1)-1).^2.*(1+(sin(3.*pi.*x(2:dim))).^2))+...
    241. ((x(dim)-1)^2)*(1+(sin(2*pi*x(dim)))^2))+sum(Ufun(x,5,100,4));
    242. end
    243.  
    244. % F14
    245.  
    246. function o = F14(x)
    247. aS=[-32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32;,...
    248. -32 -32 -32 -32 -32 -16 -16 -16 -16 -16 0 0 0 0 0 16 16 16 16 16 32 32 32 32 32];
    249.  
    250. for j=1:25
    251.     bS(j)=sum((x'-aS(:,j)).^6);
    252. end
    253. o=(1/500+sum(1./([1:25]+bS))).^(-1);
    254. end
    256. % F15
    258. function o = F15(x)
    259. aK=[.1957 .1947 .1735 .16 .0844 .0627 .0456 .0342 .0323 .0235 .0246];
    260. bK=[.25 .5 1 2 4 6 8 10 12 14 16];bK=1./bK;
    261. o=sum((aK-((x(1).*(bK.^2+x(2).*bK))./(bK.^2+x(3).*bK+x(4)))).^2);
    262. end
    264. % F16
    266. function o = F16(x)
    267. o=4*(x(1)^2)-2.1*(x(1)^4)+(x(1)^6)/3+x(1)*x(2)-4*(x(2)^2)+4*(x(2)^4);
    268. end
    270. % F17
    272. function o = F17(x)
    273. o=(x(2)-(x(1)^2)*5.1/(4*(pi^2))+5/pi*x(1)-6)^2+10*(1-1/(8*pi))*cos(x(1))+10;
    274. end
    276. % F18
    278. function o = F18(x)
    279. o=(1+(x(1)+x(2)+1)^2*(19-14*x(1)+3*(x(1)^2)-14*x(2)+6*x(1)*x(2)+3*x(2)^2))*...
    280.     (30+(2*x(1)-3*x(2))^2*(18-32*x(1)+12*(x(1)^2)+48*x(2)-36*x(1)*x(2)+27*(x(2)^2)));
    281. end
    283. % F19
    285. function o = F19(x)
    286. aH=[3 10 30;.1 10 35;3 10 30;.1 10 35];cH=[1 1.2 3 3.2];
    287. pH=[.3689 .117 .2673;.4699 .4387 .747;.1091 .8732 .5547;.03815 .5743 .8828];
    288. o=0;
    289. for i=1:4
    290.     o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));
    291. end
    292. end
    294. % F20
    296. function o = F20(x)
    297. aH=[10 3 17 3.5 1.7 8;.05 10 17 .1 8 14;3 3.5 1.7 10 17 8;17 8 .05 10 .1 14];
    298. cH=[1 1.2 3 3.2];
    299. pH=[.1312 .1696 .5569 .0124 .8283 .5886;.2329 .4135 .8307 .3736 .1004 .9991;...
    300. .2348 .1415 .3522 .2883 .3047 .6650;.4047 .8828 .8732 .5743 .1091 .0381];
    301. o=0;
    302. for i=1:4
    303.     o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));
    304. end
    305. end
    307. % F21
    309. function o = F21(x)
    310. aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6];
    311. cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];
    313. o=0;
    314. for i=1:5
    315.     o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
    316. end
    317. end
    318.  
    319. % F22
    320.  
    321. function o = F22(x)
    322. aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6];
    323. cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];
    324.  
    325. o=0;
    326. for i=1:7
    327.     o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
    328. end
    329. end
    331. % F23
    333. function o = F23(x)
    334. aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6];
    335. cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];
    337. o=0;
    338. for i=1:10
    339.     o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
    340. end
    341. end
    342.  
    343. function o=Ufun(x,a,k,m)
    344. o=k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a));
    345. end

    main.m

    1. %_________________________________________________________________________________
    2. %_________________________________________________________________________________
    3. clear all 
    4. clc
    5.  
    6. SearchAgents_no=30; % Number of search agents
    7. Function_name='F1'; % Name of the test function that can be from F1 to F23 
    8. Max_iteration=500; % Maximum numbef of iterations
    9. % Load details of the selected benchmark function
    10. [lb,ub,dim,fobj]=Get_Functions_details(Function_name);
    11. [Best_score,Best_pos,cg_curve]=TGA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj);
    12.  
    13. display(['The best solution obtained by OPTIMIZER is : ', num2str(Best_pos)]);
    14. display(['The best optimal value of the objective function found by OPTIMIZER is : ', num2str(Best_score)]);
    15.  
    16. %Draw objective space
    17. figure,
    18. subplot(1,2,1);
    19. func_plot(Function_name);
    20. title([Function_name])
    21. xlabel('x_1');
    22. ylabel('x_2');
    23. zlabel([Function_name,'( x_1 , x_2 )'])
    24. set(gca,'color','none')
    25. grid off
    26.  
    27. subplot(1,2,2);
    28. semilogy(cg_curve,'Color','b','LineWidth',4);
    29. title('Convergence curve')
    30. xlabel('Iteration');
    31. ylabel('Best fitness obtained so far');
    32. axis tight
    33. grid off
    34. box on
    35. legend('TGA')

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  • 原文地址：https://blog.csdn.net/qq_36130719/article/details/133640724