鸟群算法

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鸟群算法。。。。。

1. % ------------------------------------------------------------------------
   
2. % Bird Swarm Algorithm (BSA) (demo)
   
3. % Programmed by Xian-Bing Meng
   
4. % Updated at Jun 19, 2015.   
   
5. % Email: x.b.meng12@gmail.com
   
6. %
   
7. % This is a simple demo version only implemented the basic idea of BSA for        
   
8. % solving the unconstrained problem, namely Sphere function.  
   
9. %
   
10. % The details about BSA are illustratred in the following paper.   
    
11. % Xian-Bing Meng, et al (2015): A new bio-inspXred optimisation algorithm:
    
12. % Bird Swarm Algorithm, Journal of Experimental & Theoretical
    
13. % Artificial Intelligence, DOI: 10.1080/0952813X.2015.1042530
    
14. %
    
15. % The parameters in BSA are presented as follows.
    
16. % FitFunc    % The objective function
    
17. % M          % Maxmimal generations (iterations)
    
18. % pop        % Population size
    
19. % dim        % Dimension
    
20. % FQ         % The frequency of birds' flight behaviours
    
21. % c1         % Cognitive accelerated coefficient
    
22. % c2         % Social accelerated coefficient
    
23. % a1, a2     % Two paramters which are related to the indirect and direct
    
24. %              effect on the birds' vigilance bahaviors.
    
25. %
    
26. % Using the default value, BSA can be executed using the following code.
    
27. % [ bestX, fMin ] = BSA
    
28. % ------------------------------------------------------------------------
    
29. 
    
30. % Main programs
    
31. 
    
32. function [ bestX, fMin ] = BSA( FitFunc, M, pop, dim, FQ, c1, c2, a1, a2 )
    
33. % Display help
    
34. help BSA.m
    
35. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
36. % set the default parameters
    
37. if nargin < 1
    
38.     FitFunc = @Sphere;
    
39.     M = 1000;   
    
40.     pop = 30;  
    
41.     dim = 20;   
    
42.     FQ = 10;   
    
43.     c1 = 1.5;
    
44.     c2 = 1.5;
    
45.     a1 = 1;
    
46.     a2 = 1;
    
47. end
    
48. 
    
49. % set the parameters
    
50. lb= -100*ones( 1,dim );   % Lower bounds
    
51. ub= 100*ones( 1,dim );    % Upper bounds
    
52. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
53. %Initialization
    
54. 
    
55. for i = 1 : pop
    
56.     x( i, : ) = lb + (ub - lb) .* rand( 1, dim );
    
57.     fit( i ) = FitFunc( x( i, : ) );
    
58. end
    
59. pFit = fit; % The individual's best fitness value
    
60. pX = x;     % The individual's best position corresponding to the pFit
    
61. 
    
62. [ fMin, bestIndex ] = min( fit );  % fMin denotes the global optimum
    
63. % bestX denotes the position corresponding to fMin
    
64. bestX = x( bestIndex, : );   
    
65. 
    
66. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
67. % Start the iteration.
    
68. 
    
69. for iteration = 1 : M
    
70.      
    
71.     prob = rand( pop, 1 ) .* 0.2 + 0.8;%The probability of foraging for food
    
72.    
    
73.     if( mod( iteration, FQ ) ~= 0 )         
    
74.         %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
75.         % Birds forage for food or keep vigilance
    
76.         sumPfit = sum( pFit );
    
77.         meanP = mean( pX );
    
78.         for i = 1 : pop
    
79.             if rand < prob(i)
    
80.                 x( i, : ) = x( i, : ) + c1 * rand.*(bestX - x( i, : ))+ ...
    
81.                     c2 * rand.*( pX(i,:) - x( i, : ) );
    
82.             else
    
83.                 person = randiTabu( 1, pop, i, 1 );
    
84.                
    
85.                 x( i, : ) = x( i, : ) + rand.*(meanP - x( i, : )) * a1 * ...
    
86.                     exp( -pFit(i)/( sumPfit + realmin) * pop ) + a2 * ...
    
87.                     ( rand*2 - 1) .* ( pX(person,:) - x( i, : ) ) * exp( ...
    
88.                     -(pFit(person) - pFit(i))/(abs( pFit(person)-pFit(i) )...
    
89.                     + realmin) * pFit(person)/(sumPfit + realmin) * pop );
    
90.             end
    
91.             
    
92.             x( i, : ) = Bounds( x( i, : ), lb, ub );  
    
93.             fit( i ) = FitFunc( x( i, : ) );
    
94.         end
    
95.         %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
96.    
    
97.     else
    
98.         FL = rand( pop, 1 ) .* 0.4 + 0.5;    %The followed coefficient
    
99.         
    
100.         %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     
101.         % Divide the bird swarm into two parts: producers and scroungers.
     
102.         [ans, minIndex ] = min( pFit );
     
103.         [ans, maxIndex ] = max( pFit );
     
104.         choose = 0;
     
105.         if ( minIndex < 0.5*pop && maxIndex < 0.5*pop )
     
106.             choose = 1;
     
107.         end
     
108.         if ( minIndex > 0.5*pop && maxIndex < 0.5*pop )
     
109.             choose = 2;
     
110.         end
     
111.         if ( minIndex < 0.5*pop && maxIndex > 0.5*pop )
     
112.             choose = 3;
     
113.         end
     
114.         if ( minIndex > 0.5*pop && maxIndex > 0.5*pop )
     
115.             choose = 4;
     
116.         end
     
117.         %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     
118.         if choose < 3
     
119.             for i = (pop/2+1) : pop
     
120.                 x( i, : ) = x( i, : ) * ( 1 + randn );
     
121.                 x( i, : ) = Bounds( x( i, : ), lb, ub );
     
122.                 fit( i ) = FitFunc( x( i, : ) );
     
123.             end
     
124.             if choose == 1
     
125.                 x( minIndex,: ) = x( minIndex,: ) * ( 1 + randn );
     
126.                 x( minIndex, : ) = Bounds( x( minIndex, : ), lb, ub );
     
127.                 fit( minIndex ) = FitFunc( x( minIndex, : ) );
     
128.             end
     
129.             for i = 1 : 0.5*pop
     
130.                 if choose == 2 || minIndex ~= i
     
131.                     person = randi( [(0.5*pop+1), pop ], 1 );
     
132.                     x( i, : ) = x( i, : ) + (pX(person, :) - x( i, : )) * FL( i );
     
133.                     x( i, : ) = Bounds( x( i, : ), lb, ub );
     
134.                     fit( i ) = FitFunc( x( i, : ) );
     
135.                 end
     
136.             end
     
137.         else
     
138.             for i = 1 : 0.5*pop
     
139.                 x( i, : ) = x( i, : ) * ( 1 + randn );
     
140.                 x( i, : ) = Bounds( x( i, : ), lb, ub );
     
141.                 fit( i ) = FitFunc( x( i, : ) );
     
142.             end
     
143.             if choose == 4
     
144.                 x( minIndex,: ) = x( minIndex,: ) * ( 1 + randn );
     
145.                 x( minIndex, : ) = Bounds( x( minIndex, : ), lb, ub );
     
146.                 fit( minIndex ) = FitFunc( x( minIndex, : ) );
     
147.             end
     
148.             for i = (0.5*pop+1) : pop
     
149.                 if choose == 3 || minIndex ~= i
     
150.                     person = randi( [1, 0.5*pop], 1 );
     
151.                     x( i, : ) = x( i, : ) + (pX(person, :) - x( i, : )) * FL( i );
     
152.                     x( i, : ) = Bounds( x( i, : ), lb, ub );
     
153.                     fit( i ) = FitFunc( x( i, : ) );
     
154.                 end
     
155.             end   
     
156.         end
     
157.         
     
158.     end
     
159.     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     
160.     % Update the individual's best fitness vlaue and the global best one
     
161.    
     
162.     for i = 1 : pop
     
163.         if ( fit( i ) < pFit( i ) )
     
164.             pFit( i ) = fit( i );
     
165.             pX( i, : ) = x( i, : );
     
166.         end
     
167.         
     
168.         if( pFit( i ) < fMin )
     
169.             fMin = pFit( i );
     
170.             bestX = pX( i, : );
     
171.         end
     
172.     end
     
173.    
     
174. end
     
175. 
     
176. % End of the main program
     
177. 
     
178. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     
179. % The following functions are associated with the main program
     
180. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     
181. % This function is the objective function
     
182. function y = Sphere( x )
     
183. y = sum( x .^ 2 );
     
184. 
     
185. % Application of simple limits/bounds
     
186. function s = Bounds( s, Lb, Ub)
     
187.   % Apply the lower bound vector
     
188.   temp = s;
     
189.   I = temp < Lb;
     
190.   temp(I) = Lb(I);
     
191.   
     
192.   % Apply the upper bound vector
     
193.   J = temp > Ub;
     
194.   temp(J) = Ub(J);
     
195.   % Update this new move
     
196.   s = temp;
     
197. 
     
198. %--------------------------------------------------------------------------
     
199. % This function generate "dim" values, all of which are different from
     
200. %  the value of "tabu"
     
201. function value = randiTabu( min, max, tabu, dim )
     
202. value = ones( dim, 1 ) .* max .* 2;
     
203. num = 1;
     
204. while ( num <= dim )
     
205.     temp = randi( [min, max], 1, 1 );
     
206.     if( length( find( value ~= temp ) ) == dim && temp ~= tabu )
     
207.         value( num ) = temp;
     
208.         num = num + 1;
     
209.     end
     
210. end

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