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电梯直达

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发表于 2006-1-11 19:44 |只看该作者 |倒序浏览

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天才开始了解遗传算法，看了一天的书，昨晚做了一个基本的遗传算法的仿真（最简单的那种），希望大家多多指教。 程序如下 % Simple Genetic Algorithm % Revised according to the program which is the first appendix of the book % "Genetic Algorithms theory and Application" % Programmed by Yang Wuyi 2005.6.15 % To calculate the maximal value of the function % In this program the function is % F( x1 , x2 ) = 100 * ( x1^2 - x2 )^2 + ( 1 - x1 )^2 % s.t - XRang <= x1 , x2 <= XRang clear all close all % Some parameters of the Simple Genetic Algorithm

opulationSize = 80 ; %The population of the colony MaxGeneration = 100 ; %The maximal generation

roCro = 0.6 ; %The probability of crossover

roMut = 0.001 ; %The probability of mutation XRang = 2.048 ; Vmax = 100 ; % Vmin = 0 ; % % FunctionMode >= 0 find the maximum of the function % FunctionMode < 0 find the minimum of the function FunctionMode = 1 ; % ChromosomeLen1 = 10 ; % The lenght of the first chromosome ChromosomeLen2 = 10 ; % The lenght of the second chromosome ChromosomeLen = 10 ; ChromosomeLength = ChromosomeLen1 + ChromosomeLen2 ; % The total lenght of chromosome X1 = zeros ( 1 , PopulationSize ); X2 = zeros ( 1 , PopulationSize ); % Generate the first generation of the population rand('state',sum(100*clock)); % Resets the generator to a different state each time for j = 1 : PopulationSize for k = 1 : ChromosomeLength Temp = rand(1); if Temp < 0.5

opulation( j ) . Chromosome( k ) = 0; else

opulation( j ) . Chromosome( k ) = 1; end % End of if end % End of for - X1( j ) = DecodeChromosome(Population( j ) . Chromosome, 1 , ChromosomeLen ); X2( j ) = DecodeChromosome(Population( j ) . Chromosome, ChromosomeLen+1 , ChromosomeLen );

opulation( j ).Value = 0 ;

opulation( j ).Fitness = 0 ; end X1 = 2 * XRang * X1/1023 - XRang; X2 = 2 * XRang * X2/1023 - XRang; figure plot( X1 , X2 , '*') , grid; BestValue = zeros( 1 , MaxGeneration ) ; AverageValue = zeros( 1 , MaxGeneration ) ; for Gen = 1 : MaxGeneration % Calculate the value according to the function which we want to find its maximum % In this program the function is % F( x1 , x2 ) = 100 * ( x1^2 - x2 )^2 + ( 1 - x1 )^2 % s.t -XRang <= x1 , x2 <= XRang for j = 1 : PopulationSize TempValue = CalculateObjectValue( Population( j ).Chromosome , ChromosomeLen);

opulation( j ).Value = TempValue; end % End of for - j %Calculate fitness value for j = 1 : PopulationSize TempValue = CalculateFitnessValue( Population( j ).Value , Vmax , Vmin , FunctionMode);

opulation( j ).Fitness = TempValue; end % End of for - j % Find out the best and worst individual of this generation BestValue( Gen ) = Population( 1 ).Value ; for j = 1 : PopulationSize if Population( j ).Value > BestValue( Gen ) BestValue( Gen ) = Population( j ).Value; end end Sum = 0 ; for j = 1 : PopulationSize Sum = Sum + Population( j ).Value; end AverageValue( Gen ) = Sum / PopulationSize ; % Reproduce a chromosome by proportional selection Sum = 0 ; CFitness = zeros ( 1 , PopulationSize ); % The cumulative fitness value %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Calculate cumulative fitness for j = 1 : PopulationSize Sum = Sum + Population( j ).Fitness ; end % End of for - j for j = 1 : PopulationSize CFitness( j ) = Population( j ).Fitness / Sum ; end % End of for - j for j = 2 : PopulationSize CFitness( j ) = CFitness( j - 1 ) + CFitness( j ) ; end % End of for - j %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Select operation for j = 1 : PopulationSize RandP = rand( 1 ) ; Index = 1; while RandP > CFitness( Index ) Index = Index + 1 ; end % End of while NewPopulation( j ) = Population( Index ) ; end % End of for - j for j = 1 : PopulationSize

opulation( j ) = NewPopulation( j ) ; end % End of for - j %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Crossover two chromosome IndexPair = zeros( 1, PopulationSize); for j = 1 : PopulationSize IndexPair( j ) = j; end % End of for - j for j = 1 : PopulationSize

oint = floor ( (PopulationSize - j - 1) * rand( 1 ) ); Temp = IndexPair( j ) ; IndexPair( j ) = IndexPair( j + Point ); IndexPair( j + Point ) = Temp; end % End of for - j for j = 1 : 2 : ( PopulationSize - 1 ) RandP = rand( 1 ) ; if RandP < ProCro

oint = floor ( rand( 1 ) * ChromosomeLen ) ; if Point == 0

oint = 1; end for k = Point : (ChromosomeLen + Point - 1) Temp = Population ( IndexPair( j ) ) . Chromosome( k ) ;

opulation ( IndexPair( j ) ) . Chromosome( k ) = Population ( IndexPair( j + 1) ) . Chromosome( k ) ;

opulation ( IndexPair( j + 1) ) . Chromosome( k ) = Temp ; end % End of for - k end % End of if end % End of for - j % Crossover two chromosome %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Mutation of a chromosome for j = 1 : PopulationSize for k = 1 : 2*ChromosomeLen RandP = rand( 1 ) ; if RandP < ProMut if Population( j ) . Chromosome( k ) == 1

opulation( j ) . Chromosome( k ) = 0 ; else

opulation( j ) . Chromosome( k ) = 1 ; end% End of if end% End of if end % End of for - k end % End of for - j end % End of for - Gen for j = 1 : PopulationSize X1( j ) = DecodeChromosome(Population( j ) . Chromosome, 1 , ChromosomeLen ); X2( j ) = DecodeChromosome(Population( j ) . Chromosome, ChromosomeLen+1 , ChromosomeLen ); end Xmin = -2.5 ; Xmax = 2.5 ; Ymin = -2.5; Ymax = 2.5; X1 = 2 * XRang * X1/1023 - XRang; X2 = 2 * XRang * X2/1023 - XRang; figure plot( X1 , X2 , '*') , grid , axis([Xmin Xmax Ymin Ymax]); figure [X , Y] = meshgrid(-XRang : 0.1: XRang); Z = 100 * ( X.^2 - Y ).^2 + ( 1 - X ).^2; mesh(X , Y , Z); AimValue = ones(1 , MaxGeneration) * (100 * ( XRang^2 + XRang )^2 + ( 1 + XRang )^2) ; Xmin = 0 ; Xmax = MaxGeneration ; Ymin = 0; Ymax = 5000; figure hold on plot( BestValue , 'r' ) ; plot( AverageValue , 'b' ) ; plot( AimValue , 'g' ) ; hold off grid axis([Xmin Xmax Ymin Ymax]); 下面是四个子函数 function [ Fitness ] = CalculateFitnessValue( Value , Vmax , Vmin , FunctionMode) % To calculate fitness value % FunctionMode : % >= 0 find the maximum of the function % < 0 find the minimum of the function % Fitness is big than 0 if FunctionMode >= 0 if (Value + Vmin) > 0 Fitness = Value + Vmin ; else Fitness = 0; end else if Value < Vmax Fitness = Vmax - Value ; else Fitness = 0; end end function [Value] = CalculateObjectValue( Chromosome , Len) % To calculate value according to the function which we want to find its % maximum or minimum % In this program the function is % F( x1 , x2 ) = 100 * ( x1^2 - x2 )^2 + ( 1 - x1 )^2 % s.t -2.048 <= x1 , x2 <= 2.048 Value1 = DecodeChromosome(Chromosome, 1 , Len ); Value2 = DecodeChromosome(Chromosome, Len+1 , Len ); Value1 = 4.096 * Value1/1023 - 2.048; Value2 = 4.096 * Value2/1023 - 2.048; Value = 100 * ( Value1^2 - Value2 )^2 + ( 1 - Value1 )^2; function [Value] = DecodeChromosome( ChromosomeCode , CodePos , Len ) % Function : To decode a binary chromosome code into a decimal integer Value = 0 ; k = Len - 1; Ed = CodePos + Len -1; for j = CodePos : Ed Value = Value + ChromosomeCode( j ) * ( 2 ^ ( k ) ) ; k = k - 1; end

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