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Application of an Adaptive Differential Evolution Algorithm ... - Koszalin

Application of an Adaptive Differential Evolution Algorithm ... - Koszalin

SLOWIK: APPLICATION OF

SLOWIK: APPLICATION OF ADAPTIVE DIFFERENTIAL EVOLUTION ALGORITHM WITH MULTIPLE TRIAL VECTORS 3163Fig. 2.Structure of assumed ANN.value of coefficient A is lower when a greater improvementin the results obtained has occurred between two successivegenerations. In this case, the searching of the solution spacehas a more local nature and can lead to “fine-tuning” of the bestsolution to the optimal value.In the fourth step, a selection of individuals for the newpopulation is performed according to the following rule:If ERR(u i ) < ERR(x i ) thenreplace x i by u i in the new populationElse leave x i in the new populationIn the fifth step, it is checked whether the value ofERR(x r1 )

3164 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 8, AUGUST 2011TABLE IAVERAGE VALUES OF RESULTS OBTAINED AFTER TENFOLD REPETITIONOF DE+ ALGORITHM FOR DIFFERENT VALUES OF NTAND ϕ =0.99TABLE IIAVERAGE VALUES OF RESULTS OBTAINED AFTER TENFOLDREPETITION OF DE+ ALGORITHM (ϕ =0.90)lower than ɛ =0.0001 (this termination condition is dominantin the experiments) or when the assumed computation time wasexceeded.In Tables I–III, the symbols used are as follows: NT—thenumber of trial vectors; ME—the training method chosen;NI—the number of iterations; CC—the correct classification(%); FC—the false classification (%). The values representingthe correct CC and false FC classifications were computed asfollows:TABLE IIIAVERAGE VALUES OF RESULTS OBTAINED AFTER TENFOLDREPETITION OF DE+ ALGORITHM (ϕ =0.99)∑ Mi=1CC =i2 p · 100% (9)FC = 100% − CC (10)where CC—the correct classification (%); M—the number oftesting vectors (M ∈ [1, 2 p ]); p—the number of inputs in theANN; C i —the coefficient representing the correctness of theclassification of the ith training vector which is determined asfollows:C i ={ 1, when Uout >ϕfor B i =11, when U out < −ϕ for B i = −10, otherwise(11)where U out = f(S out )—the value of the output signal of theANN after the application of the ith testing vector to its input;ϕ—the threshold of the training correctness; B i —the valueexpected for the output of the ANN.In the first experiment, we try to determine the value of theNT parameter (the number of trial vectors). In this case, theANNs, having structures shown in Fig. 3 for the classificationof the parity-p problem (p ∈ [3; 6]), were trained using theproposed DE-ANNT+ method for different values of NT ∈[1; 10] and parameter ϕ =0.99. In Table I, the average valuesof the results obtained after a tenfold repetition of the proposedalgorithm are presented.It can be seen from Table I that the best results (the highestvalues of CC) are obtained for values NT ∈ [1; 4]. Therefore,

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