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We have pointed out in Section "A hybrid algorithm" that the sequence generated by the hybrid algorithm converges to a local optimal solution.
By means of a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solution set of GEP and common fixed point set of nonexpansive mappings.
At CER = 10−5, the average number of operations required by the hybrid algorithm is still about one order of magnitude larger than that of the corresponding IA alone.
The SIR given by the hybrid algorithm for the experimental arrangement shown in Figure 9 on all the three output streams was between 7 and 8 dB approximately and is summarised in Table 3.
The hybrid training algorithm is combined with the improved particle swarm optimization and BP algorithm, while the improved PSO-BP ANN model is developed and trained by the hybrid algorithm based on improved PSO and BP algorithm.
Performance of different optimization algorithms including GA SQP, GA, pattern search (PS), and grid search (GS) indicated that the best average absolute relative error (AARE), squared correlation coefficient (R 2), and computation time (CT) (AARE = 0.0745, R 2 = 0.997 and CT = 56 s) was accomplished by the hybrid algorithm.
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In another study [ 13], simulations have been implemented in the MATLAB environment by using the hybrid algorithm for the ventilators used in intensive care units.
Since some of the quantities are computed twice (i.e., the mean density 〈ρ〉 and the Favre averaged sensible internal energy ẽs), by the finite-volume scheme and by the particle method, the hybrid algorithm is redundant.
It is found by test problems that the hybrid algorithm shows superior performance in finding global optima compared to the so far best results in the literature.
A nonlinear limit-state function example was provided to validate the accuracy and efficiency of the hybrid algorithm by comparing the algorithm's solution with the exact solution of the example.
The results show that the hybrid algorithm by combining SVR and optimization algorithms with the exception of PSO can effectively reduce NOx emissions of the coal-fired utility boiler below the legislation requirement of China.
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