Context: There are complex inter-relationships among the branched-chain amino acids (BCAAs), making the use of full factorial design experiments more complicated, costly and time-consuming when attempting to estimate the optimal levels of the BCAAs. Aims: Two experiments were conducted to determine optimal concentrations of BCAAs by using the Taguchi method and mathematical models for broiler chickens during 15–21 days of age. Methods: In the first experiment, the optimal concentrations of BCAAs were determined for broiler chickens, and the accuracy of the results was evaluated in the second experiment. The orthogonal array layout of L16 (43) was applied to test four concentrations of leucine (Leu), isoleucine (Ile) and valine (Val). To test the validity of the results from 16 diets selected by the Taguchi method and four additional diets from the full factorial design method, a total of 960 broiler chickens was assigned to these 20 experimental diets, with six replicates of eight birds each. The Taguchi method, the multi-objective genetic algorithm (MOGA) and the random search algorithm (RSA) were used to determine the best concentration of BCAAs on the basis of optimal bird performance, which was measured by bodyweight gain, feed intake, and feed conversion ratio (FCR). In the second experiment, six dietary treatments were formulated to establish the reliability of the predictions obtained from the first experiment (Experiment 1). Key results: No exceptional concentrations of BCAAs were achieved for a maximum average daily gain and a minimum FCR; however, the diet containing 1.177–1.353% standardised ileal digestible (SID) Leu, 0.742–0.810% SID Ile, and 0.832–0.915% SID Val showed the best performance. The results of the second experiment indicated that the Taguchi method could be used instead of a full factorial design to optimise the amino acid requirements of broiler chickens. Conclusions: The requirements of BCAAs were overestimated using the MOGA and RSA methods compared with the Taguchi method.

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