The joint effect of ultrasound and magnetic Fe₃O₄ nanoparticles on the yield of 2,6-dimethoxy-ρ-benzoquinone from fermented wheat germ: Comparison of evolutionary algorithms and interactive analysis of paired-factors

2,6-Dimethoxy-ρ-benzoquinone (DMBQ) is a potential anti-tumor substance found in the fermented wheat germ. In this study, ultrasound and Fe₃O₄ nanoparticles were used to improve the DMBQ yield. An artificial neural network (ANN) embedded separately with the back-propagation algorithm (BP), genetic algorithm (GA), particle swarm optimized algorithm (PSO), ant colony optimized algorithm (ACO), GA-ACO, GA-PSO and PSO-ACO, were used to establish the relationship between 11 factors and DMBQ yield. The robustness and generalization of PSO-ACO-ANN, which gave the minimum mean squared error and mean absolute percentage error for the training and test dataset, was superior to the others. Next, a modified Garson's algorithm and mixed partial derivatives algorithm indicated that the most influential paired-parameters were ultrasonic power and concentration of nanoparticles. Finally, the factors were optimized by six optimization algorithms, and confirmatory experimental results indicated that the optimum DMBQ yield was 0.213 ± 0.007 mg/g, which was 161.2% higher than the control.