An improved real-coded genetic algorithm (IRCGA) is proposed to solve constrained optimization problems. First, a sorting grouping selection method is given with the advantage of easy realization and not needing to calculate the fitness value. Secondly, a heuristic normal distribution crossover (HNDX) operator is proposed. It can guarantee the cross-generated offsprings to locate closer to the better one among the two parents and the crossover direction to be very close to the optimal crossover direction or to be consistent with the optimal crossover direction. In this way, HNDX can ensure that there is a great chance of generating better offsprings. Thirdly, since the GA in the existing literature has many iterations, the same individuals are likely to appear in the population, thereby making the diversity of the population worse. In IRCGA, substitution operation is added after the crossover operation so that the population does not have the same individuals, and the diversity of the population is rich, thereby helping avoid premature convergence. Finally, aiming at the shortcoming of a single mutation operator which cannot simultaneously take into account local search and global search, this paper proposes a combinational mutation method, which makes the mutation operation take into account both local search and global search. The computational results with nine examples show that the IRCGA has fast convergence speed. As an example application, the optimization model of the steering mechanism of vehicles is formulated and the IRCGA is used to optimize the parameters of the steering trapezoidal mechanism of three vehicle types, with better results than the other methods used.

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A back propagation (BP) neural network-based linear constrained optimization method(BPNN-LCOM) was proposed for to solve the problems in linear constraint black box in this paper,hoping to improve the shortcoming of BP neural network-based constrained optimization method (BPNN-COM).In view of minimizing the mathematic model of network output, the basic ideas of BPNN-LCOM wereilluminated,includingmodel design and training, and BP neural network-based global optimization. Firstly, the iteration step size was calculated by optimal step size, and the adjustment step size was calculated by interpolation method, also the iteration speed was accelerated. Secondly, the search direction that iteration point locates on the boundary offeasible region was determined by gradient projection method, which ensured that the iteration process continued along a feasible search direction, and effectively solved the defect of BPNN-COM that sometimes fails to find thetrue optimal solutions. At the same time, the iteration step size along the gradient projection direction was calculated by the optimal constraint step size, which ensured the new iteration point located in the feasible region. Thirdly, the Kuhn-Tucker conditions were introduced to verify whether the iteration point is theoptimization solution that locates on the boundary of feasible region, and it made the termination criterion perfect for BPNN-LCOM.The computation results of two examples showed the effectiveness and feasibility of BPNN-LCOM. The BPNN-LOCM was used to optimize the roller-type bailing mechanism,and the optimal parameters were obtained as follows: round disc diameter was 360 mm, rotationalspeed of the steel rollerwas 250 rpm, feeding quantity was1.7 kg/s, and length-width ratio was 0.8. The corresponding minimum power consumption was 45.8 kJ/bundle. The optimization results were superior to regression analysis and BPNN-COM.The verification test was carried out and the optimization results could improve roller-type bailing mechanism. Verification results showed that the BPNN-LCOM is a feasible method for solving problems in linear constraint black box.INDEX TERMS BP neural network, Optimization method, Linear constraint, Gradient projection method.

In order to overcome the bad precision of fitted error, lower accuracy optimization results and other flaws, when extraction technology of the lotus leaf alkaloids was optimized by response surface method or regression analysis method, a linear constraint optimization method based on BP neural network is proposed. The testing program of three factors, three level was designed, which selected the hydrochloric acid mass fraction, ultrasound time, liquid-solid ratio as experimental factors. Taking the experiment data as training sample, the BP neural network model of the lotus leaf alkaloid yield and the influencing factors was obtained, and it was optimized by the proposed optimization method. The optimal parameter combination of extraction technology for lotus leaf alkaloid was obtained as follows: extraction temperature 60 °C, ultrasonic power 500W, hydrochloric acid mass fraction 0.3%, ultrasonic time 43 min, liquid-solid ratio 27, the yield of lotus leaf alkaloids under this process condition is 4.26 mg/g. It better than the best extraction technology obtained by response surface method. The obtained results is used for verification experiment, the verification results shown that the method has high fitting accuracy and stable optimization results, which optimize the extraction technology for lotus leaf alkaloid.

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