Optimization method improvement for nonlinear constrained single objective system without mathematical models

Optimization problems of nonlinear constrained single objective system are common in engineering and many other fields. Considering practical applications, many optimization methods have been proposed to optimize such systems whose accurate mathematical models are easily constructed. However, as more variables are being considered in practical applications, objective systems are becoming more complex, so that corresponding accurate mathematical models are difficult to be constructed. Many previous scholars mainly used back propagation (BP) neural network and basic optimization algorithms to successfully solve systems that are without accurate mathematical models. But the optimization accuracy still needs to be further improved. In addition, samples are needed to solve such system optimization problems. Therefore, to improve the optimization accuracy of nonlinear constrained single objective systems that are without accurate mathematical models while considering the cost of obtaining samples, a new method based on a combination of support vector machine and immune particle swarm optimization algorithm (SVM-IPSO) is proposed. First, the SVM is used to construct the predicted model of nonlinear constrained single objective system. Then, the immune particle swarm algorithm, which incorporates the self-regulatory mechanism of the immune system, is used to optimize the system based on the predicted model. The proposed method is compared with a method based on a combination of BP neural network and particle swarm optimization algorithm (BP-PSO). The optimization effects of the two methods are studied under few training samples by reducing the number of training samples. The simulation results show that the SVM-IPSO has a higher optimization ability under the same sample size conditions, and when the number of samples decreases, the SVM-IPSO method can still obtain more stable and accurate system optimization values than the BP-PSO method. Hence, the SVM-IPSO method provides a new and better solution to this kind of problems.