无数学模型的非线性约束单目标系统优化方法改进

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

为提高无法准确建立数学模型的非线性约束单目标系统优化问题的寻优精度,并考虑获取样本的代价,提出一种基于支持向量机和免疫粒子群算法的组合方法（support vector machine and immune particle swarm optimization,SVM-IPSO）.首先,运用支持向量机构建非线性约束单目标系统预测模型,然后,采用引入了免疫系统自我调节机制的免疫粒子群算法在预测模型的基础上对系统寻优.与基于BP神经网络和粒子群算法的组合方法（BP and particle swarm optimization,BP-PSO）进行仿真实验对比,同时,通过减少训练样本,研究了在训练样本较少情况下两种方法的寻优效果.实验结果表明,在相同样本数量条件下,SVM-IPSO方法具有更高的优化能力,并且当样本数量减少时,相比BP-PSO方法,SVM-IPSO方法仍能获得更稳定且更准确的系统寻优值.因此,SVM-IPSO方法为实际中此类问题提供了一个新的更优的解决途径.

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 sam-ples. 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.