Optimization method improvement for nonlinear constrained single objective system without mathematical models
-
摘要: 為提高無法準確建立數學模型的非線性約束單目標系統優化問題的尋優精度,并考慮獲取樣本的代價,提出一種基于支持向量機和免疫粒子群算法的組合方法(support vector machine and immune particle swarm optimization,SVM-IPSO).首先,運用支持向量機構建非線性約束單目標系統預測模型,然后,采用引入了免疫系統自我調節機制的免疫粒子群算法在預測模型的基礎上對系統尋優.與基于BP神經網絡和粒子群算法的組合方法(BP and particle swarm optimization,BP-PSO)進行仿真實驗對比,同時,通過減少訓練樣本,研究了在訓練樣本較少情況下兩種方法的尋優效果.實驗結果表明,在相同樣本數量條件下,SVM-IPSO方法具有更高的優化能力,并且當樣本數量減少時,相比BP-PSO方法,SVM-IPSO方法仍能獲得更穩定且更準確的系統尋優值.因此,SVM-IPSO方法為實際中此類問題提供了一個新的更優的解決途徑.
-
關鍵詞:
- 非線性約束單目標系統 /
- 支持向量機 /
- 免疫粒子群算法 /
- 仿真 /
- 優化
Abstract: 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. -
參考文獻
[1] Courant R. Variational methods for the solution of problems of equilibrium and vibrations. Bull Am Math Soc, 1943, 49(1943):1 [2] Powell M J D. A method for nonlinear constraints in minimization problems. Optimization, 1969, 5(6):283 [4] McDougall T J, Wotherspoon S J. A simple modification of Newton's method to achieve convergence of order 1+2. Appl Math Lett, 2014, 29:20 [5] Shen C G, Zhang L H, Liu W. A stabilized filter SQP algorithm for nonlinear programming. J Global Optimization, 2016, 65(4):677 [8] Beheshti Z,Shamsuddin S M,Yuhaniz S S. Binary accelerated particle swarm algorithm (BAPSA) for discrete optimization problems. J Global Optimization, 2013, 57(2):549 [18] Eberhart R, Kennedy J. A new optimizer using particle swarm theory//Proceedings of the Sixth International Symposium on Micro Machine and Human Science. Nagoya, 1995:39 [19] Kathiravan R, Ganguli R. Strength design of composite beam using gradient and particle swarm optimization. Compos Struct, 2007, 81(4):471 -
點擊查看大圖
計量
- 文章訪問數: 753
- HTML全文瀏覽量: 315
- PDF下載量: 16
- 被引次數: 0
下載:
