In this paper, we propose a K-means clustering-based integral level-value estimation algorithm to solve a kind of box-constrained global optimization problem. For this purpose, we introduce the generalized variance fu...In this paper, we propose a K-means clustering-based integral level-value estimation algorithm to solve a kind of box-constrained global optimization problem. For this purpose, we introduce the generalized variance function associated with the level-value of the objective function to be minimized. The variance function has a good property when Newton’s method is used to solve a variance equation resulting by setting the variance function to zero. We prove that the largest root of the variance equation is equal to the global minimum value of the corresponding optimization problem. Based on the K-means clustering algorithm, the multiple importance sampling technique is proposed in the implementable algorithm. The main idea of the cross-entropy method is used to update the parameters of sampling density function. The asymptotic convergence of the algorithm is proved, and the validity of the algorithm is verified by numerical experiments.展开更多
In this paper, we propose a new integral global optimization algorithm for finding the solution of continuous minimization problem, and prove the asymptotic convergence of this algorithm. In our modified method we use...In this paper, we propose a new integral global optimization algorithm for finding the solution of continuous minimization problem, and prove the asymptotic convergence of this algorithm. In our modified method we use variable measure integral, importance sampling and main idea of the cross-entropy method to ensure its convergence and efficiency. Numerical results show that the new method is very efficient in some challenging continuous global optimization problems.展开更多
In this paper,we propose a stochastic level-value estimation method to solve a kind of box-constrained global optimization problem.For this purpose,we first derive a generalized variance function associated with the c...In this paper,we propose a stochastic level-value estimation method to solve a kind of box-constrained global optimization problem.For this purpose,we first derive a generalized variance function associated with the considered problem and prove that the largest root of the function is the global minimal value.Then,Newton’s method is applied to find the root.The convergence of the proposed method is established under some suitable conditions.Based on the main idea of the cross-entropy method to update the sampling density function,an important sampling technique is proposed in the implementation.Preliminary numerical experiments indicate the validity of the proposed method.展开更多
文摘In this paper, we propose a K-means clustering-based integral level-value estimation algorithm to solve a kind of box-constrained global optimization problem. For this purpose, we introduce the generalized variance function associated with the level-value of the objective function to be minimized. The variance function has a good property when Newton’s method is used to solve a variance equation resulting by setting the variance function to zero. We prove that the largest root of the variance equation is equal to the global minimum value of the corresponding optimization problem. Based on the K-means clustering algorithm, the multiple importance sampling technique is proposed in the implementable algorithm. The main idea of the cross-entropy method is used to update the parameters of sampling density function. The asymptotic convergence of the algorithm is proved, and the validity of the algorithm is verified by numerical experiments.
基金Supported by the National Natural Science Foundation of China(No.10671117).
文摘In this paper, we propose a new integral global optimization algorithm for finding the solution of continuous minimization problem, and prove the asymptotic convergence of this algorithm. In our modified method we use variable measure integral, importance sampling and main idea of the cross-entropy method to ensure its convergence and efficiency. Numerical results show that the new method is very efficient in some challenging continuous global optimization problems.
文摘In this paper,we propose a stochastic level-value estimation method to solve a kind of box-constrained global optimization problem.For this purpose,we first derive a generalized variance function associated with the considered problem and prove that the largest root of the function is the global minimal value.Then,Newton’s method is applied to find the root.The convergence of the proposed method is established under some suitable conditions.Based on the main idea of the cross-entropy method to update the sampling density function,an important sampling technique is proposed in the implementation.Preliminary numerical experiments indicate the validity of the proposed method.
