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In this paper, a new filled function which has better properties is proposed for identifying a global minimum point for a general class of nonlinear programming problems within a closed bounded domain. An algorithm for unconstrained global optimization is developed from the new filled function. Theoretical and numerical properties of the proposed filled function are investigated. The implementation of the algorithm on seven test problems is reported with satisfactory numerical results. 相似文献
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The filled function method is an approach to find the global minimum of multidimensional functions. This paper proposes a new definition of the filled function for integer programming problem. A filled function which satisfies this definition is presented. Furthermore, we discuss the properties of the filled function and design a new filled function algorithm. Numerical experiments on several test problems with up to 50 integer variables have demonstrated the applicability and efficiency of the proposed method. 相似文献
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Ai-Fan Ling Cheng-Xian Xu Feng-Min Xu 《Journal of Computational and Applied Mathematics》2008,220(1-2):643-660
A discrete filled function algorithm is proposed for approximate global solutions of max-cut problems. A new discrete filled function is defined for max-cut problems and the properties of the filled function are studied. Unlike general filled function methods, using the characteristic of max-cut problems, the parameters in proposed filled function need not be adjusted. This greatly increases the efficiency of the filled function method. By combining a procedure that randomly generates initial points for minimization of the filled function, the proposed algorithm can greatly reduce the calculation cost and be applied to large scale max-cut problems. Numerical results on different sizes and densities test problems indicate that the proposed algorithm is efficient and stable to get approximate global solutions of max-cut problems. 相似文献
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In this paper, a discrete filled function algorithm embedded with continuous approximation is proposed to solve max-cut problems. A new discrete filled function is defined for max-cut problems, and properties of the function are studied. In the process of finding an approximation to the global solution of a max-cut problem, a continuation optimization algorithm is employed to find local solutions of a continuous relaxation of the max-cut problem, and then global searches are performed by minimizing the proposed filled function. Unlike general filled function methods, characteristics of max-cut problems are used. The parameters in the proposed filled function need not to be adjusted and are exactly the same for all max-cut problems that greatly increases the efficiency of the filled function method. Numerical results and comparisons on some well known max-cut test problems show that the proposed algorithm is efficient to get approximate global solutions of max-cut problems. 相似文献
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《Journal of Computational and Applied Mathematics》2005,181(1):200-210
The paper gives a definition of the filled function for nonlinear integer programming. This definition is modified from that of the global convexized filled function for continuous global optimization. A filled function with only one parameter which satisfies this definition is presented. We also discuss the properties of the proposed function and give a filled function method to solve the nonlinear integer programming problem. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. 相似文献
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提出一个基于滤子技术的填充函数算法, 用于求解带箱式约束的非凸全局优化问题. 填充函数算法是求解全局优化问题的有效方法之一, 而滤子技术以其良好的数值效果广泛应用于局部优化算法中. 为优化填充函数方法, 应用滤子来监控迭代过程. 首先给出一个新的填充函数并讨论了其特性, 在此基础上提出了理论算法及算法性质. 最后列出数值实验结果以说明算法的有效性. 相似文献
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For smooth or non-smooth unconstrained global optimization problems, an one parameter filled function is derived to identify their global optimizers or approximately global optimizers. The theoretical properties of the proposed function are investigated. Based on the filled function, an algorithm is designed for solving unconstrained global optimization problems. The algorithm consists of two phases: local minimization and filling. The former is intended to minimize the objective function and obtain a local optimizer, the latter aims to find a better initial point for the first phase. Numerical experimentation is also provided. The preliminary computational results confirm that the proposed filled function approach is promising. 相似文献