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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (2): 269-275.doi: 10.3969/j.issn.1005-3085.2015.02.011

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一个新的单参数填充函数算法

李  博,  鲁殿军   

  1. 青岛科技大学数理学院，青岛 266061
  • 收稿日期:2013-09-22 接受日期:2014-01-03 出版日期:2015-04-15 发布日期:2015-06-15
  • 基金资助:
    山东省博士基金 (BS2013SF014).

A New One-parameter Filled Function Algorithm

LI Bo,   LU Dian-jun   

  1. College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061
  • Received:2013-09-22 Accepted:2014-01-03 Online:2015-04-15 Published:2015-06-15
  • Supported by:
    The Science Foundation for Doctors of Shandong Province (BS2013SF014).

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摘要： 本文研究连续全局最优化问题的确定性求解方法．构造了一个单参数填充函数并证明了该填充函数的性质．该填充函数算法由极小化阶段和填充阶段两个阶段构成．其中极小化阶段利用局部优化方法获得填充函数的局部极小点，对填充函数的无约束极小化使得算法离开原目标函数的任何局部极小点．填充阶段依据原目标函数的局部极小点构造填充函数．极小化阶段和填充阶段交替重复实施直到终止准则满足．最后，给出了填充函数算法的数值结果．

关键词: 非线性规划, 全局最优化, 确定性算法, 填充函数, 单参数

Abstract:

This paper is concerned a deterministic solution method for global optimization of functions with continuous variables. A filled function with one parameter is presented and the theoretical properties of the filled function are proved. Moreover, a filled function algorithm is proposed for continuous global optimization problem. The filled function algorithm consists of two phases: a local search phase and a function filling phase. In the local search phase, we apply local minimization methods to obtain a local minimizer of the filled function. The unconstrained minimization of the filled function allows to escape from any local minima of the original objective function. In the function filling phase, based on the current local minimizer, we construct a filled function. The two phases repeat alternatively until the termination criterion is met. Finally, the numerical results of the proposed filled function algorithm are presented.

Key words: nonlinear programming, global optimization, deterministic method, filled function, one-parameter

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