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Research on the Filled Function Algorithms for Solving Nonlinear Global Optimization Problems

Author: ChenWeiLai
Tutor: HeSuXiang
School: Wuhan University of Technology
Course: Applied Mathematics
Keywords: filled function algorithm unconstrained optimization problems constrained optimization problems global minimizer numerical results
CLC: O224
Type: Master's thesis
Year: 2010
Downloads: 27
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Abstract


The filled function algorithm is one of the deterministic methods for solving nonlinear global optimization problem. It successfully solved how to start from the current local minimal solution to find better local minimal solution of the problem. This paper studied the new filled function algorithm of unconstrained global optimization problems and constrained global optimization problems. Their properties are discussed on emphasis. The main work is summarized as follows.Chapter one mainly introduced the current domestic and foreign several kind of classic methods for solving nonlinear global optimization problem. For the filled function algorithm, from the idea of the algorithm to the related theory that given the explanation. based on this, has analyzed the respective advantages. For the further promotion and construct a new filled function algorithm, provides some guidelines and methods.Chapter two proposed a new filled function with one parameter for solving continuously unconstrained global optimization problems, which was simple and easy to be calculated. Has analyzed and proven this filled function’s property under several kind of supposition conditions. A corresponding filled function algorithm is established. At last, numerical results are given to show that the new filled function algorithm is effective for solving global optimization problems.Chapter three expanded the filled function in chapter two for solving unconstrained global optimization problems to the general constrained global optimization problems. A new filled function with one parameter is proposed without the coercive condition, in which has only one adjustable parameter, contains neither exponential term nor fractional term, and the parameter easy to be select. Based on discussion on the properties of the function, a corresponding filled function algorithm is established. At last, we performed numerical experiments using the algorithm on some classic examples, and the detailed numerical results show that the algorithm for solving constrained global optimization problem is also effective.The last chapter draw conclusions of this paper and the development direction of filled function algorithm is prospected.

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Optimization of the mathematical theory
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