A Novel Penalty Function Approach to Constrained Optimization Problems with Genetic Algorithms
Xinghuo Yu*, Weixing Zheng**, Baolin Wu* and Xin Yao***
*Faculty of Informatics and Communication, Central Queensland University Rockhampton OLD 4702, Australia
**School of Science, University of Western Sydney Nepean, NSW 2747, Australia
***School of Computer Science, University College, University of New South Wales ADFA, ACT 2600, Australia
In this paper, a novel penalty function approach is proposed for constrained optimization problems with linear and nonlinear constraints. It is shown that by using a mapping function to “wrap” up the constraints, a constrained optimization problem can be converted to an unconstrained optimization problem. It is also proved mathematically that the best solution of the converted unconstrained optimization problem will approach the best solution of the constrained optimization problem if the tuning parameter for the wrapping function approaches zero. A tailored genetic algorithm incorporating an adaptive tuning method is then used to search for the global optimal solutions of the converted unconstrained optimization problems. Four test examples were used to show the effectiveness of the approach.
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