A New Filled Function Method with Two Parameters for Global Optimization

Fei Wei ； Shugang Li ； Haifei Lin

《電腦學刊》 29卷5期 (2018/10) Pp. 96-111

https://doi.org/10.3966/199115992018102905009

摘要

The filled function method is an effective approach to find the global minimizer of multi-modal functions because of its strict theoretical framework. Most of the conventional filled functions are numerical unstable due to exponential or logarithmic term and sensitive to parameters; in addition, most filled functions are discontinuous and non-differentiable that might influence effectiveness of the algorithm. In this paper, a new filled function with two parameters is proposed for solving global optimization problem, and several important theorems are proved. Unusually, this proposed filled function is continuously differentiable and non-sensitive to all parameters; although this new filled function contains two parameters, all of the parameters are easily set in numerical experiments. Based on these, a new filled function algorithm is proposed and tested on several benchmark functions. The numerical experiment results show that the new filled function algorithm is efficient. In addition, the proposed algorithm is compared, and the results indicate that the proposed filled function method can find more optimal solutions.

關鍵字

filled function ； global optimization ； local minimize ； global minimizer