A new filled function applied to global optimization
The filled function method (FFM) is an approach to find the global minimizer of multi-modal functions. The numerical applicability of conventional filled functions is limited as they are defined on either exponential or logarithmic terms. This paper proposes a new filled function that does not have such disadvantages. An algorithm is presented according to the theoretical analysis. A computer program is designed, implemented, and tested. Numerical experiments on typical testing functions show that the new approach is superior to the conventional one. The result of optimization design for an electrical machine is also reported. In the context of mathematical programming, global optimization is concerned with the theory and algorithms on minima of multi-modal functions. In general, global optimization approaches can be classified into two categories: probabilistic and deterministic. The former can usually be applied to general multi-modal functions, whereas the latter typically concentrates on some particular classes of functions. The filled function method is one of a few deterministic approaches which intend to find the global minimum for general multi-modal functions. However, the numerical performance of conventional filled functions is undesirable as they are defined on either exponential or logarithmic terms or multiple parameters. This paper proposes a new filled function that does not have the above disadvantages. The present work consists of theoretical analysis, algorithm design, computer implementation, mathematical validation, and engineering application.
global optimization filled function method minimization mathematical programming