A new filled function applied to global optimization

The filled function method is an approach to find the global minimiser 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.