A new filled function method for solving constrained global optimization problems

Filled function methods have been considered as effective algorithms for solving global optimization problems. However, their effectiveness is greatly affected by the selection of parameters, the noncontinuous or non-differentiable properties of the constructed filled function. In addition, many of the constructed filled functions are only for unconstrained optimization problems, and they are unable to solve constrained optimization problems. In this paper, a new filled function is constructed for solving constrained global optimization problems. The new filled function has only one parameter which needs to be adjusted, and, when the objective functions and constrained functions are all continuously differentiable functions, the constructed filled function is also a continuously differentiable function. Then, the classical local optimization methods can be used to find a better minimum of the proposed filled function and a few parameter adjustments are needed. At last, a new filled function algorithm for constrained global optimization is developed based on the proposed filled function. The new algorithm is applied to several test examples. The results of the numerical experiments show that the new filled function algorithm is effective and efficient.