Among numerical optimization techniques, the direct-search method which need not to evaluate the gradient is much suitable for the analysis of dynamics of complex nonlinear control system. The Modified Powell Method is well known to have ultimate fast convergence among direct-search methods, especially where the cost function is approximated well by a quadratic form of parameters to be estimated. However even if this method is applied, the minimum points obtained may not be the global minimum; most of the conventional numerical optimization can be easily be trapped in local optima or by constraints in a region of the parameter space far from the optimal solution.
The Genetic Algorithm (GA) is based on the heuristic assumptions that the "best" solutions will be found in regions of the parameter space containing a relatively high proportion of "good" solutions and that these regions can be explored by the genetic operators of selection, crossover and mutation. The GA searches from a set of designs (not from a single design), and it is not derivative-based, and it can explore and exploit the parameter space without trapping in local optima. However this method has major disadvantage that the computational cost of the large numbers of runs of the design code is considerably large.
In the present study, we proposed the hybrid numerical optimization techniques which is incorporated the GA into the Modified Powell Method. It is highly expected that a unique combination of the GA and the Modified Powell offers all advantages of both optimization techniques while offsetting their disadvantages.
The effectiveness was shown especially for the minimum search problem of a variable-separable multi-peak function; without trapping and staying in local minimum, the proposed method can explore and exploit the global minimum with considerably fast convergence.