Dynamic Filled Algorithm For Global Optimization

In this paper, we mainly study how to solve global optimization problems. Ordinarily, the solving process of global optimization problems contain two phases. One is how to find the current local minimizer of the global optimization problem, the other is how to get a new local minimizer whose value is better than the current local minimizer.Firstly, a new algorithm for the global optimization problem is proposed, which is based on the differential dynamical systems and filled function method. The new algorithm is mainly constructed by two differential dynamical systems, the dynamic minimizing system and the dynamic filled system. The dynamic minimizing system is used to find the local minimizer of the global optimization. The new dynamic filled system will achieve an equilibrium within a prescribed time. Moreover, the objective function value of the equilibrium is smaller than the current local minimizer, and a new initial condition in a lower basin will be determined. In fact, two systems above justly correspond to two phases of the global optimization problem. By repeating the two dynamic systems, the algorithm prevents itself from getting trapped in the current local minima, and a global minimizer of the problem will be rapidly obtained at last. Good numerical results of the examples given in the paper show the success of the algorithm.As there are many methods to find the local minimizer of the global optimization, to avoid the weight parameters to be used, we take the filter method. The objective function and con-straint functions are considered separately in filter method, and the trial point will be accepted if and only if the decrease of either the constrained value or the objective function value is suf-ficient. A new norm-relaxed SQP subproblem which is consistent to the optimization problem is constructed. Combined with the filter method, a norm-relaxed SQP filter algorithm will be presented. By solving the norm-relaxed SQP subproblem and taking a validly constructed filter criteria as the merit function, not only the computation of the new filter algorithm could be re-duced, but also aviod using the weight parameters. Furthermore, another correction direction is given by the new filter algorithm to avoid the Maratos effect, and the convergent properties are proved at last.