A Hybrid Method for Continuous Global Optimization Involving the Representation of the Solution

Global optimization problems involve essential difficulties as, for instance, avoiding convergence to local minima. A large variety of methods for global optimization has been proposed in the literature, where stochastic and deterministic approaches may be found. In order to get several solutions, population based methods (such as evolutionary ones) have been considered. Hybrid methods have been introduced in order to keep the flexibility of the evolutionary/stochastic approach and the efficiency of the deterministic one. Recently, a new way has been opened for the global optimization of a continuous function f:R n → R on a regular region S ≠ ∅ of R n by characterizing the solutions as means of suitable random variables. In this work, we present a hybrid method of evolutionary type for the determination of optimum. The initial population is numerically generated by using the result of representation previously mentioned. The mutations are obtained by stochastic perturbation of deterministic descent methods. Different deterministic descent methods are considered in the numerical experiments. The experiments show that the method is effective to calculate and that a significant improvement is obtained by the use of the representation of the solution: function evaluations are saved and the probability of success is increased, even when small populations are considered. We shall present a complete analysis of the effect of the different parameters of the method. The robustness of the method is established and it is applied to a relevant inverse problem: the calibration of model in transportation theory