Global Optimization for Possibly Time-Dependent Cost Functions by a Population Set-Based Algorithm with Births Control

In this paper a global optimization procedure is proposed, which can be related to the framework of the search algorithms based on models of population dynamics. In our approach the admissible set is decomposed into subsets (compartments), in each of which the search is parallelly carried out. As far as the number of born individuals is concerned, a control action is introduced, with the aim of intensifying the search in the most interesting compartments, dynamically identified. The generated individuals are localized in each compartment by exploiting the multidimensional Weyl theorem, which guarantees a dense exploration of the above-mentioned compartments. The procedure is able to deal also with dynamical or stochastic optimization problems. The algorithm performances have been widely tested against two, three, four, and six variables standard test functions. Comparisons with other similar algorithms have been performed with satisfactory results. Promising results have also been obtained in some applications to dynamical and stochastic optimization problems.