Collaborative use of a Particle Swarm Optimization algorithm and an Adaptive Covering Method for global optimization.

Evolutionary algorithms are typically prone to criticisms because of the lack of a proof of convergence: in fact, most of them do not have a convergence proof at all, some others can be supported by a partial proof of convergence to a point, without any quali¯cation of the point to which they are converging. Computational cost of these algorithms is widely considered acceptable, and they are largely applied in practice. On the other hand, other classes of algorithms have proof of global convergence, but the implications connected with this feature are rarely sustainable for real-life applications, unless strong simpli¯cations on the objective function, or a large use of special techniques, are adopted. In this paper a novel hybrid optimization algorithm is presented. The algorithm is able to take advantage of both the good qualities of the evolutionary and of the exact algorithms, that is, a fast approach to the global optima and global convergence.