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

Particle Swarm Optimization (PSO) methods gained a lot of attention in the optimization community due to the great efficiency and simplicity. In fact, the algorithm implementation is really simple, the memory usage compact, and the speed of convergence fast. On the other hand, they do not give any proof of their convergence at a stationary point: more, they do not give any proof of the convergence at all. A proper selection of the coefficients to be used by the algorithm give a partial proof of its convergence, but the qualities of the point at which the algorithm converges are not certified. A survey of these qualities can be found in [1, 2]. On the other hand, exact algorithms of the family of the Adaptive Cov- ering Methods (ACM) give proof of the global minimum with a certification provided by the largest unexplored portion of the design variable space [3]. These algorithms have the drawback of a large computational cost, due to the tendency of a complete exploration of the assigned region. A collaborative use of this two algorithms are here proposed. Algorithms are used in parallel, and they take advantage each other by the actual best location. The proof of global convergence of the ACM is preserved, while the efficiency of the PSO are exploited for a faster identification of the global minimum.