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Proceedings of GO 2005, pp. 15 – 16.Global Optimization for Problems with a Huge Numberof Local OptimaBernardetta Addis, 1 Marco Locatelli, 2 and Fabio Schoen 11 Dip. Sistemi e Informatica, Univ. di Firenze, via di Santa Marta, 3, 50139 Firenze (Italy) (b.addis,schoen)@ing.unifi.it2 Dip. Informatica, Univ. di Torino, Torino (Italy) locatell@di.unito.itKeywords:Global Optimization, Basin Hopping, Monte Carlo with minimization, Lennard Jones clusters, Morseclusters, protein-protein docking, circle packingIn this paper we will present a unifying framework for solving many difficult, large scale,global optimization problems with a huge number of local optima. Of course it is hopelessto pretend to develop a single general purpose algorithm for all kind of large scale globaloptimization problems. However, as we will show, if the objective function possesses somespecial structure, than it is possible to build optimization algorithms which are extremelyefficient even in the presence of a number of local optima which increases exponentially withthe problem dimension.In computational chemistry and biology one such common structure is known as “funnelstructure” and is commonly related to the fact that many energy functions which modelcomplex many-body interactions, although being highly multimodal, can be optimized quiteefficiently using methods of the Basin-hopping (BH) (or Montecarlo with Minimization) type.In this paper we review some of our recent results in applying BH-like methods to severalimportant problems like:global optimization of atomic clusters interacting via the Lennard-Jones potentialglobal optimization of short-range Morse clustersProtein-protein rigid dockingTwo-dimensional circle packingWhile the first three problems, although quite different from each other, all originate fromthe field of computational chemistry and biology, the last one is a totally different one andis concerned with the optimal placing of N identical and non-overlapping circles of maximumradius in the unit square. Not only the origin of this well known problem are differentfrom that of cluster optimization and protein docking, but also the structure of the problemis radically different. In fact, while in the first 3 problems, we are dealing with unconstrainedglobal optimization problems, in the last case the problem is constrained, with a non convexfeasible region. It is somewhat surprising that simple algorithmic ideas used in the context ofmolecular optimization can be quite easily ported to the constrained case.In the paper we will review some of the main ingredients of BH-like methods for the problemsdiscussed and, in particular, we will consider the following characteristics:the use of Monotonic Basin-Hopping as a general purpose algorithm for descendingtowards a funnel’s bottom (provided a suitable definition of a neighborhood structure isavailable)