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16 Bernardetta Addis, Marco Locatelli, and Fabio Schoenthe use of two-phase local searches to enlarge the basin of attraction of good local optimathe effect of coordination obtained through the embedding of BH-like methods in apopulation-based framework in which different local optima are maintained in sucha way as to guarantee a sufficiently high degree of dissimilarity between them.Careful definition of the above three elements is clearly problem-dependent, although somegeneral guidelines can be given for specific classes of problems. We will present some of theresults recently obtained and the details on the implementation of the above steps, for all ofthe problems introduced. In particular, by means of a suitable definition of the neighborhoodstructure of BH and a two-phase approach in which penalties inspired by the geometricalstructure of good solutions are introduced in the first phase, we could implement a singleunbiased global optimization method which is capable of confirming all of the putative globaloptima for Lennard-Jones and Morse clusters deposited at the Cambridge Cluster Database [3,5]. With a population-based approach we could further improve the efficiency of the methodand were able to discover several new putative optima for Morse cluster at very short range[4].Again, through a clever use of two-phase local optimization and a quite standard BH approachwe obtained encouraging results for large protein-protein docking problems [2]: here,however, given the extremely high computational cost associated to each energy evaluation,only limited computational experience has been collected.Finally we will report on the recent extension of BH-like methods to Circle Packing. Herewe have been very quicly able to code a quite simple, although not elementary, version ofBH (i.e., without two-phase local searches and with no population) which turned out to beextremely competitive with much more sophisticated methods. In very short time we havebeen able to improve more than 20 putative optima. In particular we obtained improvedconfigurations for a number of circles N equal to 53, 59, 66, 68, 73, 77, 78, 85, 86, 88 and manyothers for larger N values [1]. Work is in progress towards including a two-phase and/or apopulation based approach also in this context. However it can be quite safely assumed thatthe use of BH even in the simplest configuration enables to quickly discover excellent qualitylocal solutions to difficult global optimization algorithms.References[1] B. Addis, M. Locatelli and F. Schoen, Packing Circles in a Square: New Putative Optima Obtained Via Global Optimization,on Optimization On Linehttp://www.optimization-online.org/DB HTML/2005/03/1088.html[2] B. Addis and F. Schoen, A randomized global optimization method for protein-protein docking, available on OptimizationOn Linehttp://www.optimization-online.org/DB HTML/2003/04/638.html, (2003).[3] J. P. K. Doye, R. H.Leary, M. Locatelli and F. Schoen, The global optimization of Morse clusters by potential transformations,INFORMS J. Computing, 16, 371-379 (2004)[4] A. Grosso, M. Locatelli and F. Schoen, A population based approach for hard global optimization problems based ondissimilarity measures, submitted, available on Optimization On Linehttp://www.optimization-online.org/DB HTML/2005/02/1056.html (2005).[5] M.Locatelli and F.Schoen, Efficient algorithms for large scale global optimization: Lennard-Jones clusters, ComputationalOptimization and Applications, 26, 173-190 (2003).