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A Global Subspace Optimization Algorithm for Minimum Energy Molecular Cluster Conformation Wu, Zhiyun


We consider the problem to obtain the optimal conformation of a given molecular cluster with the lowest possible potential energy. This problem has been studied as a test case for global optimization algorithms, and considered as a starting point for the study of more complicated conformational problems such as protein folding through potential energy minimization. Here we propose a global subspace optimization algorithm for the solution of the problem, with the variables of the energy function divided into subgroups and optimization performed successively in the subspaces corresponding to the subgroups of variables. The idea behind the algorithm comes from the study of group behaviors of biological populations, where species compete for resources yet find strategies to co-exist and co-evolve. We show that such behaviors can be modeled as a multi-player evolutionary game, and the potential energy minimization problem can be reduced to such a game, with each subgroup of variables considered as a strategy set to be determined by a subpopulation of species. Thus, the successive subspace minimization of an energy function proceeds like a game played among subgroups of species in a biological population. We show that a Nash-equilibrium of the game is equivalent to a KKT point of the energy minimization problem subject to a set of linear and nonnegative constraints, and an evolutionary stable equilibrium corresponds to a strict energy minimizer. We describe the implementation of the algorithm and present some preliminary test results for a small group of clusters.

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