Abstract
To help solve difficult global optimization problems such as those arising in molecular chemistry, smoothing the objective function has been used with some efficacy. In this paper we propose a new approach to smoothing. First, we propose a simple algebraic way to smooth the Lennard-Jones and the electrostatic energy functions. These two terms are the main contributors to the energy function in many molecular models. The smoothing scheme is much cheaper than the classic spatial averaging smoothing technique. In computational tests on the proteins polyalanine with up to 58 amino acids and metenkephalin, smoothing is very successful in finding the lowest energy structures. The largest case of polyalanine is particularly significant because the lowest energy structures that are found include ones that exhibit interesting tertiary as opposed to just secondary structure.
Research Supported by Air Force Office of Scientific Research Grant F49620-97-1-0164, Army Research Office Contracts DAAG55-98-1-0176 and DAAD19-02-1-0407, and National Science Foundation Grants CDA-9502956 and CHE-0205170.
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Azmi, A.M., Byrd, R.H., Eskow, E., Schnabel, R.B. (2006). A New Smoothing-Based Global Optimization Algorithm for Protein Conformation Problems. In: Pintér, J.D. (eds) Global Optimization. Nonconvex Optimization and Its Applications, vol 85. Springer, Boston, MA . https://doi.org/10.1007/0-387-30927-6_4
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