The flexible alignment of molecular structures using simulated annealing with weighted Lagrangian multipliers

Abstract

A framework for superimposing small molecules is presented. The proposed method consists of a simple atom-based, flexible alignment. The optimization procedure used in the alignment is based on a recently published variant of the simulated annealing whereby nonlinear constraints are accommodated using Lagrangian multipliers. It differs from other published superposition algorithms in that any number of nonlinear constraints can be readily imposed on the structural alignment directly through the objective function without assuming an a priori trade-off between competing conditions. These can include equality and equality constraints on distances, angles, and energy states. Examples illustrating the use of the proposed approach are also provided.

Laser pulse design using optimal control theory-based adaptive simulated annealing technique: vibrational transitions and photo-dissociation

“…There is also no restriction on the optimising function to be appropriately quadratic or differentiable. The technique has many successful applications in several fields [27][28][29][30][31][32][33] of optimisation. SA algorithm is the repeated application of the Metropolis' simulation step over a sequence of decreasing temperatures starting from the melting point.…”