Stochastic optimization methods

It is also worth noting that the stochastic optimization methods described previously are readily adapted to the inclusion of constraints. For example, in simulated annealing, if a move suggested at random takes the solution outside of the feasible region, then the algorithm can be constrained to prevent this by simply setting the probability of that move to 0. 

Stochastic optimization methods described previously, such as simulated annealing, can also be used to solve the general nonlinear programming problem. These have the advantage that the search is sometimes allowed to move uphill in a minimization problem, rather than always searching for a downhill move. Or, in a maximization problem, the search is sometimes allowed to move downhill, rather than always searching for an uphill move. In this way, the technique is less vulnerable to the problems associated with local optima. 

Summary. We recently developed an all-atom free energy force field (PFFOl) for protein structure prediction with stochastic optimization methods. We demonstrated that PFFOl correctly predicts the native conformation of several proteins as the global optimum of the free energy surface. Here we review recent folding studies, which permitted the reproducible all-atom folding of the 20 amino-acid trp-cage protein, the 40-amino acid three-helix HIV accessory protein and the sixty amino acid bacterial ribosomal protein L20 with a variety of stochastic optimization methods. These results demonstrate that all-atom protein folding can be achieved with present day computational resources for proteins of moderate size. 

This review indicates that all-atom protein structure prediction with stochastic optimization methods becomes feasible with present-day computational resources. The fact that three proteins were reproducibly folded with different optimization methods to near-native conformation increases the confidence in the parameterization of our all-atom protein force field PFFOl. The... 

T. Herges, A. Schug, B. Burghardt, and W. Wenzel. Exploration of the free energy surface of a three helix peptide with stochastic optimization methods. Inti. J. Quant. Chem., 99 854-893, 2004. 

H. Merlitz and W. Wenzel. Comparison of stochastic optimization methods forreceptor-ligand docking. Chem. Phys. Lett., 362 271, 2002. 

To identify potentially active compounds in the virtual library, FOCUS-2D employs stochastic optimization methods such as SA (228, 229) and (jA (230-232). The latter algorithm was used for targeted pentapeptide library design as follows. Initially, a population of 100 peptides is randomly generated and encoded by use of topological indices or amino acid-dependent physicochemical descriptors. The fitness of each peptide is evaluated by its biological activity predicted from a precon-structed QSAR equation (see below). Two par-... 

The third maj or class of search methods are genetic algorithms (GAs), which are widely used for docking purposes. GAs are stochastic optimization methods inspired by the concepts of evolution (172-174). The optimization problem is generally formulated in the Ian-... 

EAs are stochastic optimization methods that simulate the process of natural evolution (Van Veldhuizen, 1999). The basic principles of these algorithms are the following ... 

Merlitz, H. and Wenzel, W. (2002) Comparison of stochastic optimization methods for receptor-ligand docking. Journal of Physical Chemistry Letters,... 

The retrofitted HEN by MOO may have small heaters/coolers, mainly because stochastic optimization methods do not give a precise optimum. Study the effect of removing these heaters/coolers in Figure 7.9 on the utility and retrofit costs. 

Particle Swarm Optimization (PSO) is a stochastic optimization method evolved from Swarm Theory and Evolutionary Computation [4]. It is instigated by animals natural swarming behavior [5]. PSO has been proven to be a suitable technique for solving various optimization problems [6, 7]. Among the advantages of PSO are that it allows efficient and rapid optimization of the problem, due to its parallel nature, it requires only basic mathematical operators for optimization and it provides low computational and memory costs for each iteration [8]. Many variants of the PSO algorithm exist, such as PSO with inertia weight [9], PSO with constriction factor [10], and mutative PSO [11]. 

Parameters describing crystallization were optimized using the genetic algorithm inverse method—a stochastic optimization method based on the mechanism of natural selection [52]. 

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