Stochastic simulation optimization

By dealing with the evolution of constraints (i.e., Ramachandran basins) rather than the backbone torsional coordinates themselves, the dynamics are judiciously simplified [31]. The algorithm consists of a stochastic simulation of the coarsely resolved dynamics, simplified to the level of time-evolving Ramachandran basin assignments. An operational premise is that steric restrictions imposed by the side chains on the backbone may be subsumed into the basin-hopping dynamics. The side chain constraints define regions in the Ramachandran map that can be explored in order to obtain an optimized pattern of nonbonded interactions. 

Figure4.11 Multistep optimization for the estimation of parameters in stochastic simulation codes.

Figure 4.12 Multistep optimization for design and control using stochastic simulation codes [9].

Subramanian D., Pekny J. and Reklaitis G.V. 2000. A simulation-optimization framework for addressing combinatorial and stochastic aspects on an R D pipeline management problem. Comp. Chem. Eng., 24, 1005-1011. 

In addition, the models can be used for generating virtual materials, that is, they can generate microstructures of GDIs which have not been recorded so far. The combination of stochastic simulation of microstructures and numerical simulation of functionality leads to the concept of the so-called virtual material design, that is, the investigation and/or optimization of GDL morphologies based on computer experiments. This approach can be a valuable extension to physical experiments since computer experiments can be executed fairly fast and cheaply. Hence, many more scenarios than with physical experiments can be generated and analyzed in detail. 

For uncertainty function U -. X) E F X,Pno,Wfio) in the model of this chapter, we use stochastic simulation technology to find an optimal solution within all possible range of random variable pno and Wno-... 

The optimal solution is obtained in the possible range of random variables paj and Vfiij by using stochastic simulation approach. maxF can be achieved when the equal-sign of Eq. (5.22) is tenable, i.e. 

Subramanian, D., Pekny, J. F, Reklaitis, G. V., Blau, G. E. (2003). Simulation-optimization framework for stochastic optimization of R D pipeline management. AIChE Journal, 49, 96-112. 

We now consider probability theory, and its applications in stochastic simulation. First, we define some basic probabihstic concepts, and demonstrate how they may be used to model physical phenomena. Next, we derive some important probability distributions, in particular, the Gaussian (normal) and Poisson distributions. Following this is a treatment of stochastic calculus, with a particular focus upon Brownian dynamics. Monte Carlo methods are then presented, with apphcations in statistical physics, integration, and global minimization (simulated annealing). Finally, genetic optimization is discussed. This chapter serves as a prelude to the discussion of statistics and parameter estimation, in which the Monte Carlo method will prove highly usefiil in Bayesian analysis. 

The software package is freely available at hysss.sourceforge.net and at statthermo.sourceforge.net and includes multiple different hybrid stochastic simulation methods implemented in FORTRAN 95 and a simple Matlab (Mathworks) driven graphics user interface. It uses the NetCDF (Unidata) interface to store both model and solution data in an optimized, platform-independent, array-based, binary format. 

Understanding the free surface flow of viscoelastic fluids in micro-channels is important for the design and optimization of micro-injection molding processes. In this paper, flow visualization of a non-Newtonian polyacrylamide (PA) aqueous solution in a transparent polymethylmethacrylate (PMMA) channel with microfeatures was carried out to study the flow dynamics in micro-injection molding. The transient flow near the flow front and vortex formation in microfeatures were observed. Simulations based on the control volume finite element method (CVFEM) and the volume of fluid (VOF) technique were carried out to investigate the velocity field, pressure, and shear stress distributions. The mesoscopic CONNFFESSIT (Calculation of Non-Newtonian How Finite Elements and Stochastic Simulation Technique) method was also used to calculate the normal stress difference, the orientation of the polymer molecules and the vortex formation at steady state. 

Note The segmentation operation yields a near-optimal estimate x that may be used as initialization point for an optimization algoritlim that has to find out the global minimum of the criterion /(.). Because of its nonlinear nature, we prefer to minimize it by using a stochastic optimization algorithm (a version of the Simulated Annealing algorithm [3]). 

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. 

In summary, models can be classified in general into deterministic, which describe the system as cause/effect relationships and stochastic, which incorporate the concept of risk, probability or other measures of uncertainty. Deterministic and stochastic models may be developed from observation, semi-empirical approaches, and theoretical approaches. In developing a model, scientists attempt to reach an optimal compromise among the above approaches, given the level of detail justified by both the data availability and the study objectives. Deterministic model formulations can be further classified into simulation models which employ a well accepted empirical equation, that is forced via calibration coefficients, to describe a system and analytic models in which the derived equation describes the physics/chemistry of a system. 

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