Monte-Carlo optimization

Statistical characteristics of QSPRs obtained by the SMILES-based descriptors in three runs of the Monte Carlo optimization are presented in Table 14.1. One can see from Table 14.1 that statistical quality of these models is reproduced in all the three mns of optimization... 

Table 14.1 Statistical characteristics of the models for fullerene C60 solubility for three runs of the Monte Carlo optimization of the correlation weights of SMILES attributes...

An example of calculation of the DCW with correlation weights obtained in the first ran of the Monte Carlo optimization is shown in Table 14.3. 

Table 14.4 Experimental and calculated values of the fullerene C60 solubility (run 1 of the Monte Carlo optimization)...

In the literature, some computer models describing the evolution of copolymer sequences have been proposed [26,28]. Most of them are based on a stochastic Monte Carlo optimization principle (Metropolis scheme) and aimed at the problems of protein physics. Such optimization algorithms start with arbitrary sequences and proceed by making random substitutions biased to minimize relative potential energy of the initial sequence and/or to maximize the folding rate of the target structure. 

Fig. 2.4.5. Left Monte Carlo-optimized structure of 6 Ac-Orn-Ala-OMe in chloroform (1000 steps). Right Arrows indicate complexation-induced shifts in host and guest during the titration.

Closely related to this approach is that of Monte Carlo optimizations. Starting from a given structure, a random change in the structure is proposed. The total-energy difference between the two structures, AE, is calculated, and the change/move/displacement is accepted with probability 1 if AE < 0 and... 

Guda, C., et al., A new algorithm for the alignment of multiple protein structures using Monte Carlo optimization. Pac Symp Biocomput, 2001 p. 275-86. 

Chikhradze, N., L. Kurdadze, and G. Abashidze. 2011. Monte Carlo optimization of concentrations of gadolinium and boron in composites aimed for neutron shielding. In Abstracts of the International Scientific Conference on Modem Issues of Applied Physics, Tbilisi, GA, p. 99. 

Alignment of Molecules by the Monte Carlo Optimization of Molecular Similarity Indices. 

Figure 12.5 contains the graphical representation of the Monte Carlo optimization. This approach is based on calculations of the correlation weights which give maximum correlation coefficient between experimental and predicted endpoint. 

Fig. 12.5 The general scheme of the Monte Carlo optimization used as the basis of caleulation of optimal descriptors. The row Correlation weight contains graphical images of various features (extracted from graph or SMILES) characterized by positive values of the correlation weights (they are indicated by white color) or by negative values of correlation weights (those are indieated by black color). Blocked (rare) features have correlation weights which are fixed to be equal to zero (indicated by grey b ). The R(X,Y) is correlation coefficient between descriptor and endpoint...

Fig. 5. Determination of concentration profiles in thermally treated HPEC containing a HAS-derived nitroxide. (a) Concentration profile obtained by deconvolution followed by Monte Carlo optimization (left), and ID image and the residual to the fit (right), (b) Concentration profile obtained by simulation of the ID image on the right with the Genetic algorithm (left), and the residual to the fit (right). The ID image was obtained with a gradient of 200 G cm .

Once the retention models have been established by the procedures described above, no further experiments are conducted. The software automatically generates tens of thousands of linear and multi-step gradient profiles in a very short time. It predicts the retention of compounds for each gradient profile generated, evaluates the predicted separation using an optimization function, and searches for the best gradient profile using a super-fast Monte Carlo optimization method [5]. 

Monte Carlo optimization operates in the same way as Monte Carlo simulation." As with the previously discussed GAs, we provide a short overview of MC methods, pointing out key aspects. The Monte Carlo method begins with a random initial point in molecular configuration space (Al, X2, , Ajv). Where the configuration space is understood to include both the three dimensional position of the atoms in the molecule and the identity of the atoms. From Ai, A2,. .Xn new point in configuration space is selected by an elementary Monte Carlo move. This new point is called Xi,triai, X2,triah Xf riai is Set equal to Ai, A2,. .., Ajv with probability... 

Where 6[H[X, X2,..., Xn is the function that maps the point in multi-dimensional configuration space Ai, A2,..., A to a point in single dimensional property space. Note that this equation corresponds to a minimization of the desired property function 0[H X, X2,...,Xn. T is a fictitious temperature parameter, kept constant when performing Monte Carlo optimizations. However, it can be ramped up and slowly decreased to trap the system in the optimal Xj, A, ..., A . This is known as simulated annealing." ... 

Key issues in implementation. The algorithm described above is the minimal ingredient required to perform Monte Carlo optimization. In practice, several other issues must be addressed to get meaningful results in an acceptable amount of time. MC optimizations permit great flexibility in the specific implementation of how the MC trial configurations are generated. There are in fact many different kinds of ways to make an elementary... 

---