Exchange algorithm

Nymeyer H, Gnanakaran S, Garcfa AE (2004) Atomic simulations of protein folding using the replica exchange algorithm. Methods Enzymol 383 119-149. 

The adaptations introduced in the fast exchange algorithm to optimize the UCC criterion allow selection from databases of hundreds of thousands of compounds. Currently, the implementation is limited to tens of continuous descriptors, though discrete descriptors like fragment counts could be handled in principle. Further work is also needed for even larger databases with hundreds of descriptors. 

The experimental designs of non-simplex experimental regions are D-optimal for the selected model, obtained by an exchange algorithm. 

The approach of using a mathematical model to map responses predictively and then to use these models to optimize is limited to cases in which the relatively simple, normally quadratic model describes the phenomenon in the optimum region with sufficient accuracy. When this is not the case, one possibility is to reduce the size of the domain. Another is to use a more complex model or a non-polynomial model better suited to the phenomenon in question. The D-optimal designs and exchange algorithms are useful here as in all cases of change of experimental zone or mathematical model. In any case, response surface methodology in optimization is only applicable to continuous functions. 

Kunz RF, Siebert BW, Cope WK, Foster NF, Antal SP, Ettorre SM (1998) A coupled phasic exchange algorithm for three-dimensional multi-field analysis of heated flows with mass transfer. Computers Fluids 27(7) 741-768... 

Kunz RF, Yu W-S, Antal SP, Ettorre SM (2001) An Unstructured Two-Fluid Method Based on the Coupled Phasic Exchange Algorithm. American Institute of Aeronautics and Astronautics, AlAA-2001-2672, pp 1-13... 

Chiticariu L (2005) Computing the core in data exchange Algorithmic issues. MS Project Report, unpublished manuscript... 

D-optimum Any number equal to or greater than the number of independent coefficients in the model. Factors have different numbers of levels Experiments selected from the full factorial design using an exchange algorithm. 

The initial designs of this type were proposed by Roquemore (10), who derived designs for 3, 4 and 6 factors. These were modified by Franquart (11) and Peissik (12) using the methods of exchange algorithms described in a chapter 8. 

Quality criteria for an experimental design Principle of the exchange algorithm method... 

The main problem with these designs is that they do not take into account specific experimental constraints which may render them inefficient or impossible to use. We will now outline various situations where this might occur. Exchange algorithms are used in all of these. 

The use of exchange algorithms to construct D-optimal designs for mixtures with constraints is described in some detail in chapter 10. 

The objective of using an exchange algorithm is to construct the "best" design within the proposed experimental domain for determining the proposed... 

III. EXAMPLES OF EXCHANGE ALGORITHMS A. Process Study for a Wet Granulation... 

There are three reasons why this problem could not be solved using a standard design, and required the use of an exchange algorithm. 

The number of experiments is fixed at 18, the maximum possible. The D-optimal design thus obtained by running the exchange algorithm is described in table 6.3, and in figure 8.4. The experimental results for each run are given in chapter 6 (see table 6.3), where they were used for determination of the model and optimization of the process. 

We have shown the principle of the exchange algorithm in paragraph II.D, for a fixed number of experiments. The next question to be answered is how do we decide on the number of experiments Subject to possible external constraints, this depends on the statistical properties of the design. We demonstrate this by determining D-optimal designs for different values of N, in the above process study, and examine trends in their properties. 

For each number of experiments N = 12 to 20 we determined the final design, to which the exchange algorithm converged. Figures 8.6a-d show the trends in the four properties of the design that we have already used. I X X I and IM are again normalised as I X X I and IM 1 where p= 12. All of these show that the most efficient solution contains 16 experiments ... 

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