Parallel direct search

Torczon V, Trosset MW Prom evolutionary operation to parallel direct search pattern search algorithms for numerical optimization, Comput Sci Stat 29 396—401, 1998. 

Derivative-free Optimization (DFO) In the past decade, the availability of parallel computers and faster computing hardware and the need to incorporate complex simulation models within optimization studies have led a number of optimization researchers to reconsider classical direct search approaches. In particular, Dennis and Torczon [SIAM J. Optim. 1 448 (1991)] developed a multidimensional search algorithm that extends the simplex approach of Nelder... 

Figure 3.11 The steepest-descent method the search in one direction is discontinued when no further decrease is possible, i.e., when the search direction is parallel to the local contour line. The next step starts in a perpendicular direction, i.e., in the direction opposite to the local gradient.

Pierce introduced an array-of-arrays microplate product called Search-Light in which antibodies are directly printed into the wells of the microplate. Also, we have reviewed MSD s Multi-Spot plate products having antibodies immobilized onto multiple working electrodes. These products (albeit with some novel approaches to create microarrays and means for detection) utilize the classic immunosorbent sandwich assay but have the advantage of parallel processing using microarrays. 

Unfortunately, activity and stability for a given material as a rule do not proceed in parallel. Rather, they vary in opposite directions. Hence the search for more and more active materials must find a compromise with an acceptable stability. Academic research as a rule overemphasizes activity, whereas industry does so for stability. For this reason, it can happen that academic research reports very interesting activity properties but without any industrial interest. On the other hand, industrial breakthroughs may be emphasized that have in fact no scientific relevance. This is just to stress that a single point of view never offers an exhaustive picture of a problem. 

This type of search, in which information provided by points previously visited is used to provide clues to where to look next, is far more viable than random or exhaustive searches for moderate to large search spaces. The fact that evolutionary search combines a random element which allows it to move directly to distant parts of the search space with mechanisms to investigate local regions in detail, and that it runs several searches in parallel to provide broad coverage of the search space, gives it great power. 

A different approach to the estimation of the overall effectiveness factor in porous catalysts was recently presented by Ho et al. (1994). These authors analyze the case of parallel bimolecular reactions, a case that is in general not one of uniform kinetics. Rather than trying to solve the coupled set of differential equations, Ho et al. chose to search directly for upper and lower bounds to the overall effectiveness factor, which are found by reducing the problem to that of finding the effectiveness factor for a single second-order reaction. The bounds can be es-... 

The procedure continues from Step 1, searching in both direction (parallel and antiparallel) along eigenvectors with successively larger eigenvalues from the modified position. 

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