Algorithm combinatorial

Key words Combinatorial chemistry, genetic algorithms, combinatorial optimisation, QSAR, evolutionary chemistry, very large compound libraries... 

Coffman, Jr., E. G., G. Galambos, S. Martello, and D. Vigo. Bin packing approximation algorithms Combinatorial analysis. In D.-Z. Du and M. Pardalos (Eds.), Handbook of Combinatorial Optimization, Supplement Volume A, pp. 151-207. Boston Kluwer Academic, 1999. 

The basic scheme of this algorithm is similar to cell-to-cell mapping techniques [14] but differs substantially In one important aspect If applied to larger problems, a direct cell-to-cell approach quickly leads to tremendous computational effort. Only a proper exploitation of the multi-level structure of the subdivision algorithm (also for the eigenvalue problem) may allow for application to molecules of real chemical interest. But even this more sophisticated approach suffers from combinatorial explosion already for moderate size molecules. In a next stage of development [19] this restriction will be circumvented using certain hybrid Monte-Carlo methods. 

HTS data as well as virtual screening can guide and direct the design of combinatorial libraries. A genetic algorithm (GA) can be applied to the generation of combinatorial libraries [18. The number of compounds accessible by combinatorial synthesis often exceeds the number of compounds which can be syiithcsii ed... 

P Willett, J Bradshaw and D V S Green 1999. Selecting Combinatorial Libraries to Optimize rsity and Physical Properties. Journal of Chemical Information and Computer Science 39 169-177. 1 and A W R Payne 1995. A Genetic Algorithm for the Automated Generation of Molecules in Constraints. Journal of Computer-Aided Molecular Design 9 181-202. 

RP Sheridan, SK Kearsley. Using a genetic algorithm to suggest combinatorial libraries. J Chem Inf Comput Sci 35 310-320, 1995. 

RD Brown, YC Martin. Designing combinatorial library mixtures using a genetic algorithm. I Med Chem 40(15) 2304-2313, 1997. 

MulI69 Mullat, I. E. On the Redfield-Read combinatory algorithm. Mat. Zametki 6 (1969) 213-223. (Translated in Math. Notes 6 (1969) 583-588.)... 

Waldman M, Li H, Hassan M. Novel algorithms for the optimization of molecular diversity of combinatorial libraries. / Mo/ Graph Model 2000 18 412-26. 

CombiGlide A combinatorial version of the Glide algorithm which can be used for the design of focused libraries Schrodinger, Inc. http //www.schrodinger.com [34]... 

Rarey M, Lengauer T. A recnrsive algorithm for efficient combinatorial library docking perspective in drug discovery and design. Perspect Drug Discov Des 2000 20 63-81. 

To identify this set of final feasible solutions, X e 1, with low scores, we developed a greedy search procedure, S (Saraiva and Stephanopoulos, 1992c), that has resulted, within an acceptable computation time, in almost-optimal solutions for all the cases studied so far, while avoiding the combinatorial explosion with the number of (x, y) pairs of an exhaustive enumeration/evaluation of all feasible alternatives. The algorithm starts by partitioning the decision space into a number of isovolu-... 

To solve the problems of representation and control, we will employ the framework of the branch-and-bound algorithm, which has been used to solve many types of combinatorial optimization problems, in chemical engineering, other domains of engineering, and a broad range of management problems. Specifically, we will use the framework proposed by Ibaraki (1978), which is characterized by the following features ... 

The first step in solving a combinatorial optimization problem is to model the solution space itself. Such a model should be declarative in character, if it is to be independent of the characteristics of the specific algorithm that will be used to find the solution within the solution space. The model we have adopted for the scheduling of flowshop operations is the discrete decision process (DDP) introduced originally by Karp and Held (1967). As defined by Ibaraki (1978) a DDP, Y, is a triple (.S,S,/) with its elements defined as follows ... 

The large size of the solution space for combinatorial optimization problems forces us to represent it implicitly. The branch-and-bound algorithm encodes the entire solution space in a root node, which is successively expanded into branching nodes. Each of these nodes represents a subset of the original solution space specialized to contain some particular element of the problem structure. 

Realff, M.J., Machine Learning for the Improvement of Combinatorial Optimization Algorithms A Case Study in Batch Scheduling. Ph.D Thesis, MIT., Cambridge, MA, 1992. 

There are numerous definitions of combinatorial optimization. We will use this definition Combinatorial optimization means algorithms which generate quants and assign them to resources such that the costs summarized over all quants are minimized and all constraints are met. ... 

As there is no simple algorithm which can generate a solution just in one step several algorithms have to be combined [7-10]. Those algorithms which may improve the solution are called operators. The overall combinatorial solution algorithm consists of many operators. Any operator may work in any combination on the solution. Some examples are ... 

Fig. 4.3 Sketch of an often used branch and bound algorithm and corresponds to the box combinatorial optimization" in Figure 4.2.

Goldberg, A., Oldham, J., Plotkin, S. and Stein, C. (1997) An Implementation of a Combinatorial Approximation Algorithm for Minimum-Cost Multicommodity Flow, Springer, London. 

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