Optimal assignment methods

In the computer program which we have developed for the minimization of the chemical distance we use algorithms from the field of operations research known as optimal assignment -methods.  

ACS Symposium Series American Chemical Society Washington, DC, 1977. 

Approaches that use starting and/or final products as a vehicle for describing and classifying reactions must be regarded unsuitable in the light of our mathematical model A reaction is a path between points on the subspace, that is defined by an FIEM. Although an individual path may be described by its starting, final (and possibly some intermediate points) equivalence classes of such paths cannot be adequately described and classified that way. What we need is a description of the path itself. 

A hierarchy is thereby achieved, that will lead to a reaction file structure, where each entry is referenced through the various levels of specificity up to the R-categories. Queries can be entered at any degree of generality. 

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Jahn A, Hinselman G, Fechner N, et al. Optimal assignment methods for ligand-based virtual screening. J Chemoinform. http //www.jcheminf.eom/content/l/l/14. Accessed 2013 Jan 6. 

Optimization of the toleranees assigned to the toleranee staek to satisfy the assembly toleranee is required beeause of the risk of assigning impraetieal and eostly values. The toleranee staek models, presented later, do not optimize the toleranees and additional methods are required. The aetual optimization operations usually take the form of minimization or maximization of the results from the eost... 

The method of lines formulation for solving Equation (8.52) does not require that T aii be constant, but allows T aiiiz) to be an arbitrary function of axial position. A new value of T aii may be used at each step in the calculations, just as a new may be assigned at each step (subject to the stability criterion). The design engineer is thus free to pick a T au z) that optimizes reactor performance. 

Bertsekas, D. (1994) Mathematical equivalence of the auction algorithm for assignment and the e-relaxation (preflow-push) method for min cost flow, in Large Scale Optimization. State-of-the-Art (ed. W.W. Hager), Papers Presented... 

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