A two-stage parallel branch and bound algorithm for mixed integer programs

Mixed integer programming (MIP) models are extensively usedto aid strategic and tactical decision making in many businesssectors. Solving MIP models is a computationally intensive processand there is a need to develop solution approaches that enablelarger models to be solved within acceptable timeframes. Inthis paper, we describe the implementation of a two-stage parallelbranch and bound (PB & B) algorithm for MIP. In stage 1of the algorithm, a multiple heuristic search is implementedin which a number of alternative search trees are investigatedusing a forest search in the hope of finding a good solutionquickly. In stage 2, the search is reorganized so that the branchesof a chosen tree are investigated in parallel. A new heuristicis introduced, based on a best projection criterion, which evaluatesalternative B & B trees in order to choose one for investigationin stage 2 of the algorithm. The heuristic also serves as away of implementing a quality load balancing scheme for stage2 of the algorithm. The results of experimental investigationsare reported for a range of models taken from the MIPLIB libraryof benchmark problems.     

A comparison of two algorithms for the assignment problem

State-of-the-art computational results have shown that the shortest augmenting path (SAP) methods are more efficient than other primal-dual and primal-simplex based methods for solving the linear assignment problem on uniprocessor computers. There is, however, some controversy concerning their merits when compared with Bertsekas' auction algorithm on multiprocessor computers. In this study we investigate the performance of these competing methods on the Alliant FX/8. For each method, theoretical motivation, sources of parallelism and computational results are presented.     

Solving large-scale semidefinite programs in parallel

We describe an approach to the parallel and distributed solution of large-scale, block structured semidefinite programs using the spectral bundle method. Various elements of this approach (such as data distribution, an implicitly restarted Lanczos method tailored to handle block diagonal structure, a mixed polyhedral-semidefinite subdifferential model, and other aspects related to parallelism) are combined in an implementation called LAMBDA, which delivers faster solution times than previously possible, and acceptable parallel scalability on sufficiently large problems. This work was supported in part by NSF grants DMS-0215373 and DMS-0238008.     

论浮力的计算

通过讨论物体下表面不与液体接触时浮力的计算,总结浮力计算的一般方法.     

Computing Aviation Sparing Policies: Solving a Large Nonlinear Integer Program

Deployed US Navy aircraft carriers must stock a large number of spare parts to support the various types of aircraft embarked on the ship. The sparing policy determines the spares that will be stocked on the ship to keep the embarked aircraft ready to fly. Given a fleet of ten or more aircraft carriers and a cost of approximately 50 million dollars per carrier plus the cost of spares maintained in warehouses in the United States, the sparing problem constitutes a significant portion of the Navy’s resources. The objective of this work is to find a minimum-cost sparing policy that meets the readiness requirements of the embarked aircraft. This is a very large, nonlinear, integer optimization problem. The cost function is piecewise linear and convex while the constraint mapping is highly nonlinear. The distinguishing characteristics of this problem from an optimization viewpoint are that a large number of decision variables are required to be integer and that the nonlinear constraint functions are essentially “black box” functions; that is, they are very difficult (and expensive) to evaluate and their derivatives are not available. Moreover, they are not convex. Integer programming problems with a large number of variables are difficult to solve in general and most successful approaches to solving nonlinear integer problems have involved linear approximation and relaxation techniques that, because of the complexity of the constraint functions, are inappropriate for attacking this problem. We instead employ a pattern search method to each iteration of an interior point-type algorithm to solve the relaxed version of the problem. From the solution found by the pattern search on each interior point iteration, we begin another pattern search on the integer lattice to find a good integer solution. The best integer solution found across all interations is returned as the optimal solution. The pattern searches are distributed across a local area network of non-dedicated, heterogeneous computers in an office environment, thus, drastically reducing the time required to find the solution.     

The application of chromatography to the analysis of pharmaceutical creams

Summary The application of GLC, HPLC and TLC to the analysis of pharmaceutical creams is discussed with special attention to sample clean-up. The results of the determination of hydrocortisone acetate, salicylic acid, benzoic acid, diethyl stilbestrol, chloramphenicol, diphenhydramine HCl, tretinoin and some cream base components by reversed phase HPLC are given.Presented at the 14th International Symposium on Chromatography London, September, 1982     

Donator-Acceptor Komplex Chromatographie Tetrachlorphthalimidopropylsilica,eine neue,chemisch gebundene Phase,geeignet zur Trennung von Kohleverflüssigungsprodukten und anderen technischen aromatischen Gemischen mit der Hochleistungsflüssigkeitschromatographie

Summary The preparation of a new tetrachlorophthalimidophase for HPLC is described. The capacity ratios (k) of about forty aromatics and twenty nitrogen-containing aromatics were determined. Most of the compounds used were alkylated. It was shown that the aromatics were eluted according to the number of rings, only slightly influenced by the substituents. A similar elution order was not observed with the heteroaromatics. The performance of the stationary phase is demonstrated, performing separations of coal liquids and other aromatic mixtures.

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Donator-Acceptor Komplex Chromatographie Tetrachlorphthalimidopropylsilica, eine neue, chemisch gebundene Phase, geeignet zur Trennung von Kohleverflüssigungsprodukten und anderen technischen aromatischen Gemischen mit der Hochleistungsflüssigkeitschromatographie

Zusammenfassung Es wird die Synthese einer neuen Tetrachlorphthalimid-Phase für die HPLC beschrieben. Anhand von Elutionsversuchen mit über vierzig Aromaten und zwanzig N-Heteroaromaten, die größtenteils alkyliert waren, konnte gezeigt werden, daß kondensierte Aromaten unabhängig vom Alkylierungsgrad streng nach der Zahl der aromatischen Ringe eluiert werden, was für die Heterocyclen nicht zutrifft. Die Kapazitätsverhältnisse (k) der untersuchten Verbindungen werden angegeben. Die Leistungsfähigkeit der Phase wird an der chromatographischen Trennung von Kohleverflüssigungsprodukten und anderen komplexen, aromatischen Gemischen demonstriert.

     

Determination of thiol by high-performance liquid chromatography and fluorescence detection with 5-methyl-(2-(<Emphasis Type="Italic">m</Emphasis>-iodoacetylaminophenyl)benzoxazole

A new high-performance liquid chromatographic (HPLC) method for measuring low molecular weight (LMW) thiol-containing compounds, including cysteine (CysH), glutathione (GSH), N-acetylcysteine (Nac), penicillamine (PA), and 2-mercaptoethanol (2-ME), has been developed by using 5-methyl-(2-(m-iodoacetylaminophenyl)benzoxazole (MIPBO) as fluorescence-labeling reagent. The derivatization and separation conditions have been investigated in detail. Detection limits ranging from 3.5 to 15.0 fmol were achieved for the thiols investigated in a 16 min separation with detection wavelengths 310 and 375 nm for the excitation and emission, respectively. The utility of the proposed method has been validated by measuring CysH in human urine samples.