Browsing by Author "Bixby, R.E."
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Item A Note on Detecting Simple Redundancies in Linear Systems(1986-06) Bixby, R.E.; Wagner, Donald K.Two efficient algorithms are presented that, for a given linear system Ax=b, eliminate equations that are nonzero multiples of other equations. The second algorithm runs in linear time when the entries of A are +1, -1, or 0.Item An Updated Mixed Integer Programming Library: MIPLIB 3.0(1998-02) Bixby, R.E.; Ceria, S.; McZeal, C.M.; Savelsbergh, M.W.P.In response to the needs of researchers for access to challenging mixed integer programs, Bixby et al. [1] created MIPLIB, an electronically available library of both pure and mixed integer programs, most of which arise from real-world applications. Since its introduction, MIPLIB has become a standard test set for comparing the performance of mixed integer optimization codes. Its availability has provided an important stimulus for researchers in this very active area. As technology has progressed, however, there have been significant improvements in state-of-the-art optimizers and computing machinery. Consequently, several instances have become too easy, and a need has emerged for more difficult instances. Also, it has been observed that certain types of problems are overrepresented in MIPLIB and others underrepresented. These considerations have prompted the present update. Since mixed integer programming is such an active research area, and the performance of optimizers keep improving, we anticipate that this update will not be the last. Subsequent updates are planned on a yearly basis. We encourage both researchers and practitioners in integer programming to submit real-world instances for consideration and possible inclusion in MIPLIB. This note describes the MIPLIB update. We have added several new problems and deleted some existing ones. In addition, we have included, for each problem, certain auxiliary information describing the structure of the constraint matrix. The purpose of this information is to identify constraint classes that may be useful in the various phases of problem solving, such as preprocessing, constraint generation, and branching.Item Solving Linear Programs with Two Processors(1989-11) Bixby, R.E.; Schwabacher, MarkA linear programming problem can be solved in parallel using two processors. One processor performs iterations of the main algorithm, while the other processor continuously refactorizes the basis matrix. Using this method we have been able to solve linear programs in as little as 73% of the time needed with one processor.Item The MIPLIB Mixed Integer Programming Library(1992-11) Bixby, R.E.; Boyd, E. Andrew; Dadmehr, Shireen S.; Indovina, Ronni R.