MIPLIB 2010
(2011)
Branching Rules Revisited
(2005)
MIPLIB 2003
(2006)
We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of over 5,000 instances, the new MIPLIB 2017 collection consists of 1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, the compilation of these sets was done using a data-driven selection process supported by the solution of a sequence of mixed integer optimization problems, which encoded requirements on diversity and balancedness with respect to instance features and performance data.
Mixed integer programming has become a very powerful tool for modeling and
solving real-world planning and scheduling problems, with the breadth of
applications appearing to be almost unlimited. A critical component in
the solution of these mixed-integer programs is a set of routines commonly
referred to as presolve. Presolve can be viewed as a collection of
preprocessing techniques that reduce the size of and, more importantly,
improve the ``strength'' of the given model formulation, that is, the degree
to which the constraints of the formulation accurately describe the
underlying polyhedron of integer-feasible solutions. As our computational
results will show, presolve is a key factor in the speed with which we can
solve mixed-integer programs, and is often the difference between a model
being intractable and solvable, in some cases easily solvable. In this
paper we describe the presolve functionality in the Gurobi commercial
mixed-integer programming code.
This includes an overview, or taxonomy of the different methods that are
employed, as well as more-detailed descriptions of several of the techniques,
with some of them appearing, to our knowledge, for the first time in the
literature.
制約整数計画ソルバ SCIP の並列化
(2013)
制約整数計画(CIP: Constraint Integer Programs)は,制約プログラミング(CP: Constraint Programming),混合整数計画(MIP: Mixed Integer Programming),充足可能性問題(SAT: Satisfability Problem)の研究分野におけるモデリング技術と解法を統合している.その結果,制約整数計画は,広いクラスの最適化問題を扱うことができる.SCIP(Solving Constraint Integer Programs)は,CIP を解くソルバとして実装され,Zuse Institute Berlin(ZIB)の研究者を中心として継続的に拡張が続けられている.本論文では,著者らによって開発された SCIP に対する2 種類の並列化拡張を紹介する.一つは,複数計算ノード間で大規模に並列動作する ParaSCIPである.もう一つは,複数コアと共有メモリを持つ 1 台の計算機上で(スレッド)並列で動作する FiberSCIP である.ParaSCIP は,HLRN II スーパーコンピュータ上で,一つのインスタンスを解くために最大 7,168 コアを利用した動作実績がある.また,統計数理研究所の Fujitsu PRIMERGY RX200S5 上でも,最大 512 コアを利用した動作実績がある.統計数理研究所のFujitsu PRIMERGY RX200S5 上では,これまでに最適解が得られていなかった MIPLIB2010のインスタンスである dg012142 に最適解を与えた.