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We investigate how the numerical properties of the LP relaxations evolve
throughout the solution procedure in a solver employing the branch-and-cut
algorithm. The long-term goal of this work is to determine whether the effect
on the numerical conditioning of the LP relaxations resulting from the
branching and cutting operations can be effectively predicted
and whether such predictions can be used to make better algorithmic
choices. In a first step towards this goal, we discuss here the numerical
behavior of an existing solver in order to determine whether our
intuitive understanding of this behavior is correct.
We investigate how the numerical properties of the LP relaxations evolve
throughout the solution procedure in a solver employing the branch-and-cut
algorithm. The long-term goal of this work is to determine whether the effect
on the numerical conditioning of the LP relaxations resulting from the
branching and cutting operations can be effectively predicted
and whether such predictions can be used to make better algorithmic
choices. In a first step towards this goal, we discuss here the numerical
behavior of an existing solver in order to determine whether our
intuitive understanding of this behavior is correct.
In this article, we introduce parallel mixed integer linear programming (MILP) solvers. MILP solving algorithms have been improved tremendously in the last two decades. Currently, commercial MILP solvers are known as a strong optimization tool. Parallel MILP solver development has started in 1990s. However, since the improvements of solving algorithms have much impact to solve MILP problems than application of parallel computing, there were not many visible successes. With the spread of multi-core CPUs, current state-of-the-art MILP solvers have parallel implementations and researches to apply parallelism in the solving algorithm also getting popular. We summarize current existing parallel MILP solver architectures.
MIPLIB 2010
(2011)
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.