Gamrath, Gerald
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Strong branching is an important component of most variable selection rules in branch-and-bound based mixed-integer linear programming solvers. It predicts the dual bounds of potential child nodes by solving auxiliary LPs and thereby helps to keep the branch-and-bound tree small. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Computational experiments on standard MIP instances indicate that this is beneficial in three aspects: It helps to reduce the average number of LP iterations per strong branching call, the number of branch-and-bound nodes, and the overall solving time.
Presolving attempts to eliminate redundant information from the problem formulation and simultaneously tries to strengthen the formulation. It can be very effective and is often essential for solving instances. Especially for mixed integer programming problems, fast and effective presolving algorithms are very important. In this paper, we report on three new presolving techniques. The first method searches for singleton continuous columns and tries to fix the corresponding variables. Then we present a presolving technique which exploits a partial order of the variables to induce fixings. Finally, we show an approach based on connected components in graphs. Our computational results confirm the profitable use of the algorithms in practice.
One of the essential components of a branch-and-bound based mixed-integer linear programming (MIP) solver is the branching rule. Strong branching is a method used by many state-of-the-art branching rules to select the variable to branch on. It precomputes the dual bounds of potential child nodes by solving auxiliary linear programs (LPs) and thereby helps to take good branching decisions that lead to a small search tree. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Domain propagation is a technique usually used at every node of the branch-and-bound tree to tighten the local domains of variables. Computational experiments on standard MIP instances indicate that our improved strong branching method significantly improves the quality of the predictions and causes almost no additional effort. For a full strong branching rule, we are able to obtain substantial reductions of the branch-and-bound tree size as well as the solving time. Moreover, also the state-of-the-art hybrid branching rule can be improved this way.
This paper extends previous work by the author published in the proceedings of the CPAIOR 2013.
MIPLIB 2010
(2011)
Strong branching is an important component of most variable selection rules in branch-and-bound based mixed-integer linear programming solvers.
It predicts the dual bounds of potential child nodes by solving auxiliary LPs and thereby helps to keep the branch-and-bound tree small.
In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching.
Computational experiments on standard MIP instances indicate that this is beneficial in three aspects: It helps to reduce the average number of LP iterations per strong branching call, the number of branch-and-bound nodes, and the overall solving time.
This paper introduces the SCIP Optimization Suite and discusses the capabilities of its three components: the modeling language Zimpl, the linear programming solver SoPlex, and the constraint integer programming framework SCIP. We explain how these can be used in concert to model and solve challenging mixed integer linear and nonlinear optimization problems. SCIP is currently one of the fastest non-commercial MIP and MINLP solvers. We demonstrate the usage of Zimpl, SCIP, and SoPlex by selected examples, we give an overview of available interfaces, and outline plans for future development.
MIPLIB 2010
(2010)
This paper reports on the fifth version of the Mixed Integer Programming Library.
The MIPLIB 2010 is the first MIPLIB release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the community. The new version comprises 361 instances sorted into several groups.
This includes the main benchmark test set of 87 instances, which
are all solvable by today's codes, and also the challenge test set with 164 instances, many of which are currently unsolved.
For the first time, we include scripts to run automated tests in a predefined way. Further, there is a solution checker to
test the accuracy of provided solutions using exact arithmetic.