ZIB-Report
Refine
Year of publication
- 2013 (5) (remove)
Document Type
- ZIB-Report (5)
Language
- English (5)
Has Fulltext
- yes (5)
Is part of the Bibliography
- no (5)
Keywords
- branch-and-bound (2)
- domain propagation (2)
- mixed integer programming (2)
- mixed-integer programming (2)
- MINLP (1)
- MIP (1)
- SCIP (1)
- bivariate functions (1)
- branching rule (1)
- constraint integer programming (1)
Institute
- Mathematical Optimization Methods (5) (remove)
13-02
This is a technical report for the SCIP constraint handler cons_bivariate. We describe a cut-generation algorithm for a class of bivariate twice continuously differentiable functions with
fixed convexity behavior over a box.
Computational results comparing our cut-generation algorithms with
state-of-the-art global
optimization software on a series of randomly generated test instances are reported and discussed.
13-03
Shift-And-Propagate
(2013)
For mixed integer programming, recent years have seen a growing interest in the design of general purpose primal heuristics for use inside complete solvers. Many of these heuristics rely on an optimal LP solution. Finding this may itself take a significant amount of time.
The presented paper addresses this issue by the introduction of the Shift-And-Propagate heuristic. Shift-And-Propagate is a pre-root primal heuristic that does not require a previously found LP solution. It applies domain propagation techniques to quickly drive a variable assignment towards feasibility. Computational experiments indicate that this heuristic is a powerful supplement of existing rounding and propagation heuristics.
13-55
Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a MIP solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, the basic concept of having two parallel extensions and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator) is presented, including an implementation of deterministic parallelization. Second, the difficulties to achieve a good performance that utilizes all resources on an actual computing environment and the difficulties of performance evaluation of the parallel solvers are discussed. Third, a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions is presented. Finally, current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer non-linear programs (MINLPs) in parallel is demonstrated.
13-48
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.
13-47
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.