18 research outputs found
Safe and Verified Gomory Mixed Integer Cuts in a Rational MIP Framework
This paper is concerned with the exact solution of mixed-integer programs
(MIPs) over the rational numbers, i.e., without any roundoff errors and error
tolerances. Here, one computational bottleneck that should be avoided whenever
possible is to employ large-scale symbolic computations. Instead it is often
possible to use safe directed rounding methods, e.g., to generate provably
correct dual bounds. In this work, we continue to leverage this paradigm and
extend an exact branch-and-bound framework by separation routines for safe
cutting planes, based on the approach first introduced by Cook, Dash, Fukasawa,
and Goycoolea in 2009. Constraints are aggregated safely using approximate dual
multipliers from an LP solve, followed by mixed-integer rounding to generate
provably valid, although slightly weaker inequalities. We generalize this
approach to problem data that is not representable in floating-point
arithmetic, add routines for controlling the encoding length of the resulting
cutting planes, and show how these cutting planes can be verified according to
the VIPR certificate standard. Furthermore, we analyze the performance impact
of these cutting planes in the context of an exact MIP framework, showing that
we can solve 21.5% more instances and reduce solving times by 26.8% on the
MIPLIB 2017 benchmark test set
Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization
This article studies a combination of the two state-of-the-art algorithms for
the exact solution of linear programs (LPs) over the rational numbers, i.e.,
without any roundoff errors or numerical tolerances. By integrating the method
of precision boosting inside an LP iterative refinement loop, the combined
algorithm is able to leverage the strengths of both methods: the speed of LP
iterative refinement, in particular in the majority of cases when a
double-precision floating-point solver is able to compute approximate solutions
with small errors, and the robustness of precision boosting whenever extended
levels of precision become necessary. We compare the practical performance of
the resulting algorithm with both puremethods on a large set of LPs and
mixed-integer programs (MIPs). The results show that the combined algorithm
solves more instances than a pure LP iterative refinement approach, while being
faster than pure precision boosting. When embedded in an exact branch-and-cut
framework for MIPs, the combined algorithm is able to reduce the number of
failed calls to the exact LP solver to zero, while maintaining the speed of the
pure LP iterative refinement approach
Multi-messenger observations of a binary neutron star merger
On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta
The SCIP Optimization Suite 6.0
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders’ decomposition in a generic framework. GCG’s detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders’ framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver SoPlex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP