TY - GEN A1 - Cook, William A1 - Koch, Thorsten A1 - Steffy, Daniel A1 - Wolter, Kati T1 - An Exact Rational Mixed-Integer Programming Solver N2 - We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. The software is incorporated into the SCIP optimization framework, using the exact LP solver QSopt_ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann collections. T3 - ZIB-Report - 11-07 KW - mixed integer programming KW - branch-and-bound KW - exact computation Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12329 ER - TY - GEN A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Vigerske, Stefan T1 - On the computational impact of MIQCP solver components N2 - We provide a computational study of the performance of a state-of-the-art solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs). Since successful general-purpose solvers for large problem classes necessarily comprise a variety of algorithmic techniques, we focus especially on the impact of the individual solver components. The solver SCIP used for the experiments implements a branch-and-cut algorithm based on linear outer approximation to solve MIQCPs to global optimality. Our analysis is based on a set of 86 publicly available test instances. T3 - ZIB-Report - 11-01 KW - MIQCP KW - MIP KW - mixed-integer quadratically constrained programming KW - computational KW - nonconvex Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11998 ER -