TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Schulz, Jens T1 - An approximative Criterion for the Potential of Energetic Reasoning N2 - Energetic reasoning is one of the most powerful propagation algorithms in cumulative scheduling. In practice, however, it is not commonly used because it has a high running time and its success highly depends on the tightness of the variable bounds. In order to speed up energetic reasoning, we provide an easy-to-check necessary condition for energetic reasoning to detect infeasibilities. We present an implementation of energetic reasoning that employs this condition and that can be parametrically adjusted to handle the trade-off between solving time and propagation overhead. Computational results on instances from the PSPLIB are provided. These results show that using this condition decreases the running time by more than a half, although more search nodes need to be explored. T3 - ZIB-Report - 11-12 KW - conflict analysis KW - constraint integer programming KW - cumulative constraint KW - resource-constrained project scheduling KW - energetic reasoning Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12655 ER - 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 - Heinz, Stefan A1 - Schulz, Jens T1 - Explanations for the Cumulative Constraint: an Experimental Study N2 - In cumulative scheduling, conflict analysis seems to be one of the key ingredients to solve such problems efficiently. Thereby, the computational complexity of explanation algorithms plays an important role. Even more when we are faced with a backtracking system where explanations need to be constructed on the fly. In this paper we present extensive computational results to analyze the impact of explanation algorithms for the cumulative constraint in a backward checking system. The considered explanation algorithms differ in their quality and computational complexity. We present results for the domain propagation algorithms time-tabling, edge-finding, and energetic reasoning. T3 - ZIB-Report - 11-13 KW - conflict analysis KW - constraint integer programming KW - cumulative constraint KW - resource-constrained project scheduling KW - propagation algorithms Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12668 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 - TY - GEN A1 - Heinz, Stefan A1 - Beck, J. Christopher T1 - Solving Resource Allocation/Scheduling Problems with Constraint Integer Programming N2 - Constraint Integer Programming (CIP) is a generalization of mixed-integer programming (MIP) in the direction of constraint programming (CP) allowing the inference techniques that have traditionally been the core of \P to be integrated with the problem solving techniques that form the core of complete MIP solvers. In this paper, we investigate the application of CIP to scheduling problems that require resource and start-time assignments to satisfy resource capacities. The best current approach to such problems is logic-based Benders decomposition, a manual decomposition method. We present a CIP model and demonstrate that it achieves performance competitive to the decomposition while out-performing the standard MIP and CP formulations. T3 - ZIB-Report - 11-14 KW - constraint integer programming KW - cumulative constraint KW - optional resources KW - mixed integer programming KW - constraint programming Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12691 ER - TY - GEN A1 - Steffy, Daniel A1 - Wolter, Kati T1 - Valid Linear Programming Bounds for Exact Mixed-Integer Programming N2 - Fast computation of valid linear programming (LP) bounds serves as an important subroutine for solving mixed-integer programming problems exactly. We introduce a new method for computing valid LP bounds designed for this application. The algorithm corrects approximate LP dual solutions to be exactly feasible, giving a valid bound. Solutions are repaired by performing a projection and a shift to ensure all constraints are satisfied; bound computations are accelerated by reusing structural information through the branch-and-bound tree. We demonstrate this method to be widely applicable and faster than solving a sequence of exact LPs. Several variations of the algorithm are described and computationally evaluated in an exact branch-and-bound algorithm within the mixed-integer programming framework SCIP. T3 - ZIB-Report - 11-08 KW - linear programming bounds 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-12332 ER -