TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten T1 - ParaSCIP - a parallel extension of SCIP N2 - Mixed integer programming (MIP) has become one of the most important techniques in Operations Research and Discrete Optimization. SCIP (Solving Constraint Integer Programs) is currently one of the fastest non-commercial MIP solvers. It is based on the branch-and-bound procedure in which the problem is recursively split into smaller subproblems, thereby creating a so-called branching tree. We present ParaSCIP, an extension of SCIP, which realizes a parallelization on a distributed memory computing environment. ParaSCIP uses SCIP solvers as independently running processes to solve subproblems (nodes of the branching tree) locally. This makes the parallelization development independent of the SCIP development. Thus, ParaSCIP directly profits from any algorithmic progress in future versions of SCIP. Using a first implementation of ParaSCIP, we were able to solve two previously unsolved instances from MIPLIB2003, a standard test set library for MIP solvers. For these computations, we used up to 2048 cores of the HLRN~II supercomputer. T3 - ZIB-Report - 10-27 KW - massive parallization KW - mixed integer programming KW - ParaSCIP KW - branch-and-cut KW - branch-and-bound Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11921 UR - http://www.springerlink.com/content/t2160206253v7661/ ER - TY - GEN A1 - Heinz, Stefan A1 - Ku, Wen-Yang A1 - Beck, J. Christopher T1 - Recent improvements using constraint integer programming for resource allocation and scheduling N2 - Recently, we compared the performance of mixed-integer programming (MIP), constraint programming (CP), and constraint integer programming (CIP) to a state-of-the-art logic-based Benders manual decomposition (LBBD) for a resource allocation/scheduling problem. For a simple linear relaxation, the LBBD and CIP models deliver comparable performance with MIP also performing well. Here we show that algorithmic developments in CIP plus the use of an existing tighter relaxation substantially improve one of the CIP approaches. Furthermore, the use of the same relaxation in LBBD and MIP models significantly improves their performance. While such a result is known for LBBD, to the best of our knowledge, the other results are novel. Our experiments show that both CIP and MIP approaches are competitive with LBBD in terms of the number of problems solved to proven optimality, though MIP is about three times slower on average. Further, unlike the LBBD and CIP approaches, the MIP model is able to obtain provably high-quality solutions for all problem instances. T3 - ZIB-Report - 13-05 KW - constraint integer programming KW - constraint programming KW - cumulative constraint KW - mixed integer programming KW - optional activities Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17676 SN - 1438-0064 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 - 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 - 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 - Achterberg, Tobias A1 - Berthold, Timo A1 - Koch, Thorsten A1 - Wolter, Kati T1 - Constraint Integer Programming: a New Approach to Integrate CP and MIP N2 - This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for non-commercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly non-linear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the non-linear constraints by employing constraint programming techniques. T3 - ZIB-Report - 08-01 KW - Constraint Programming KW - Ganzzahlige Programmierung KW - Branch-And-Cut KW - Optimierungssoftware KW - Chipverifikation KW - constraint programming KW - mixed integer programming KW - branch-and-cut KW - optimization software KW - chip verification Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10520 SN - 1438-0064 ER - TY - GEN A1 - Heinz, Stefan A1 - Beck, J. Christopher T1 - Reconsidering Mixed Integer Programming and MIP-based Hybrids for Scheduling N2 - Despite the success of constraint programming (CP) for scheduling, the much wider penetration of mixed integer programming (MIP) technology into business applications means that many practical scheduling problems are being addressed with MIP, at least as an initial approach. Furthermore, there has been impressive and well-documented improvements in the power of generic MIP solvers over the past decade. We empirically demonstrate that on an existing set of resource allocation and scheduling problems standard MIP and CP models are now competitive with the state-of-the-art manual decomposition approach. Motivated by this result, we formulate two tightly coupled hybrid models based on constraint integer programming (CIP) and demonstrate that these models, which embody advances in CP and MIP, are able to out-perform the CP, MIP, and decomposition models. We conclude that both MIP and CIP are technologies that should be considered along with CP for solving scheduling problems. T3 - ZIB-Report - 12-05 KW - constraint integer programming KW - constraint programming KW - cumulative constraint KW - mixed integer programming KW - optional activities Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14660 SN - 1438-0064 ER -