@misc{HeinzBeck, author = {Heinz, Stefan and Beck, J. Christopher}, title = {Solving Resource Allocation/Scheduling Problems with Constraint Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12691}, number = {11-14}, abstract = {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.}, language = {en} } @misc{HeinzBeck, author = {Heinz, Stefan and Beck, J. Christopher}, title = {Reconsidering Mixed Integer Programming and MIP-based Hybrids for Scheduling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14660}, number = {12-05}, abstract = {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.}, language = {en} } @misc{HeinzSchulzBeck, author = {Heinz, Stefan and Schulz, Jens and Beck, J. Christopher}, title = {Using dual presolving reductions to reformulate cumulative constraints}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-16321}, abstract = {Dual presolving reductions are a class of reformulation techniques that remove feasible or even optimal solutions while guaranteeing that at least one optimal solution remains, as long as the original problem was feasible. Presolving and dual reductions are important components of state-of-the-art mixed-integer linear programming solvers. In this paper, we introduce them both as unified, practical concepts in constraint programming solvers. Building on the existing idea of variable locks, we formally define and justify the use of dual information for cumulative constraints during a presolving phase of a solver. In particular, variable locks are used to decompose cumulative constraints, detect irrelevant variables, and infer variable assignments and domain reductions. Since the computational complexity of propagation algorithms typically depends on the number of variables and/or domain size, such dual reductions are a source of potential computational speed-up. Through experimental evidence on resource constrained project scheduling problems, we demonstrate that the conditions for dual reductions are present in well-known benchmark instances and that a substantial proportion of them can be solved to optimality in presolving -- without search. While we consider this result very promising, we do not observe significant change in overall run-time from the use of our novel dual reductions.}, language = {en} } @misc{HeinzKuBeck, author = {Heinz, Stefan and Ku, Wen-Yang and Beck, J. Christopher}, title = {Recent improvements using constraint integer programming for resource allocation and scheduling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17676}, abstract = {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.}, language = {en} } @inproceedings{HeinzBeck, author = {Heinz, Stefan and Beck, J. Christopher}, title = {Reconsidering Mixed Integer Programming and MIP-based Hybrids for Scheduling}, series = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2012)}, volume = {7298}, booktitle = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2012)}, pages = {211 -- 227}, language = {en} }