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ItemScheduling and rostering with learning constraint solversDowning, Nicholas Ronald ( 2016)In this research we investigate using Constraint Programming (CP) with Lazy Clause Generation (LCG), that is, constraint solvers with nogood learning, to tackle a number of well known scheduling, rostering, and planning problems. We extend a number of CP constraints to be useable in an LCG solver, and we investigate alternative search strategies that use the Unsatisfiable Cores, i.e. reasons for failure returned by the LCG solver, to guide the search for optimal solutions. We give comprehensive analysis and experiments. These experiments show that while adding more and more sophisticated constraint propagators to LCG delivers diminishing returns, unsatisfiable-core optimization which leverages the infrastructure provided by LCG can deliver significant benefits which are unavailable in CP without LCG. Overall, we demonstrate that LCG is a highly competitive technology for solving realistic industrial scheduling and rostering problems to optimality, allowing that the problems are smaller than those tackled by competing algorithms which do not prove optimality.
ItemImproving scheduling by learningSCHUTT, ANDREAS ( 2011)Scheduling problems appear in many industrial problems with different facets and requirements of a solution. A solution is a schedule of a set of activities subject to constraints such as precedence relations and resource restrictions on the maximum number of concurrent activities. This dissertation presents new deductive techniques for precedence and cumulative resource constraints in constraint programming to improve solution processes of combinatorial scheduling problems, in particular, and combinatorial problems, in general. Due to their intractability, many schedulers either solve a simplified problem or are tailored to a specific problem, but are inflexible with respect to changes in the problem statement. Constraint Programming (CP) offers a powerful framework for combinatorial problems which also tackles the demand of flexibility of changes in the problem statement due to a strict separation of problem modelling, search algorithms, and high-specialised deduction techniques. Moreover, recent advanced CP solvers such as lazy clause generation (LCG) additionally include sophisticated conflict learning technologies. Their efficiency depends, amongst other things, on reusable explanations formulated by deductive algorithms. Unit two variable per inequality (UTVPI) constraints are one of the largest integer constraint class that is solvable in polynomial time. These constraints can model precedence relations between activities. A new theoretical result about reasoning of UTVPI systems is shown, based on that, new incremental deductive algorithms are created for manipulating UTVPI constraints including satisfiability, implication, and explanation. These algorithms are asymptotically faster on sparse UTVPI systems than current algorithms. Cumulative constraints enforce resource restrictions in scheduling problems. We show how, by adding explanation to the cumulative constraint in an LCG solver, we can solve resource-constrained project scheduling problems far faster than other comparable methods. Furthermore, a complete LCG-based approach including cumulative constraints is developed for an industrial carpet cutting problem. This approach outperforms the current incomplete method on all industrial instances provided.