We consider the torpedo scheduling problem in steel production, which is concerned with the transport of hot metal from a blast furnace to an oxygen converter. A schedule must satisfy, amongst other considerations, resource capacity constraints along the path and the locations traversed as well as the sulfur level of the hot metal. The goal is first to minimize the number of torpedo cars used during the planning horizon and second to minimize the time spent desulfurizing the hot metal. We propose an exact solution method based on Logic based Benders Decomposition using Mixed-Integer and Constraint Programming, which optimally solves and proves, for the first time, the optimality of all instances from the ACP Challenge 2016 within 10 minutes. In addition, we adapted our method to handle large-scale instances and instances with a more general rail network. This adaptation optimally solved all challenge instances within one minute and was able to solve instances of up to 100,000 hot metal pickups.

MiniZinc is a solver agnostic modeling language for defining and solver combinatorial satisfaction and optimization problems. MiniZinc provides a solver independent modeling language which is now supported by constraint programming solvers, mixed integer programming solvers, SAT and SAT modulo theory solvers, and hybrid solvers. Since 2008 we have run the MiniZinc challenge every year, which compares and contrasts the different strengths of different solvers and solving technologies on a set of MiniZinc models. Here we report on what we have learnt from running the competition for 6 years.

MiniZinc is a solver agnostic modeling language for defining and solver combinatorial satisfaction and optimization problems. MiniZinc provides a solver independent modeling language which is now supported by constraint programming solvers, mixed integer programming solvers, SAT and SAT modulo theory solvers, and hybrid solvers. Since 2008 we have run the MiniZinc challenge every year, which compares and contrasts the different strengths of different solvers and solving technologies on a set of MiniZinc models. Here we report on what we have learnt from running the competition for 6 years.

We investigate the computational complexity of two global constraints, CUMULATIVE and INTERDISTANCE. These are key constraints in modeling and solving scheduling problems. Enforcing domain consistency on both is NP-hard. However, restricted versions of these constraints are often sufficient in practice. Some examples include scheduling problems with a large number of similar tasks, or tasks sparsely distributed over time. Another example is runway sequencing problems in air-traffic control, where landing periods have a regular pattern. Such cases can be characterized in terms of structural restrictions on the constraints. We identify a number of such structural restrictions and investigate how they impact the computational complexity of propagating these global constraints. In particular, we prove that such restrictions often make propagation tractable.

Cumulative resource constraints can model scarce resources in scheduling problems or a dimension in packing and cutting problems. In order to efficiently solve such problems with a constraint programming solver, it is important to have strong and fast propagators for cumulative resource constraints. One such propagator is the recently developed time-table-edge-finding propagator, which considers the current resource profile during the edge-finding propagation. Recently, lazy clause generation solvers, i.e. constraint programming solvers incorporating nogood learning, have proved to be excellent at solving scheduling and cutting problems. For such solvers, concise and accurate explanations of the reasons for propagation are essential for strong nogood learning. In this paper, we develop the first explaining version of time-table-edge-finding propagation and show preliminary results on resource-constrained project scheduling problems from various standard benchmark suites. On the standard benchmark suite PSPLib, we were able to close one open instance and to improve the lower bound of about 60% of the remaining open instances. Moreover, 6 of those instances were closed.

The technical report presents a generic exact solution approach for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedences (Rcpsp/max). The approach uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply nogood learning and conflict-driven search on the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solutions and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. The method is highly robust: it matched or bettered the best known results on all of the 2340 instances we examined except 3, according to the currently available data on the PSPLib. Of the 631 open instances in this set it closed 573 and improved the bounds of 51 of the remaining 58 instances.