Decision-Focused Learning (DFL) focuses on a setting where a system gets as input some features and needs to predict coefficients to a downstream optimization problem. Classically, one would apply a two-stage solution, which trains the predictor as a regression task and only uses the optimizer during evaluation. However, the two-stage solution fails to optimize the downstream optimization problem. As such, one might use DFL techniques to train the predictor. Nonetheless, these fail to take the entire solution space into account and only optimize toward the optimal true solution, and as such, they might fail to optimize the total downstream value. Furthermore, these techniques are computationally expensive.

We tackle these two problems using Decision Diagrams (DDs) for DFL. DDs for DFL have three main benefits. First, the DD can be cached between runs, speeding up the training loop. Second, we present four novel loss functions that use DDs to reason efficiently over entire solution spaces. Furthermore, we introduce a novel method to relax the DDs to reduce solve-time during training.

We experimentally show that the DDs speed up the training loop substantially. We further show that the DFL losses perform on par with other state-of-the-art DFL losses. Finally, we experimentally show when and which losses work with relaxed DDs.

This paper provides a novel method of solving the resource-constrained project scheduling problem (RCPSP) with logical constraints (RCPSP-log) using satisfiability (SAT) solving and integrating variable selection heuristics. The extension provides two additional precedences: OR constraints and bidirectional (BI) relations, making it possible to express more complex dependencies between tasks. OR constraints enable a task to be dependent on multiple preceding tasks, while BI relations do not allow tasks to be executed at the same time. Both problems are known to be NP-hard.

The solution method consists of using a max satisfiability (MaxSAT) solver combined with variable selection heuristics. The paper investigates two heuristics, based on the greedy approach of scheduling each activity as early as possible and variable conflict analysis.

The results on well-known datasets from the literature show that most of the instances can be solved within the designated time limit. The proposed approaches contribute to reducing the makespan, especially when dealing with no logical constraints or only OR relations. For BI constraints, the algorithm is having difficulties in finding solutions, especially when increasing the number of activities, reporting fewer solutions than the baselines. Overall, the results provide insight into the integration of variable selection heuristics for SAT solving, with the potential for more investigation into problem-specific ideas.

This paper solves job sequencing with one common and multiple secondary resources (JSOCMSR) problem by encoding it as a Boolean satisfiability (SAT) problem and applying domain-specific heuristics to improve the SAT solver’s performance. JSOCMSR problem is an NP-hard scheduling problem where each job utilizes two resources: a shared resource and a secondary job-dependent resource. First, the problem was modeled as an instance of SAT and then the SAT solver was augmented with a static greedy variable-ordering heuristic. This heuristic has led to significant improvement in the solver’s speed compared to a generic SAT heuristic for problem instances of larger size.

The Variable State Independent Decaying Sum (VSIDS) heuristic is one of the most effective variable selection heuristics for Conflict-Driven Clause-Learning (CDCL) SAT solvers. It works by keeping track of the activity values for each variable, which get bumped and decayed based on conflict analysis. These activity values usually start out arbitrarily at zero, which prompts the question if initializing these values can result in better performance.
This paper presents several adaptations of the VSIDS heuristic specialized for solving the Resource-Constraint Project Scheduling Problem with time varying resource availabilities and demands (RCPSP/t). The approach uses domain-specific knowledge to initialize the activity values of VSIDS with more relevant values. The experiments presented in this paper show that this domain-specific knowledge can indeed benefit the heuristic and can lead to better solve times, allowing the solver to find solutions for 17% more of the instances and find proven optimal solutions for 5% more instances of the PSPLIB data set.

This paper presents a new greedy heuristic to extend SAT Solvers when solving the Preemptive resource-constrained project scheduling problem (PRCPSP-ST). The heuristic uses domain-specific knowledge to generate a fixed order of variable selection. We also extend previous work into encoding PRCPSP-ST by providing an alternative upper bound. The heuristic was tested against VSDIS on the J12 dataset. These experiments show that it performed, on average, six times slower than VSDIS.

The multi-mode resource-constrained project scheduling problem (MRCPSP) is an extension of the resource-constrained project scheduling problem (RCPSP), which allows activities to be executed in multiple modes. The state-of-the-art solutions for solving this NP-Hard problem are dedicated algorithms and (meta-)heuristics. However, this paper considers a more flexible approach using a MaxSAT solver. The idea is to replace the existing variable selection strategy of the solver, Variable State Independent Decaying Sum (VSIDS), with two scheduling heuristics, Earliest Starting Time (EST) and Shortest Feasible Mode (SFM). We examine that combining the three heuristics results in a more efficient solver. In contrast, scheduling rules alone lead to a solver that performs significantly worse on any of the chosen metrics and benchmarks.