This paper studies the scheduling of jobs of different families on parallel machines with qualification constraints. Originating from semiconductor manufacturing, this constraint imposes a time threshold between the execution of two jobs of the same family. Otherwise, the machine becomes disqualified for this family. The goal is to minimize both the flow time and the number of disqualifications. Recently, an efficient constraint programming model has been proposed. However, when priority is given to the flow time objective, the efficiency of the model can be improved. This paper uses a polynomial-time algorithm which minimize the flow time for a single machine relaxation where disqualifications are not considered. Using this algorithm one can derived filtering rules on different variables of the model. Experimental results are presented showing the effectiveness of these rules. They improve the competitiveness with the mixed integer linear program of the literature.

Catastrophic forgetting in continual learning is a common destructive phenomenon in gradient-based neural networks that learn sequential tasks, and it is much different from forgetting in humans, who can learn and accumulate knowledge throughout their whole lives. Catastrophic forgetting is the fatal shortcoming of a large decrease in performance on previous tasks when the model is learning a novel task. To alleviate this problem, the model should have the capacity to learn new knowledge and preserve learned knowledge. We propose an average gradient episodic memory (A-GEM) with a soft constraint $\epsilon \in [0, 1]$, which is a balance factor between learning new knowledge and preserving learned knowledge; our method is called gradient episodic memory with a soft constraint $\epsilon$ ($\epsilon$-SOFT-GEM). $\epsilon$-SOFT-GEM outperforms A-GEM and several continual learning benchmarks in a single training epoch; additionally, it has state-of-the-art average accuracy and efficiency for computation and memory, like A-GEM, and provides a better trade-off between the stability of preserving learned knowledge and the plasticity of learning new knowledge.

Ill-managed intersections are the primary reasons behind the increasing traffic problem in urban areas, leading to nonoptimal traffic-flow and unnecessary deadlocks. In this paper, we propose an automated intersection management system that extracts data from a well-defined grid of sensors and optimizes traffic flow by controlling traffic signals. The data extraction mechanism is independent of the optimization algorithm and this paper primarily emphasizes the later one. We have used MiniZinc modeling language to define our system as a constraint satisfaction problem which can be solved using any off-the-shelf solver. The proposed system performs much better than the systems currently in use. Our system reduces the mean waiting time and standard deviation of the waiting time of vehicles and avoids deadlocks.

Class Scheduling is a highly constrained task. Educational institutes spend a lot of resources, in the form of time and manual computation, to find a satisficing schedule that fulfills all the requirements. A satisficing class schedule accommodates all the students to all their desired courses at convenient timing. The scheduler also needs to take into account the availability of course teachers on the given slots. With the added limitation of available classrooms, the number of solutions satisfying all constraints in this huge search-space, further decreases. This paper proposes an efficient system to generate class schedules that can fulfill every possible need of a typical university. Though it is primarily a fixed-credit scheduler, it can be adjusted for open-credit systems as well. The model is designed in MiniZinc and solved using various off-the-shelf solvers. The proposed scheduling system can find a balanced schedule for a moderate-sized educational institute in less than a minute.

Numerous real-life decision-making processes involve solving a combinatorial optimization problem with uncertain input that can be estimated from historic data. There is a growing interest in decision-focused learning methods, where the loss function used for learning to predict the uncertain input uses the outcome of solving the combinatorial problem over a set of predictions. Different surrogate loss functions have been identified, often using a continuous approximation of the combinatorial problem. However, a key bottleneck is that to compute the loss, one has to solve the combinatorial optimisation problem for each training instance in each epoch, which is computationally expensive even in the case of continuous approximations. We propose a different solver-agnostic method for decision-focused learning, namely by considering a pool of feasible solutions as a discrete approximation of the full combinatorial problem. Solving is now trivial through a single pass over the solution pool. We design several variants of a noise-contrastive loss over the solution pool, which we substantiate theoretically and empirically. Furthermore, we show that by dynamically re-solving only a fraction of the training instances each epoch, our method performs on par with the state of the art, whilst drastically reducing the time spent solving, hence increasing the feasibility of predict-and-optimize for larger problems.

The study of random constraint satisfaction problems (CSPs) has received tremendous ideas from combinatorics, computer science and statistical physics. Random CSPs contain a large set of variables which interact through a large set of constraints, where each variable ranges over a domain and a configuration (solution) to all the variables should satisfy all of the constraints. A fundamental question in the study of random CSPs is the average-case computational complexity of solving ensembles of CSPs. Great amount of theoretical and algorithmic work has been devoted to establish and locate the satisfiability threshold, and studies show that complexity attains the maximum at the SAT-UNSAT transition. Many of the studied CSP models (such as random k-SAT, graph coloring) have fixed domain size, constraint length, and the number of constraints is linear compared with the number of variables. In recent years, a lot of attention has been paid to the study of CSPs with growing domains or constraint length ([13, 7, 4, 5]).

Combinatorial optimization problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral solutions of certified quality. Inspired by Erdos' probabilistic method, we use a neural network to parametrize a probability distribution over sets. Crucially, we show that when the network is optimized w.r.t. a suitably chosen loss, the learned distribution contains, with controlled probability, a low-cost integral solution that obeys the constraints of the combinatorial problem. The probabilistic proof of existence is then derandomized to decode the desired solutions. We demonstrate the efficacy of this approach to obtain valid solutions to the maximum clique problem and to perform local graph clustering. Our method achieves competitive results on both real datasets and synthetic hard instances.

We propose a novel non-randomized anytime orienteering algorithm for finding k-optimal goals that maximize reward on a specialized graph with budget constraints. This specialized graph represents a real-world scenario which is analogous to an orienteering problem of finding k-most optimal goal states.

Temporal planning offers numerous advantages when based on an expressive representation. Timelines have been known to provide the required expressiveness but at the cost of search efficiency. We propose here a temporal planner, called FAPE, which supports many of the expressive temporal features of the ANML modeling language without loosing efficiency. FAPE's representation coherently integrates flexible timelines with hierarchical refinement methods that can provide efficient control knowledge. A novel reachability analysis technique is proposed and used to develop causal networks to constrain the search space. It is employed for the design of informed heuristics, inference methods and efficient search strategies. Experimental results on common benchmarks in the field permit to assess the components and search strategies of FAPE, and to compare it to IPC planners. The results show the proposed approach to be competitive with less expressive planners and often superior when hierarchical control knowledge is provided. FAPE, a freely available system, provides other features, not covered here, such as the integration of planning with acting, and the handling of sensing actions in partially observable environments.

We study query containment in three closely related formalisms: monadic disjunctive Datalog (MDDLog), MMSNP (a logical generalization of constraint satisfaction problems), and ontology-mediated queries (OMQs) based on expressive description logics and unions of conjunctive queries. Containment in MMSNP was known to be decidable due to a result by Feder and Vardi, but its exact complexity has remained open. We prove 2NEXPTIME-completeness and extend this result to monadic disjunctive Datalog and to OMQs.