Issues of inequity in U.S. high schools' course scheduling did not previously exist. However, in recent years, with the increase in student population and course variety, students perceive that the course scheduling method is unfair. Current integer programming (IP) methods to the high school scheduling problem (HSSP) fall short in addressing these fairness concerns. The purpose of this research is to develop a solution methodology that generates feasible and fair course schedules using student preferences. Utilizing principles of fairness, which have been well studied in market design, we define the fair high school scheduling problem (FHSSP), a novel extension to the HSSP, and devise a corresponding algorithm based on integer programming to solve the FHSSP. We test our approach on a real course request dataset from a high school in California, USA. Results show that our algorithm can generate schedules that are both feasible and fair. In this paper, we demonstrate that our IP algorithm not only solves the HSSP and FHSSP in the United States but has the potential to be applied to various real-world scheduling problems. Additionally, we show the feasibility of integrating human emotions into mathematical modeling.

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest due to their potential impact on advancing scientific research and industrial practices by improving predictive models with small- or large-scale datasets and expressive predictive models with useful inductive biases. The survey has two parts. The first considers incorporating physics knowledge on an architectural level through objective functions, structured predictive models, and data augmentation. The second considers data as physics knowledge, which motivates looking at multi-task, meta, and contextual learning as an alternative approach to incorporating physics knowledge in a data-driven fashion. Finally, we also provide an industrial perspective on the application of these methods and a survey of the open-source ecosystem for physics-informed machine learning.

Don't Get Stuck: A Deadlock Recovery Approach Abstract-- When multiple agents share space, interactions can lead to deadlocks, where no agent can advance towards its goal. This STL-MPPI framework ensures system compliance to specifications and dynamics while ensuring the safety of the resulting maneuvers, indicating a strong potential for application to complex traffic scenarios (and rules) in practice. Validation studies are conducted in simulations and on scaled cars, respectively, to demonstrate the effectiveness of the proposed algorithm. These unable to move forward. This presents concerns for traffic situations, which require intricate agent prediction, routing flow and safety, especially in urban settings where real-time and rerouting strategies, and navigation through expanded decision-making is crucial and where AVs must coexist with dynamic spaces, make resolving deadlocks a complex issue human-driven vehicles, each relying on distinct decisionmaking for AV technology.

Since its formal introduction by Dantzig in 1947, LP has been widely applied across various fields, including operations research, economics, and engineering, due to its ability to optimize objectives subject to linear constraints (Dantzig, 1951; Bazaraa et al., 2013). However, traditional LP approaches have certain limitations, particularly in dealing with non-linear, high-dimensional, and dynamic environments where relationships among variables are complex and non-linear (Bertsimas & Tsitsiklis, 1997). By contrast, machine learning (ML) methods, especially deep learning, have demonstrated remarkable success in modeling complex patterns and making predictions based on large datasets (LeCun et al., 2015; Goodfellow et al., 2016). Despite these strengths, ML models often lack the explicit interpretability and rigorous constraint satisfaction that LP offers (Rudin, 2019). This has motivated researchers to explore hybrid approaches that combine the strengths of LP and ML, aiming to develop models that are both interpretable and powerful in their predictive capabilities. This paper proposes a novel hybrid method that integrates LP within the loss function of an unsupervised machine learning model. By embedding LP constraints directly into the ML framework, this approach not only maintains the interpretability and constraint satisfaction of LP but also leverages the flexibility and learning capacity of ML. This integration is particularly beneficial in unsupervised or semi-supervised settings, where traditional LP methods may struggle to provide robust solutions due to the lack of labeled data (Amos & Kolter, 2017).

Streamliners are certain constraints added to a constraint model to reduce the search space, thereby improving the feasibility and speed of finding solutions to complex constraint satisfaction problems. By incorporating domain-specific knowledge, streamliners can guide the constraint solver, allowing it to bypass less promising areas of the search space. Gomes and Sellmann (2004a) introduced streamliners to speed up the constrained-based search for hard combinatorial design problems. Today, streamliners are a standard tool for speeding up constrained-based search. Streamliners are closely related to implied/redundant constraints, symmetry-breaking constraints, and dominance-breaking constraints; however, adding a streamliner may even cause the constraint model to become inconsistent. Originally, streamliners were hand-crafted by researchers who used their theoretical insight to analyze the constrained model. However, progress has also been made on the automated generation of streamliners (Spracklen et al. 2023) by systematically trying the effect of some atomic constraints, such as imposing specific constraints on integer and function domains, like enforcing odd or even values, monotonicity, and properties like commutativity, as well as facilitating specific attributes in binary relations. These atomic restrictions are tested on thousands of problem instances, and those that show a good streamlining effect are systematically combined.

By representing any constraint-based causal learning algorithm via a placeholder property, we decompose the correctness condition into a part relating the distribution and the true causal graph, and a part that depends solely on the distribution. This provides a general framework to obtain correctness conditions for causal learning, and has the following implications. We provide exact correctness conditions for the PC algorithm, which are then related to correctness conditions of some other existing causal discovery algorithms. We show that the sparsest Markov representation condition is the weakest correctness condition resulting from existing notions of minimality for maximal ancestral graphs and directed acyclic graphs. We also reason that additional knowledge than just Pearl-minimality is necessary for causal learning beyond faithfulness.

We are interested in automating reasoning with and about study regulations, catering to various stakeholders, ranging from administrators, over faculty, to students at different stages. Our work builds on an extensive analysis of various study programs at the University of Potsdam. The conceptualization of the underlying principles provides us with a formal account of study regulations. In particular, the formalization reveals the properties of admissible study plans. With these at end, we propose an encoding of study regulations in Answer Set Programming that produces corresponding study plans. Finally, we show how this approach can be extended to a generic user interface for exploring study plans.

The Job-shop Scheduling Problem (JSP) is a well-known and challenging combinatorial optimization problem in which tasks sharing a machine are to be arranged in a sequence such that encompassing jobs can be completed as early as possible. In this paper, we investigate problem decomposition into time windows whose operations can be successively scheduled and optimized by means of multi-shot Answer Set Programming (ASP) solving. From a computational perspective, decomposition aims to split highly complex scheduling tasks into better manageable subproblems with a balanced number of operations such that good-quality or even optimal partial solutions can be reliably found in a small fraction of runtime. We devise and investigate a variety of decomposition strategies in terms of the number and size of time windows as well as heuristics for choosing their operations. Moreover, we incorporate time window overlapping and compression techniques into the iterative scheduling process to counteract optimization limitations due to the restriction to window-wise partial schedules. Our experiments on different JSP benchmark sets show that successive optimization by multi-shot ASP solving leads to substantially better schedules within tight runtime limits than single-shot optimization on the full problem. In particular, we find that decomposing initial solutions obtained with proficient heuristic methods into time windows leads to improved solution quality.

Planning for a wide range of real-world robotic tasks necessitates to know and write all constraints. However, instances exist where these constraints are either unknown or challenging to specify accurately. A possible solution is to infer the unknown constraints from expert demonstration. This paper presents a novel Positive-Unlabeled Constraint Learning (PUCL) algorithm to infer a continuous arbitrary constraint function from demonstration, without requiring prior knowledge of the true constraint parameterization or environmental model as existing works. Within our framework, we treat all data in demonstrations as positive (feasible) data, and learn a control policy to generate potentially infeasible trajectories, which serve as unlabeled data. In each iteration, we first update the policy and then a two-step positive-unlabeled learning procedure is applied, where it first identifies reliable infeasible data using a distance metric, and secondly learns a binary feasibility classifier (i.e., constraint function) from the feasible demonstrations and reliable infeasible data. The proposed framework is flexible to learn complex-shaped constraint boundary and will not mistakenly classify demonstrations as infeasible as previous methods. The effectiveness of the proposed method is verified in three robotic tasks, using a networked policy or a dynamical system policy. It successfully infers and transfers the continuous nonlinear constraints and outperforms other baseline methods in terms of constraint accuracy and policy safety.

In the realm of machine learning and artificial intelligence, ensuring fairness in algorithmic decisionmaking has become an imperative challenge. This concern is driven by the growing awareness of the ethical and societal consequences stemming from automated systems. Unlike the traditional focuses that solely enhance statistical and machine learning algorithms across various performance metrics, the emphasis on fairness injects a nuanced layer of complexity into predictive modeling. It mandates a conscientious evaluation of how algorithmic predictions may perpetuate or mitigate existing biases, thereby influencing real-world outcomes across diverse societal sectors. The notion of fairness within the machine learning community includes a diverse array of definitions for what it means for an algorithm to be fair, with each definition informed by distinct ethical considerations and operational implications [Mitchell et al., 2021, Plecko and Bareinboim, 2022, Barocas et al., 2023]. This diversity often leads to a challenging paradox for practitioners and theorists alike, as adhering to one notion of fairness can sometimes contradict the requirements or objectives of another [Kleinberg et al., 2017, Corbett-Davies and Goel, 2018, Friedler et al., 2021]. The task of ensuring algorithmic fairness is made more complex by its inherently contextspecific nature, which demands careful consideration in selecting fairness criteria that are not only theoretically sound but also practically applicable and aligned with prevailing societal values.