Sparse decision tree learning provides accurate and interpretable predictive models that are ideal for high-stakes applications by finding the single most accurate tree within a (soft) size limit. Rather than relying on a single "best" tree, Rashomon sets-trees with similar performance but varying structures-can be used to enhance variable importance analysis, enrich explanations, and enable users to choose simpler trees or those that satisfy stakeholder preferences (e.g., fairness) without hard-coding such criteria into the objective function. However, because finding the optimal tree is NP-hard, enumerating the Rashomon set is inherently challenging. Therefore, we introduce SORTD, a novel framework that improves scalability and enumerates trees in the Rashomon set in order of the objective value, thus offering anytime behavior. Our experiments show that SORTD reduces runtime by up to two orders of magnitude compared with the state of the art. Moreover, SORTD can compute Rashomon sets for any separable and totally ordered objective and supports post-evaluating the set using other separable (and partially ordered) objectives. Together, these advances make exploring Rashomon sets more practical in real-world applications.

Decision Trees are prominent prediction models for interpretable Machine Learning. They have been thoroughly researched, mostly in the batch setting with a fixed labelled dataset, leading to popular algorithms such as C4.5, ID3 and CART. Unfortunately, these methods are of heuristic nature, they rely on greedy splits offering no guarantees of global optimality and often leading to unnecessarily complex and hard-to-interpret Decision Trees. Recent breakthroughs addressed this suboptimality issue in the batch setting, but no such work has considered the online setting with data arriving in a stream. To this end, we devise a new Monte Carlo Tree Search algorithm, Thompson Sampling Decision Trees (TSDT), able to produce optimal Decision Trees in an online setting. We analyse our algorithm and prove its almost sure convergence to the optimal tree. Furthermore, we conduct extensive experiments to validate our findings empirically. The proposed TSDT outperforms existing algorithms on several benchmarks, all while presenting the practical advantage of being tailored to the online setting.

Constraint Optimization Problems (COP) pose intricate challenges in combinatorial problems usually addressed through Branch and Bound (B\&B) methods, which involve maintaining priority queues and iteratively selecting branches to search for solutions. However, conventional approaches take a considerable amount of time to find optimal solutions, and it is also crucial to quickly identify a near-optimal feasible solution in a shorter time. In this paper, we aim to investigate the effectiveness of employing a depth-first search algorithm for solving COP, specifically focusing on identifying optimal or near-optimal solutions within top $n$ solutions. Hence, we propose a novel heuristic neural network algorithm based on MCTS, which, by simultaneously conducting search and training, enables the neural network to effectively serve as a heuristic during Backtracking. Furthermore, our approach incorporates encoding COP problems and utilizing graph neural networks to aggregate information about variables and constraints, offering more appropriate variables for assignments. Experimental results on stochastic COP instances demonstrate that our method identifies feasible solutions with a gap of less than 17.63% within the initial 5 feasible solutions. Moreover, when applied to attendant Constraint Satisfaction Problem (CSP) instances, our method exhibits a remarkable reduction of less than 5% in searching nodes compared to state-of-the-art approaches.

An efficient robot path-planning model is vulnerable to the number of search nodes, path cost, and time complexity. The conventional A-star (A*) algorithm outperforms other grid-based algorithms for its heuristic search. However it shows suboptimal performance for the time, space, and number of search nodes, depending on the robot motion block (RMB). To address this challenge, this study proposes an optimal RMB for the A* path-planning algorithm to enhance the performance, where the robot movement costs are calculated by the proposed adaptive cost function. Also, a selection process is proposed to select the optimal RMB size. In this proposed model, grid-based maps are used, where the robot's next move is determined based on the adaptive cost function by searching among surrounding octet neighborhood grid cells. The cumulative value from the output data arrays is used to determine the optimal motion block size, which is formulated based on parameters. The proposed RMB significantly affects the searching time complexity and number of search nodes of the A* algorithm while maintaining almost the same path cost to find the goal position by avoiding obstacles. For the experiment, a benchmarked online dataset is used and prepared three different dimensional maps. The proposed approach is validated using approximately 7000 different grid maps with various dimensions and obstacle environments. The proposed model with an optimal RMB demonstrated a remarkable improvement of 93.98% in the number of search cells and 98.94% in time complexity compared to the conventional A* algorithm. Path cost for the proposed model remained largely comparable to other state-of-the-art algorithms. Also, the proposed model outperforms other state-of-the-art algorithms.

JPS (Jump Point Search) is a state-of-the-art optimal algorithm for online grid-based pathfinding. Widely used in games and other navigation scenarios, JPS nevertheless can exhibit pathological behaviours which are not well studied: (i) it may repeatedly scan the same area of the map to find successors; (ii) it may generate and expand suboptimal search nodes. In this work, we examine the source of these pathological behaviours, show how they can occur in practice, and propose a purely online approach, called Constrained JPS (CJPS), to tackle them efficiently. Experimental results show that CJPS has low overheads and is often faster than JPS in dynamically changing grid environments: by up to 7x in large game maps and up to 14x in pathological scenarios.

Conflict-Based Search is one of the most popular methods for multi-agent path finding. Though it is complete and optimal, it does not scale well. Recent works have been proposed to accelerate it by introducing various heuristics. However, whether these heuristics can apply to non-grid-based problem settings while maintaining their effectiveness remains an open question. In this work, we find that the answer is prone to be no. To this end, we propose a learning-based component, i.e., the Graph Transformer, as a heuristic function to accelerate the planning. The proposed method is provably complete and bounded-suboptimal with any desired factor. We conduct extensive experiments on two environments with dense graphs. Results show that the proposed Graph Transformer can be trained in problem instances with relatively few agents and generalizes well to a larger number of agents, while achieving better performance than state-of-the-art methods.

Pathfinding in Euclidean space is a common problem faced in robotics and computer  games. For long-distance navigation on the surface of the earth or in outer space however,  approximating the geometry as Euclidean can be insufficient for real-world applications  such as the navigation of spacecraft, aeroplanes, drones and ships. This article describes an any-angle pathfinding algorithm for calculating the shortest path between point pairs  over the surface of a sphere. Introducing several novel adaptations, it is shown that Anya  as described by Harabor & Grastien for Euclidean space can be extended to Spherical  geometry. There, where the shortest-distance line between coordinates is defined instead by a great-circle path, the optimal solution is typically a curved line in Euclidean space.  In addition the turning points for optimal paths in Spherical geometry are not necessarily  corner points as they are in Euclidean space, as will be shown, making further substantial  adaptations to Anya necessary. Spherical Anya returns the optimal path on the sphere,  given these different properties of world maps defined in Spherical geometry. It preserves all primary benefits of Anya in Euclidean geometry, namely the Spherical Anya algorithm always returns an optimal path on a sphere and does so entirely on-line, without any  preprocessing or large memory overheads. Performance benchmarks are provided for several  game maps including Starcraft and Warcraft III as well as for sea navigation on Earth  using the NOAA bathymetric dataset. Always returning the shorter path compared with  the Euclidean approximation yielded by Anya, Spherical Anya is shown to be faster than  Anya for the majority of sea routes and slower for Game Maps and Random Maps. 

Reconfiguration aims at recovering a system from a fault by automatically adapting the system configuration, such that the system goal can be reached again. Classical approaches typically use a set of pre-defined faults for which corresponding recovery actions are defined manually. This is not possible for modern hybrid systems which are characterized by frequent changes. Instead, AI-based approaches are needed which leverage on a model of the non-faulty system and which search for a set of reconfiguration operations which will establish a valid behavior again. This work presents a novel algorithm which solves three main challenges: (i) Only a model of the non-faulty system is needed, i.e. the faulty behavior does not need to be modeled. (ii) It discretizes and reduces the search space which originally is too large -- mainly due to the high number of continuous system variables and control signals. (iii) It uses a SAT solver for propositional logic for two purposes: First, it defines the binary concept of validity. Second, it implements the search itself -- sacrificing the optimal solution for a quick identification of an arbitrary solution. It is shown that the approach is able to reconfigure faults on simulated process engineering systems.

Pathfinding in Euclidean space is a common problem faced in robotics and computer games. For long-distance navigation on the surface of the earth or in outer space however, approximating the geometry as Euclidean can be insufficient for real-world applications such as the navigation of spacecraft, aeroplanes, drones and ships. This article describes an any-angle pathfinding algorithm for calculating the shortest path between point pairs over the surface of a sphere. Introducing several novel adaptations, it is shown that Anya as described by (Harabor & Grastien, 2013) for Euclidean space can be extended to Spherical geometry. There, where the shortest-distance line between coordinates is defined instead by a great-circle path, the optimal solution is typically a curved line in Euclidean space. In addition the turning points for optimal paths in Spherical geometry are not necessarily corner points as they are in Euclidean space, as will be shown, making further substantial adaptations to Anya necessary. Spherical Anya returns the optimal path on the sphere, given these different properties of world maps defined in Spherical geometry. It preserves all primary benefits of Anya in Euclidean geometry, namely the Spherical Anya algorithm always returns an optimal path on a sphere and does so entirely on-line, without any preprocessing or large memory overheads. Performance benchmarks are provided for several game maps including Starcraft and Warcraft III as well as for sea navigation on Earth using the NOAA bathymetric dataset. Always returning the shorter path compared with the Euclidean approximation yielded by Anya, Spherical Anya is shown to be faster than Anya for the majority of sea routes and slower for Game Maps and Random Maps.

The majority of search-based HTN planning systems can be divided into those searching a space of partial plans (a plan space) and those performing progression search, i.e., that build the solution in a forward manner. So far, all HTN planners that guide the search by using heuristic functions are based on plan space search. Those systems represent the set of search nodes more effectively by maintaining a partial ordering between tasks, but they have only limited information about the current state during search. In this article, we propose the use of progression search as basis for heuristic HTN planning systems. Such systems can calculate their heuristics incorporating the current state, because it is tracked during search. Our contribution is the following: We introduce two novel progression algorithms that avoid unnecessary branching when the problem at hand is partially ordered and show that both are sound and complete. We show that defining systematicity is problematic for search in HTN planning, propose a definition, and show that it is fulfilled by one of our algorithms. Then, we introduce a method to apply arbitrary classical planning heuristics to guide the search in HTN planning. It relaxes the HTN planning model to a classical model that is only used for calculating heuristics. It is updated during search and used to create heuristic values that are used to guide the HTN search. We show that it can be used to create HTN heuristics with interesting theoretical properties like safety, goal-awareness, and admissibility. Our empirical evaluation shows that the resulting system outperforms the state of the art in search-based HTN planning.