Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional solvers have had decades to build. We drew inspiration from the warm-start technique used in conventional solvers to address one of the major challenges faced by decision diagram based methods. Decision diagrams become more useful the wider they are allowed to be, but also become more costly to generate, especially with large numbers of variables. In the original version of this paper, we presented a method of peeling off a sub-graph of previously constructed diagrams and using it as the initial diagram for subsequent iterations that we call peel-and-bound. We tested the method on the sequence ordering problem, and our results indicate that our peel-and-bound scheme generates stronger bounds than a branch-and-bound scheme using the same propagators, and at significantly less computational cost. In this extended version of the paper, we also propose new methods for using relaxed decision diagrams to improve the solutions found using restricted decision diagrams, discuss the heuristic decisions involved with the parallelization of peel-and-bound, and discuss how peel-and-bound can be hyper-optimized for sequencing problems. Furthermore, we test the new methods on the sequence ordering problem and the traveling salesman problem with time-windows (TSPTW), and include an updated and generalized implementation of the algorithm capable of handling any discrete optimization problem. The new results show that peel-and-bound outperforms ddo (a decision diagram based branch-and-bound solver) on the TSPTW. We also close 15 open benchmark instances of the TSPTW.

Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce efficient, machine-verifiable certificates that solutions have been computed correctly. Building on the cutting planes proof system, we develop a certification method for optimisation problems in which symmetry and dominance breaking is easily expressible. Our experimental evaluation demonstrates that we can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes cardinality and parity (XOR) reasoning. In addition, we apply our method to maximum clique solving and constraint programming as a proof of concept that the approach applies to a wider range of combinatorial problems.

Additionally, new on-demand modalities including ride-share, bike-share, and e-scooters have been introduced in recent years and transformed the transportation landscape in urban environments. A wellfunctioning transit system fosters the growth and expansion of businesses, distributes social and economic benefits, and links the capabilities of community members, thereby enhancing what they can accomplish as a society [6, 11, 15]. However, the explosion in transportation options and the complicated relationship between public and private offerings present myriad new challenges in the design and operation of these systems. There are also complex, and often competing, operational objectives that complicate the implementation of efficient services. Since affordable public transit services are the backbones of many communities, solving these problems and understanding state-of-the-art methods for AI-driven smart transportation has the potential to strengthen urban communities, address the climate challenge, and foster equitable growth. Fundamentally, the design of a well-functioning transit system requires solving complex combinatorial optimization problems related to planning and real-time operations. These problems span many well studied fields, from classical line planning to offline and online vehicle routing problems (VRPs). While there are many ways to assess the performance of smart transportation systems, we largely focus on evaluating these systems in the context of optimizing utilization (i.e.

Path planning in obstacle-dense environments is a key challenge in robotics, and depends on inferring scene attributes and associated uncertainties. We present a multiple-hypothesis path planner designed to navigate complex environments using obstacle detections. Path hypotheses are generated by reasoning about uncertainty and range, as initial detections are typically at far ranges with high uncertainty, before subsequent detections reduce this uncertainty. Given estimated obstacles, we build a graph of pairwise connections between objects based on the probability that the robot can safely pass between the pair. The graph is updated in real time and pruned of unsafe paths, providing probabilistic safety guarantees. The planner generates path hypotheses over this graph, then trades between safety and path length to intelligently optimize the best route. We evaluate our planner on randomly generated simulated forests, and find that in the most challenging environments, it increases the navigation success rate over an A* baseline from 20% to 75%. Results indicate that the use of evolving, range-based uncertainty and multiple hypotheses are critical for navigating dense environments.

The main idea of our algorithm is to carefully leverage the structure of the minimax problem, performing Nesterov acceleration on the individual component and optimistic gradient on the coupling component. Equipped with proper restarting, we show that AG-OG achieves the optimal convergence rate (up to a constant) for a variety of settings, including bilinearly coupled strongly convex-strongly concave minimax optimization (bi-SC-SC), bilinearly coupled convex-strongly concave minimax optimization (bi-C-SC), and bilinear games. We also extend our algorithm to the stochastic setting and achieve the optimal convergence rate in both bi-SC-SC and bi-C-SC settings. AG-OG is the first single-call algorithm with optimal convergence rates in both deterministic and stochastic settings for bilinearly coupled minimax optimization problems.

We investigate time-optimal Multi-Robot Coverage Path Planning (MCPP) for both unweighted and weighted terrains, which aims to minimize the coverage time, defined as the maximum travel time of all robots. Specifically, we focus on a reduction from MCPP to Min-Max Rooted Tree Cover (MMRTC). For the first time, we propose a Mixed Integer Programming (MIP) model to optimally solve MMRTC, resulting in an MCPP solution with a coverage time that is provably at most four times the optimal. Moreover, we propose two suboptimal yet effective heuristics that reduce the number of variables in the MIP model, thus improving its efficiency for large-scale MCPP instances. We show that both heuristics result in reduced-size MIP models that remain complete (i.e., guaranteed to find a solution if one exists) for all MMRTC instances. Additionally, we explore the use of model optimization warm-startup to further improve the efficiency of both the original MIP model and the reduced-size MIP models. We validate the effectiveness of our MIP-based MCPP planner through experiments that compare it with two state-of-the-art MCPP planners on various instances, demonstrating a reduction in the coverage time by an average of 27.65% and 23.24% over them, respectively.

Given a traversal algorithm, cover time is the expected number of steps needed to visit all nodes in a given graph. A smaller cover time means a higher exploration efficiency of traversal algorithm. Although random walk algorithms have been studied extensively in the existing literature, there has been no cover time result for any non-Markovian method. In this work, we stand on a theoretical perspective and show that the negative feedback strategy (a count-based exploration method) is better than the naive random walk search. In particular, the former strategy can locally improve the search efficiency for an arbitrary graph. It also achieves smaller cover times for special but important graphs, including clique graphs, tree graphs, etc. Moreover, we make connections between our results and reinforcement learning literature to give new insights on why classical UCB and MCTS algorithms are so useful. Various numerical results corroborate our theoretical findings.

Retrosynthesis consists of breaking down a chemical compound recursively step-by-step into molecular precursors until a set of commercially available molecules is found with the goal to provide a synthesis route. Its two primary research directions, single-step retrosynthesis prediction, which models the chemical reaction logic, and multi-step synthesis planning, which tries to find the correct sequence of reactions, are inherently intertwined. Still, this connection is not reflected in contemporary research. In this work, we combine these two major research directions by applying multiple single-step retrosynthesis models within multi-step synthesis planning and analyzing their impact using public and proprietary reaction data. We find a disconnection between high single-step performance and potential route-finding success, suggesting that single-step models must be evaluated within synthesis planning in the future. Furthermore, we show that the commonly used single-step retrosynthesis benchmark dataset USPTO-50k is insufficient as this evaluation task does not represent model performance and scalability on larger and more diverse datasets. For multi-step synthesis planning, we show that the choice of the single-step model can improve the overall success rate of synthesis planning by up to +28% compared to the commonly used baseline model. Finally, we show that each single-step model finds unique synthesis routes, and differs in aspects such as route-finding success, the number of found synthesis routes, and chemical validity, making the combination of single-step retrosynthesis prediction and multi-step synthesis planning a crucial aspect when developing future methods.

Anomaly detection (AD) in images, identifying significant deviations from normality, is a critical issue in computer vision. This paper introduces a novel approach to dimensionality reduction for AD using pre-trained convolutional neural network (CNN) that incorporate EfficientNet models. We investigate the importance of component selection and propose two types of tree search approaches, both employing a greedy strategy, for optimal eigencomponent selection. Our study conducts three main experiments to evaluate the effectiveness of our approach. The first experiment explores the influence of test set performance on component choice, the second experiment examines the performance when we train on one anomaly type and evaluate on all other types, and the third experiment investigates the impact of using a minimum number of images for training and selecting them based on anomaly types. Our approach aims to find the optimal subset of components that deliver the highest performance score, instead of focusing solely on the proportion of variance explained by each component and also understand the components behaviour in different settings. Our results indicate that the proposed method surpasses both Principal Component Analysis (PCA) and Negated Principal Component Analysis (NPCA) in terms of detection accuracy, even when using fewer components. Thus, our approach provides a promising alternative to conventional dimensionality reduction techniques in AD, and holds potential to enhance the efficiency and effectiveness of AD systems.

Intelligent autonomous path planning is crucial to improve the exploration efficiency of planetary rovers. In this paper, we propose a learning-based method to quickly search for optimal paths in an elevation map, which is called NNPP. The NNPP model learns semantic information about start and goal locations, as well as map representations, from numerous pre-annotated optimal path demonstrations, and produces a probabilistic distribution over each pixel representing the likelihood of it belonging to an optimal path on the map. More specifically, the paper computes the traversal cost for each grid cell from the slope, roughness and elevation difference obtained from the DEM. Subsequently, the start and goal locations are encoded using a Gaussian distribution and different location encoding parameters are analyzed for their effect on model performance. After training, the NNPP model is able to perform path planning on novel maps. Experiments show that the guidance field generated by the NNPP model can significantly reduce the search time for optimal paths under the same hardware conditions, and the advantage of NNPP increases with the scale of the map.