Simple temporal problems represent a powerful class of models capable of describing the temporal relations between events that arise in many real-world applications such as logistics, robot planning and management systems. The classic simple temporal problem permits each event to have only a single release and due date. In this paper, we focus on the case where events may have an arbitrarily large number of release and due dates. This type of problem, however, has been referred to by various names. In order to simplify and standardize nomenclatures, we introduce the name Simple Disjunctive Temporal Problem. We provide three mathematical models to describe this problem using constraint programming and linear programming. To efficiently solve simple disjunctive temporal problems, we design two new algorithms inspired by previous research, both of which exploit the problem's structure to significantly reduce their space complexity. Additionally, we implement algorithms from the literature and provide the first in-depth empirical study comparing methods to solve simple disjunctive temporal problems across a wide range of experiments. Our analysis and conclusions offer guidance for future researchers and practitioners when tackling similar temporal constraint problems in new applications. All results, source code and instances are made publicly available to further assist future research.

The convex hull cheapest insertion heuristic is known to generate good solutions to the Euclidean Traveling Salesperson Problem. This paper presents an adaptation of this heuristic to the non-Euclidean version of the problem and further extends it to the problem with precedence constraints, also known as the Sequential Ordering Problem. To test the proposed algorithm, the well-known TSPLIB benchmark data-set is modified in a replicable manner to create non-Euclidean instances and precedence constraints. The proposed algorithm is shown to outperform the commonly used Nearest Neighbor algorithm in 97% of the cases that do not have precedence constraints. When precedence constraints exist such that the child nodes are centrally located, the algorithm again outperforms the Nearest Neighbor algorithm in 98% of the studied instances. Considering all spatial layouts of precedence constraints, the algorithm outperforms the Nearest Neighbor heuristic 68% of the time.

We propose online nonstochastic control algorithms that achieve both sublinear regret and sublinear adversarial constraint violation while keeping static constraint violation minimal against the optimal constrained linear control policy in hindsight. To establish the results, we introduce an online convex optimization with memory framework under adversarial and static constraints, which serves as a subroutine for the constrained online nonstochastic control algorithms. This subroutine also achieves the state-of-the-art regret and constraint violation bounds for constrained online convex optimization problems, which is of independent interest. Our experiments demonstrate the proposed control algorithms are adaptive to adversarial constraints and achieve smaller cumulative costs and violations. Moreover, our algorithms are less conservative and achieve significantly smaller cumulative costs than the state-of-the-art algorithm.

Autonomous exploration is one of the important parts to achieve the fast autonomous mapping and target search. However, most of the existing methods are facing low-efficiency problems caused by low-quality trajectory or back-and-forth maneuvers. To improve the exploration efficiency in unknown environments, a fast autonomous exploration planner (FAEP) is proposed in this paper. Different from existing methods, we firstly design a novel frontiers exploration sequence generation method to obtain a more reasonable exploration path, which considers not only the flight-level but frontier-level factors in the asymmetric traveling salesman problem (ATSP). Then, according to the exploration sequence and the distribution of frontiers, an adaptive yaw planning method is proposed to cover more frontiers by yaw change during an exploration journey. In addition, to increase the speed and fluency of flight, a dynamic replanning strategy is also adopted. We present sufficient comparison and evaluation experiments in simulation environments. Experimental results show the proposed exploration planner has better performance in terms of flight time and flight distance compared to typical and state-of-the-art methods. Moreover, the effectiveness of the proposed method is further evaluated in real-world environments.

This letter concerns optimal power transmission line inspection formulated as a proposed generalization of the traveling salesman problem for a multi-route one-depot scenario. The problem is formulated for an inspection vehicle with a limited travel budget. Therefore, the solution can be composed of multiple runs to provide full coverage of the given power lines. Besides, the solution indicates how many vehicles can perform the inspection in a single run. The optimal solution of the problem is solved by the proposed Integer Linear Programming (ILP) formulation, which is, however, very computationally demanding. Therefore, the computational requirements are addressed by the combinatorial metaheuristic. The employed greedy randomized adaptive search procedure is significantly less demanding while providing competitive solutions and scales better with the problem size than the ILP-based approach. The proposed formulation and algorithms are demonstrated in a real-world scenario to inspect power line segments at the electrical substation.

An important variant of the classic Traveling Salesman Problem (TSP) is the Dynamic TSP, in which a system with dynamic constraints is tasked with visiting a set of n target locations (in any order) in the shortest amount of time. Such tasks arise naturally in many robotic motion planning problems, particularly in exploration, surveillance and reconnaissance, and classical TSP algorithms on graphs are typically inapplicable in this setting. An important question about such problems is: if the target points are random, what is the length of the tour (either in expectation or as a concentration bound) as n grows? This problem is the Dynamic Stochastic TSP (DSTSP), and has been studied both for specific important vehicle models and for general dynamic systems; however, in general only the order of growth is known. In this work, we explore the connection between the distribution from which the targets are drawn and the dynamics of the system, yielding a more precise lower bound on tour length as well as a matching upper bound for the case of symmetric (or driftless) systems. We then extend the symmetric dynamics results to the case when the points are selected by a (non-random) adversary whose goal is to maximize the length, thus showing worst-case bounds on the tour length.

We consider non-clairvoyant scheduling with online precedence constraints, where an algorithm is oblivious to any job dependencies and learns about a job only if all of its predecessors have been completed. Given strong impossibility results in classical competitive analysis, we investigate the problem in a learning-augmented setting, where an algorithm has access to predictions without any quality guarantee. We discuss different prediction models: novel problem-specific models as well as general ones, which have been proposed in previous works. We present lower bounds and algorithmic upper bounds for different precedence topologies, and thereby give a structured overview on which and how additional (possibly erroneous) information helps for designing better algorithms. Along the way, we also improve bounds on traditional competitive ratios for existing algorithms.

Online resource allocation is a prominent paradigm for sequential decision making during a finite horizon subject to the resource constraints, increasingly attracting the wide attention of researchers and practitioners in theoretical computer science (Mehta et al., 2007; Devanur and Jain, 2012; Devanur et al., 2019), operations research (Agrawal et al., 2014; Li and Ye, 2021) and machine learning communities (Balseiro et al., 2020; Li et al., 2020). In these settings, the requests arrive online and we need to serve each request via one of the available channels, which consumes a certain amount of resources and generates a corresponding service charge. The objective of the decision maker is to maximize the cumulative revenue subject to the resource capacity constraints. Such problem frequently appears in many applications including online advertising (Mehta et al., 2007; Buchbinder et al., 2007), online combinatorial auctions (Chawla et al., 2010), online linear programming(Agrawal et al., 2014; Buchbinder and Naor, 2009), online routing(Buchbinder and Naor, 2006), online multi-leg flight seats and hotel rooms allocation (Talluri et al., 2004), etc. The aforementioned online resource allocation framework only considers the capacity (upper bound) constraints for resources.

The last decade witnessed an ever-increasing stream of successes in Machine Learning (ML). These successes offer clear evidence that ML is bound to become pervasive in a wide range of practical uses, including many that directly affect humans. Unfortunately, the operation of the most successful ML models is incomprehensible for human decision makers. As a result, the use of ML models, especially in high-risk and safety-critical settings is not without concern. In recent years, there have been efforts on devising approaches for explaining ML models. Most of these efforts have focused on so-called model-agnostic approaches. However, all model-agnostic and related approaches offer no guarantees of rigor, hence being referred to as non-formal. For example, such non-formal explanations can be consistent with different predictions, which renders them useless in practice. This paper overviews the ongoing research efforts on computing rigorous model-based explanations of ML models; these being referred to as formal explanations. These efforts encompass a variety of topics, that include the actual definitions of explanations, the characterization of the complexity of computing explanations, the currently best logical encodings for reasoning about different ML models, and also how to make explanations interpretable for human decision makers, among others.

Offline safe RL is of great practical relevance for deploying agents in real-world applications. However, acquiring constraint-satisfying policies from the fixed dataset is non-trivial for conventional approaches. Even worse, the learned constraints are stationary and may become invalid when the online safety requirement changes. In this paper, we present a novel offline safe RL approach referred to as SaFormer, which tackles the above issues via conditional sequence modeling. In contrast to existing sequence models, we propose cost-related tokens to restrict the action space and a posterior safety verification to enforce the constraint explicitly. Specifically, SaFormer performs a two-stage auto-regression conditioned by the maximum remaining cost to generate feasible candidates. It then filters out unsafe attempts and executes the optimal action with the highest expected return. Extensive experiments demonstrate the efficacy of SaFormer featuring (1) competitive returns with tightened constraint satisfaction; (2) adaptability to the in-range cost values of the offline data without retraining; (3) generalizability for constraints beyond the current dataset.