Planning for hybrid systems is important for dealing with real-world applications, and PDDL+ supports this representation of domains with mixed discrete and continuous dynamics. In this paper we present a new approach for planning for hybrid systems, based on encoding the planning problem as a Satisfiability Modulo Theories (SMT) formula. This is the first SMT encoding that can handle the whole set of PDDL+ features (including processes and events), and is implemented in the planner SMTPlan. SMTPlan not only covers the full semantics of PDDL+, but can also deal with non-linear polynomial continuous change without discretization. This allows it to generate plans with non-linear dynamics that are correct-by-construction. The encoding is based on the notion of happenings, and can be applied on domains with nonlinear continuous change. We describe the encoding in detail and provide in-depth examples. We apply this encoding in an iterative deepening planning algorithm. Experimental results show that the approach dramatically outperforms existing work in finding plans for PDDL+ problems. We also present experiments which explore the performance of the proposed approach on temporal planning problems, showing that the scalability of the approach is limited by the size of the discrete search space. We further extend the encoding to include planning with control parameters. The extended encoding allows the definition of actions to include infinite domain parameters, called control parameters. We present experiments on a set of problems with control parameters to demonstrate the positive effect they provide to the approach of planning via SMT.
To achieve practical execution, planners must produce temporal plans with some degree of run-time adaptability. Such plans can be expressed as Simple Temporal Networks (STN), that constrain the timing of action activations, and implicitly represent the space of choices for the plan executor.A first problem is to verify that all the executor choices allowed by the STN plan will be successful, i.e. the plan is valid. An even more important problem is to assess the effect of discrepancies between the model used for planning and the execution environment.We propose an approach to compute the “robustness envelope” (i.e., alternative action durations or resource consumption rates) of a given STN plan, for which the plan remains valid. Plans can have boolean and numeric variables as well as discrete and continuous change. We leverage Satisfiability Modulo Theories (SMT) to make the approach formal and practical.
Scheduling is the task of assigning a set of scarce resources distributed over time to a set of agents, who typically have preferences over the assignments they would like to get. Due to the constrained nature of these problems, satisfying all agents' preferences often turns infeasible, which might lead to some agents not being happy with the resulting schedule. Providing explanations has been shown to increase satisfaction and trust in solutions produced by AI tools. However, explaining schedules poses some particular challenges such as problem interpretability (i.e., generating explanations from a huge and dense amount of information) and privacy preservation (i.e., generating explanations respecting the privacy of other agents involved). In this paper we introduce the EXPRES framework, that can explain why a given preference was unsatisfied in a given optimal schedule. The EXPRES framework consists of (i) an explanation generator, that, based on a Mixed-Integer Linear Programming model, finds the best set of reasons that can explain an unsatisfied preference; and (ii) an explanation parser, which translates the generated explanations into human interpretable ones, while preserving agents' privacy. Through simulations, we show that the explanation generator can efficiently scale to large instances. Finally, through a set of user studies within J.P. Morgan, we show that employees preferred the explanations generated by EXPRES over human-generated ones when considering workforce scheduling scenarios.
We consider a novel queuing problem where the decision-maker must choose to accept or reject randomly arriving tasks into a no buffer queue which are processed by N identical servers. Each task has a price, which is a positive real number, and a class. Each class of task has a different price distribution, service rate, and arrives according to an inhomogenous Poisson process. The objective is to decide which tasks to accept so that the total price of tasks processed is maximised over a finite horizon. We formulate the problem using a discrete time Markov Decision Process (MDP) with a hybrid state space. We show that the optimal value function has a specific structure, which enables us to solve the hybrid MDP exactly. Moreover, we rigorously prove that as the gap between successive decision epochs grows smaller, the discrete time solution approaches the optimal solution to the original continuous time problem. To improve the scalability of our approach to a greater number of servers and task classes, we present an approximation based on state abstraction. We validate our approach on synthetic data, as well as a real financial fraud data set, which is the motivating application for this work.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.