Scheduling agents can use the Multiagent Simple Temporal Problem (MaSTP) formulation to efficiently find and represent the complete set of alternative consistent joint schedules in a distributed and privacy-maintaining manner. However, continually revising this set of consistent joint schedules as new constraints arise may not be a viable option in environments where communication is uncertain, costly, or otherwise problematic. As an alternative, agents can find and represent a temporal decoupling in terms of locally independent sets of consistent schedules that, when combined, form a set of consistent joint schedules. Unlike current algorithms for calculating a temporal decoupling that require centralization of the problem representation, in this paper we present a new, provably correct, distributed algorithm for calculating a temporal decoupling. We prove that this algorithm has the same theoretical computational complexity as current state-of-the-art MaSTP solution algorithms, and empirically demonstrate that it is more efficient in practice. We also introduce and perform an empirical cost/benefit analysis of new techniques and heuristics for selecting a maximally flexible temporal decoupling.

This research focuses on building foundational algorithms for scheduling agents that assist people in managing their activities in environments where tempo and complex activity interdependencies outstrip people’s cognitive capacity. We address the critical challenge of reasoning over individuals ’ interacting schedules to efficiently answer queries about how to meet scheduling goals while respecting individual privacy and autonomy to the extent possible. We formally define the Multiagent Simple Temporal Problem for naturally capturing and reasoning over the distributed but interconnected scheduling problems of multiple individuals. Our hypothesis is that combining bottom-up and top-down approaches will lead to effective solution techniques. In our bottom-up phase, an agent externalizes constraints that compactly summarize how its local subproblem affects other agents ’ subproblems, whereas in our top-down phase an agent proactively constructs and internalizes new local constraints that decouple its subproblem from others’. We confirm this hypothesis by devising distributed algorithms that calculate summaries of the joint solution space for multiagent scheduling problems, without centralizing or otherwise redistributing the problems. The distributed algorithms permit concurrent execution to achieve significant speedup over the current art and also increase the level of privacy and independence in individual agent reasoning. These algorithms are most advantageous for problems where interactions between the agents are sparse compared to the complexity of agents ’ individual problems. 1.

The Multiagent Disjunctive Temporal Problem (MaDTP) is a general constraint-based formulation for scheduling problems that involve interdependent agents. Decoupling agents ’ interdependent scheduling problems, so that each agent can manage its schedule independently, requires agents to adopt additional local constraints that effec-tively subsume their interdependencies. In this paper, we present the first algorithm for decoupling MaDTPs. Our distributed algorithm is provably sound and com-plete. Our experiments show that the relative efficiency of using temporal decoupling to find solution spaces for MaDTPs, compared to algorithms that find complete solution spaces, improves with the interconnectedness be-tween agents schedules, leading to orders of magnitude relative speeedup. However, decoupling by its nature restricts agents ’ scheduling flexibility; we define novel flexibility metrics for MaDTPs, and show empirically how the flexibility sacrificed depends on the degree of coupling between agents ’ schedules.

Flexibility in agent scheduling increases the resilience of temporal plans in the face of new constraints. How-ever, current metrics of flexibility ignore domain knowl-edge about how such constraints might arise in practice, e.g., due to the uncertain duration of a robot’s transition time from one location to another. Probabilistic tempo-ral planning accounts for actions whose uncertain dura-tions can be modeled with probability density functions. We introduce a new metric called robustness that mea-sures the likelihood of success for probabilistic tempo-ral plans. We show empirically that in multi-robot plan-ning, robustness may be a better metric for assessing the quality of temporal plans than flexibility, thus reframing many popular scheduling optimization problems.

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Abstract The Multiagent Disjunctive Temporal Problem (MaDTP) is a general constraint-based formulation for scheduling problems that involve interdependent agents. Decoupling agents' interdependent scheduling problems, so that each agent can manage its schedule independently, requires agents to adopt additional local constraints that effectively subsume their interdependencies. In this paper, we present the first algorithm for decoupling MaDTPs. Our distributed algorithm is provably sound and complete. Our experiments show that the relative efficiency of using temporal decoupling to find solution spaces for MaDTPs, compared to algorithms that find complete solution spaces, improves with the interconnectedness between agents schedules, leading to orders of magnitude relative speeedup. However, decoupling by its nature restricts agents' scheduling flexibility; we define novel flexibility metrics for MaDTPs, and show empirically how the flexibility sacrificed depends on the degree of coupling between agents' schedules.

In this paper we concentrate on finding a suitable metric to determine the flexibility of a Simple Temporal Problem (STP). After reviewing some flexibility metrics that have been proposed, we conclude that these metrics fail to capture the correlation between events specified in the STP, resulting in an overestimation of the available flexibility in the system. We propose to use an intuitively more acceptable flexibility metric based upon uncorrelated time-intervals for the allowed starting times of events in an STP. This metric is shown to be computable in low-polynomial time. As a byproduct of the flexibility computation, we get a decomposition of the STN almost for free: for every possible k-partitioning of the event space, a decomposition can be computed in O(k)-time. Even more importantly, we show that contrary to popular belief, such a decomposition does not affect the flexibility of the original STP. 1

Consider a scheduling scenario in a furniture factory where two robotic agents work together to apply finish to custom table pieces. Robot A is set up to paint, while Robot B must apply varnish. Both actions take an uncertain amount of time

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To all of my parents and mentors, thank you for everything. ii ACKNOWLEDGEMENTS Thank you... To my advisor Professor Anouck Girard, thank you for always making sure I didn’t go hungry. Thank you for excusing and supporting my many interests. It has been my pleasure to work with you and grow as your student. Professor Pierre Kabamba, thank you for your clarity in aspects from moral character to technical things and stuff. Thank you for imparting on me the importance of seeking the same for myself. Mariam Faied, thank you for having the patience to support so many long technical discussions, for reading all of my writing, and trying my cooking. Professor Edmund Durfee, thank you for taking the time to offer your perspective that has helped me to dig deeper and improve my own knowledge. Your work in distributed systems has helped spark my own related interest. Professor Alec Gallimore, thank you for giving me the idea to apply to the University of Michigan, for helping me my first