Simple Temporal Network With Uncertainty Research Articles

On Expected Value Strong Controllability

The Probabilistic Simple Temporal Network with Uncertainty (PSTNU) is a variant of the Simple Temporal Network with Uncertainty (STNU) in which known probability distributions govern the timing of uncontrollable timepoints. Previous approaches to solving PSTNUs focus mininizing risk, that is, the probability of violating constraints. These approaches are not applicable in over-constrained controllability problems, when it is certain that all constraints can’t be satisfied. We introduce the Weighted Probabilistic Simple Temporal Network with Uncertainty (WPSTNU), which extends the PSTNU by attaching a fixed value to the satisfaction of temporal constraints, and allows the schedule to violate some constraints in order to maximize the expected value of satisfying others. We study the problem of Expected Value Strong Controllability (EvSC) of WPSTNUs, which seeks a fixed-time schedule maximizing the expected value of satisfied constraints. We solve the EvSC problem using a mixed integer linear program (MILP) that bounds below the probability of satisfying constraints involving uncontrollable timepoints. While solving MILPs generally takes exponential time, we demonstrate our formulation’s effective performance using scheduling problems derived from the HEATlab and MIT ROVERS data sets. We then show how to use this MILP to reschedule during execution, after time has passed and uncertainty is reduced. We describe different fixed-period rescheduling approaches, including time-based and event-based, and report on the most successful strategies compared to the expected value of the fixed schedule produced by the MILP. All of our methods are evaluated on problems with both symmetric and asymmetric (skewed) probability distributions. We show that periodically rescheduling improves the expected value when compared to the fixed schedule, and describe how the benchmark and skewness impact the schedule value improvement. The resulting analysis shows that solving EvSC problems on WPSTNUs is a viable alternative to solving over-constrained controllability problems.

Dynamic Controllability of Temporal Plans in Uncertain and Partially Observable Environments

The formalism of Simple Temporal Networks (STNs) provides methods for evaluating the feasibility of temporal plans. The basic formalism deals with the consistency of quantitative temporal requirements on scheduled events. This implicitly assumes a single agent has full control over the timing of events. The extension of Simple Temporal Networks with Uncertainty (STNU) introduces uncertainty into the timing of some events. Two main approaches to the feasibility of STNUs involve (1) where a single schedule works irrespective of the duration outcomes, called Strong Controllability, and (2) whether a strategy exists to schedule future events based on the outcomes of past events, called Dynamic Controllability. Case (1) essentially assumes the timing of uncertain events cannot be observed by the agent while case (2) assumes full observability. The formalism of Partially Observable Simple Temporal Networks with Uncertainty (POSTNU) provides an intermediate stance between these two extremes, where a known subset of the uncertain events can be observed when they occur. A sound and complete polynomial algorithm to determining the Dynamic Controllability of POSTNUs has not previously been known; we present one in this paper. This answers an open problem that has been posed in the literature. The approach we take factors the problem into Strong Controllability micro-problems in an overall Dynamic Controllability macro-problem framework. It generalizes the notion of labeled distance graph from STNUs. The generalized labels are expressed as max/min expressions involving the observables. The paper introduces sound generalized reduction rules that act on the generalized labels. These incorporate tightenings based on observability that preserve dynamic viable strategies. It is shown that if the generalized reduction rules reach quiescence without exposing an inconsistency, then the POSTNU is Dynamically Controllable (DC). The paper also presents algorithms that apply the reduction rules in an organized way and reach quiescence in a polynomial number of steps if the POSTNU is Dynamically Controllable. Remarkably, the generalized perspective leads to a simpler and more uniform framework that applies also to the STNU special case. It helps illuminate the previous methods inasmuch as the max/min label representation is more semantically clear than the ad-hoc upper/lower case labels previously used.

A faster algorithm for converting simple temporal networks with uncertainty into dispatchable form

A Simple Temporal Network with Uncertainty (STNU) is a data structure for reasoning about time constraints on actions that may have uncertain durations. An STNU is dispatchable if it can be executed in real-time with minimal computation 1) satisfying all constraints no matter how the uncertain durations play out and 2) retaining maximum flexibility. The fastest known algorithm for converting STNUs into dispatchable form runs in O(n3) time, where n is the number of timepoints. This paper presents a faster algorithm that runs in O(mn+kn2+n2log⁡n) time, where m is the number of edges and k is the number of uncertain durations. This performance is particularly meaningful in fields like Business Process Management, where sparse STNUs can represent temporal processes or plans. For sparse STNUs, our algorithm generates dispatchable forms in time O(n2log⁡n), a significant improvement over the O(n3)-time previous fastest algorithm.

Speeding Up the RUL¯ Dynamic-Controllability-Checking Algorithm for Simple Temporal Networks with Uncertainty

A Simple Temporal Network with Uncertainty (STNU) includes real-valued variables, called time-points; binary difference constraints on those time-points; and contingent links that represent actions with uncertain durations. STNUs have been used for robot control, web-service composition, and business processes. The most important property of an STNU is called dynamic controllability (DC); and algorithms for checking this property are called DC-checking algorithms. The DC-checking algorithm for STNUs with the best worst-case time-complexity is the RUL¯ algorithm due to Cairo, Hunsberger and Rizzi. Its complexity is O(mn + k²n + kn log n), where n is the number of time-points, m is the number of constraints, and k is the number of contingent links. It is expected that this worst-case complexity cannot be improved upon. However, this paper provides a new algorithm, called RUL2021, that improves its performance in practice by an order of magnitude, as demonstrated by a thorough empirical evaluation.

Quantifying Degrees of Controllability in Temporal Networks with Uncertainty

Controllability for Simple Temporal Networks with Uncertainty (STNUs) has thus far been limited to three levels: strong, dynamic, and weak. Because of this, there is currently no systematic way for an agent to assess just how far from being controllable an uncontrollable STNU is. We use a new geometric interpretation of STNUs to introduce the degrees of strong and dynamic controllability – continuous metrics that measure how far a network is from being controllable. We utilize these metrics to approximate the probabilities that an STNU can be dispatched successfully offline and online respectively. We introduce new methods for predicting the degrees of strong and dynamic controllability for uncontrollable networks. In addition, we show empirically that both metrics are good predictors of the actual dispatch success rate.

Quantifying controllability in temporal networks with uncertainty

Controllability for Simple Temporal Networks with Uncertainty (STNUs) has thus far been limited to three levels: strong, dynamic, and weak. Because of this, there is currently no systematic way for an agent to assess just how far from being controllable an uncontrollable STNU is. We provide new insights inspired by a geometric interpretation of STNUs to introduce the degrees of strong and dynamic controllability — continuous metrics that measure how far a network is from being controllable. We utilize these metrics to approximate the probabilities that an STNU can be dispatched successfully offline and online respectively. We introduce new methods for predicting the degrees of strong and dynamic controllability for uncontrollable networks. We further generalize these metrics by defining likelihood of controllability, a controllability measure that applies to Probabilistic Simple Temporal Networks (PSTNs). Finally, we empirically demonstrate that these metrics are good predictors of actual dispatch success rate for STNUs and PSTNs.

Dynamic controllability of simple temporal networks with uncertainty: Simple rules and fast real-time execution

Simple Temporal Networks (STNs) are a well-studied model for representing temporal constraints. They comprise a set of time-points (real-valued variables representing execution times) and binary difference constraints among them. Simple Temporal Networks with Uncertainty (STNUs) extend STNs in that some time-points (called contingent) are treated as exogenous variables, whose execution times, bound to fall within a given interval from the corresponding activation time-points (as specified by a “contingent link”), get revealed only during real-time execution. An STNU is dynamically controllable (DC) if there exists a strategy to execute its time-points satisfying all the constraints, regardless of the execution times of contingent time-points revealed during execution.In this work we present a new system of constraint propagation rules for STNUs, which is sound-and-complete for DC checking. Our system comprises just three rules which, differently from the ones proposed in all previous works, only generate unconditioned constraints. In particular, after applying any of our rules, the network remains an STNU in all respects. Moreover, our completeness proof is short and non-algorithmic, based on the explicit construction of a valid execution strategy. This is a substantial simplification of the theory which underlies all the previous efficient algorithms for DC-checking.Our analysis also shows: (1) the existence of late execution strategies for STNUs, (2) the equivalence of the notion of DC among several variants of the semantics of STNUs, (3) the existence of a fast algorithm for real-time execution of STNUs, which runs in O(KN) total time in a network with K≥1 contingent links and N≥K time points, considerably improving the previous O(N3)-time bound.

Efficient processing of simple temporal networks with uncertainty: algorithms for dynamic controllability verification

Temporal formalisms are essential for reasoning about actions that are carried out over time. The exact durations of such actions are generally hard to predict. In temporal planning, the resulting uncertainty is often worked around by only considering upper bounds on durations, with the assumption that when an action happens to be executed more quickly, the plan will still succeed. However, this assumption is often false: if we finish cooking too early, the dinner will be cold before everyone is ready to eat. Using simple temporal networks with uncertainty (STNU), a planner can correctly take both lower and upper duration bounds into account. It must then verify that the plans it generates are executable regardless of the actual outcomes of the uncertain durations. This is captured by the property of dynamic controllability (DC), which should be verified incrementally during plan generation. Recently a new incremental algorithm for verifying dynamic controllability was proposed: EfficientIDC, which can verify if an STNU that is DC remains DC after the addition or tightening of a constraint (corresponding to a new action being added to a plan). The algorithm was shown to have a worst case complexity of $$O(n^4)$$O(n4) for each addition or tightening. This can be amortized over the construction of a whole STNU for an amortized complexity in $$O(n^3)$$O(n3). In this paper we improve the EfficientIDC algorithm in a way that prevents it from having to reprocess nodes. This improvement leads to a lower worst case complexity in $$O(n^3)$$O(n3).

Efficient execution of dynamically controllable simple temporal networks with uncertainty

A simple temporal network with uncertainty (STNU) is a data structure for representing and reasoning about temporal constraints where the durations of certain temporal intervals--the contingent links--are only discovered during execution. The most important property of an STNU is whether it is dynamically controllable (DC)--that is, whether there exists a strategy for executing its time-points that will guarantee that all of its constraints will be satisfied no matter how the durations of the contingent links turn out. The literature on STNUs includes a variety of DC-checking algorithms and execution algorithms. The fastest DC-checking algorithm reported so far is the $$O(N^3)$$O(N3)-time algorithm due to Morris (Integration of AI and OR techniques in constraint programming--11th international conference, CPAIOR 2014, volume 8451 of Lecture Notes in Computer Science. Springer, Berlin, pp 464---479, 2014). The fastest execution algorithm for dynamically controllable STNUs is the $$O(N^3)$$O(N3)-time algorithm due to Hunsberger (Proceedings of the 20th international symposium on temporal representation and reasoning (TIME-2013). IEEE Computer Society, Washington, 2013). This paper begins by providing the first comprehensive, rigorous, and yet streamlined treatment of the theoretical foundations of STNUs, including execution semantics, dynamic controllability, and a set of results that have been collected into what has recently been called the fundamental theorem of STNUs. The paper carefully argues from basic definitions to proofs of the major theorems on which all of the important algorithmic work on STNUs depends. Although many parts of this presentation have appeared in various forms, in various papers, the scattered nature of the STNU literature has allowed too many holes in the theory to persist, and has relied all too often on proof sketches that leave important details unexamined. The presentation combines results from many sources, while also introducing novel approaches and proofs. The paper concludes by presenting a modified version of a recent algorithm for managing the execution of dynamically controllable STNUs, the fastest reported so far in the literature. The modified version organizes its computations more efficiently and corrects an oversight in the original algorithm.

Optimising Bounds in Simple Temporal Networks with Uncertainty under Dynamic Controllability Constraints

Dynamically controllable simple temporal networks with uncertainty (STNU) are widely used to represent temporal plans or schedules with uncertainty and execution flexibility. While the problem of testing an STNU for dynamic controllability is well studied, many use cases — for example, problem relaxation or schedule robustness analysis — require optimising a function over STNU time bounds subject to the constraint that the network is dynamically controllable. We present a disjunctive linear constraint model of dynamic controllability, show how it can be used to formulate a range of applications, and compare a mixed-integer, a non-linear programming, and a conflict-directed search solver on the resulting optimisation problems. Our model also provides the first solution to the problem of optimisation over a probabilistic STN subject to dynamic controllability and chance constraints.

Using Timed Game Automata to Synthesize Execution Strategies for Simple Temporal Networks with Uncertainty

A Simple Temporal Network with Uncertainty (STNU) is a structure for representing and reasoning about temporal constraints in domains where some temporal durations are not controlled by the executor. The most important property of an STNU is whether it is dynamically controllable (DC) whether there exists a strategy for executing the controllable time-points that guarantees that all constraints will be satisfied no matter how the uncontrollable durations turn out. This paper provides a novel mapping from STNUs to Timed Game Automata (TGAs) that: (1) explicates the deep theoretical relationships between STNUs and TGAs; and (2) enables the memoryless strategies generated from the TGA to be transformed into equivalent STNU execution strategies that reduce the real-time computational burden for the executor. The paper formally proves that the STNU-to-TGA encoding properly captures the execution semantics of STNUs.

Flexibility and decoupling in Simple Temporal Networks

We propose a new metric to determine the flexibility of a Simple Temporal Network (STN). After reviewing some existing flexibility metrics, we conclude that these metrics fail to capture the dependencies between events specified in the STN. As a consequence, these metrics will usually overestimate the available flexibility in such a system. We propose to use an intuitively more acceptable flexibility metric. This metric is based upon the notion of an interval schedule for an STN. Such an interval schedule specifies an interval for every event in the STN in such a way that, for every event, we are free to choose a starting time within its interval independently from the choice made for other events. We show that an interval schedule that maximizes our flexibility metric is computable in low-order polynomial time. As byproducts of this flexibility metric, we discuss simple solutions to problems in STNs with uncertainty (STNUs) and temporal decoupling in STNs. With respect to the latter we show that after computing our flexibility metric, we get a decomposition of the STN almost for free. Even more importantly, we show that contrary to popular belief, such a decomposition does not affect the flexibility of the original STN.

Incremental Dynamic Controllability Revisited

Simple Temporal Networks with Uncertainty (STNUs) allow the representation of temporal problems where some durations are determined by nature, as is often the case for actions in planning. As such networks are generated it is essential to verify that they are dynamically controllable -- executable regardless of the outcomes of uncontrollable durations -- and to convert them to a dispatchable form. The previously published FastIDC algorithm achieves this incrementally and can therefore be used efficiently during plan construction. In this paper we show that FastIDC is not sound when new constraints are added, sometimes labeling networks as dynamically controllable when they are not. We analyze the algorithm, pinpoint the cause, and show how the algorithm can be modified to correctly detect uncontrollable networks.

OPTIMIZATION OF BOUNDS IN TEMPORAL FLEXIBLE PLANS WITH DYNAMIC CONTROLLABILITY

A temporal flexible planning problem that involves contingent and requirement events can be formulated as a simple temporal network with uncertainty (STNU). An STNU is controllable when there is a strategy for executing the requirement events (or actions) in such a way that all the conditions involving contingent events can be satisfied in all situations. The most interesting and useful controllability property is dynamic controllability in which the remaining actions in an STNU can always be scheduled under all possible feasible durations of future contingent events when all the past contingent events are known. In this paper, we propose and study a novel problem of assigning bounds on the duration of each requirement link in order for the resulting STNU to be dynamically controllable and to minimize the total cost over the allowed durations of all requirement links. We first prove the NP hardness of the problem with a linear cost function. We then formulate the dynamic controllability of an STNU as the constraints in a nonlinear optimization problem. Finally, we present methods for reducing the number of constraints in order to make the problem tractable and to demonstrate the computational performance of our methods.