Translation-based approaches for solving disjunctive temporal problems with preferences

Disjunctive Temporal Problems (DTPs) with Preferences (DTPPs) extend DTPs with piece-wise constant preference functions associated to each constraint of the form l 64 x 12 y 64 u, where x, y are (real or integer) variables, and l, u are numeric constants. The goal is to find an assignment to the variables of the problem that maximizes the sum of the preference values of satisfied DTP constraints, where such values are obtained by aggregating the preference functions of the satisfied constraints in it under a \u201cmax\u201d semantic. The state-of-the-art approach in the field, implemented in the native DTPP solver Maxilitis, extends the approach of the native DTP solver Epilitis. In this paper we present alternative approaches that translate DTPPs to Maximum Satisfiability of a set of Boolean combination of constraints of the form l ./ x 12 y ./ u, ./ 08 {<, 64}, that extend previous work dealing with constant preference functions only. We prove correctness and completeness of the approaches. Results obtained with the Satisfiability Modulo Theories (SMT) solvers Yices and MathSAT on randomly generated DTPPs and DTPPs built from real-world benchmarks, show that one of our translation is competitive to, and can be faster than, Maxilitis

Optimising Flexibility of Temporal Problems with Uncertainty

Temporal networks have been applied in many autonomous systems. In real situations, we cannot ignore the uncertain factors when using those autonomous systems. Achieving robust schedules and temporal plans by optimising flexibility to tackle the uncertainty is the motivation of the thesis. This thesis focuses on the optimisation problems of temporal networks with uncertainty and controllable options in the field of Artificial Intelligence Planning and Scheduling. The goal of this thesis is to construct flexibility and robustness metrics for temporal networks under the constraints of different levels of controllability. Furthermore, optimising flexibility for temporal plans and schedules to achieve robust solutions with flexible executions. When solving temporal problems with uncertainty, postponing decisions according to the observations of uncertain events enables flexible strategies as the solutions instead of fixed schedules or plans. Among the three levels of controllability of the Simple Temporal Problem with Uncertainty (STPU), a problem is dynamically controllable if there is a successful dynamic strategy such that every decision in it is made according to the observations of past events. In the thesis, we make the following contributions. (1) We introduce an optimisation model for STPU based on the existing dynamic controllability checking algorithms. Some flexibility and robustness measures are introduced based on the model. (2) We extend the definition and verification algorithm of dynamic controllability to temporal problems with controllable discrete variables and uncertainty, which is called Controllable Conditional Temporal Problems with Uncertainty (CCTPU). An entirely dynamically controllable strategy of CCTPU consists of both temporal scheduling and variable assignments being dynamically decided, which maximize the flexibility of the execution. (3) We introduce optimisation models of CCTPU under fully dynamic controllability. The optimisation models aim to answer the questions how flexible, robust or controllable a schedule or temporal plan is. The experiments show that making decisions dynamically can achieve better objective values than doing statically. The thesis also contributes to the field of AI planning and scheduling by introducing robustness metrics of temporal networks, proposing an envelope-based algorithm that can check dynamic controllability of temporal networks with uncertainty and controllable discrete decisions, evaluating improvements from making decisions strongly controllable to temporally dynamically controllable and fully dynamically controllable and comparing the runtime of different implementations to present the scalability of dynamically controllable strategies

Chance-Constrained Probabilistic Simple Temporal Problems

Scheduling under uncertainty is essential to many autonomous systems and logistics tasks. Probabilistic methods for solving temporal problems exist which quantify and attempt to minimize the probability of schedule failure. These methods are overly conservative, resulting in a loss in schedule utility. Chance constrained formalism address over-conservatism by imposing bounds on risk, while maximizing utility subject to these risk bounds. In this paper we present the probabilistic Simple Temporal Network (pSTN), a probabilistic formalism for representing temporal problems with bounded risk and a utility over event timing. We introduce a constrained optimisation algorithm for pSTNs that achieves compactness and efficiency through a problem encoding in terms of a parameterised STNU and its reformulation as a parameterised STN. We demonstrate through a car sharing application that our chance-constrained approach runs in the same time as the previous probabilistic approach, yields solutions with utility improvements of at least 5% over previous arts, while guaranteeing operation within the specified risk bound.National Science Foundation (U.S.) (Grant No. IIS-1017992

Uncertainty in Soft Temporal Constraint Problems:A General Framework and Controllability Algorithms forThe Fuzzy Case

In real-life temporal scenarios, uncertainty and preferences are often essential and coexisting aspects. We present a formalism where quantitative temporal constraints with both preferences and uncertainty can be defined. We show how three classical notions of controllability (that is, strong, weak, and dynamic), which have been developed for uncertain temporal problems, can be generalized to handle preferences as well. After defining this general framework, we focus on problems where preferences follow the fuzzy approach, and with properties that assure tractability. For such problems, we propose algorithms to check the presence of the controllability properties. In particular, we show that in such a setting dealing simultaneously with preferences and uncertainty does not increase the complexity of controllability testing. We also develop a dynamic execution algorithm, of polynomial complexity, that produces temporal plans under uncertainty that are optimal with respect to fuzzy preferences

On Expected Value Strong Controllability

The Probabilistic Simple Temporal Network (PSTN) generalizes Simple Temporal Networks with Uncertainty (STNUs) by introducing probability distributions over the timing of uncontrollable timepoints. PSTNs are controllable if there is a strategy to execute the controllable timepoints while bounding the risk of violating any constraint to a small value. If this risk bound can't be satisfied, PSTNs are not considered controllable. We introduce the Expected Value Probabilistic SimpleTemporal Network (EPSTN), which extends PSTNs by including a benefit to the satisfaction of temporal constraints. We study the problem of Expected Value Strong Controllability (EvSC) of EPSTNs, which seeks a schedule maximizing the expected value of satisfied constraints. We solve the EvSC problem by extending a previously developed linear program, combined with search over constraints to violate at execution time. We describe conditions under which the solution to this linear program is the maximum expected value schedule. We then show how to search for constraints to discard, using the linear program at the core of the search. While the general problem is shown to be exponential, we conclude by providing several methods to bound the complexity of search

Controlling Narrative Generation with Planning Trajectories: The Role of Constraints

Abstract. AI planning has featured in a number of Interactive Storytelling prototypes: since narratives can be naturally modelled as a sequence of actions it has been possible to exploit state of the art planners in the task of narrative generation. However the characteristics of a “good ” plan, such as optimality, aren’t necessarily the same as those of a “good ” narrative, where errors and convoluted sequences may offer more reader interest, so some narrative structuring is required. In our work we have looked at injecting narrative control into plan generation through the use of PDDL3.0 state trajectory constraints which enable us to express narrative control information within the planning representation. As part of this we have developed an approach to planning with such trajectory constraints. The approach decomposes the problem into a set of smaller subproblems using the temporal orderings described by the constraints and then solves these subproblems incrementally. In this paper we outline our method and present results that illustrate the potential of the approach.