Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization

Structure and Problem Hardness: Goal Asymmetry and DPLL Proofs in<br> SAT-Based Planning

In Verification and in (optimal) AI Planning, a successful method is to formulate the application as boolean satisfiability (SAT), and solve it with state-of-the-art DPLL-based procedures. There is a lack of understanding of why this works so well. Focussing on the Planning context, we identify a form of problem structure concerned with the symmetrical or asymmetrical nature of the cost of achieving the individual planning goals. We quantify this sort of structure with a simple numeric parameter called AsymRatio, ranging between 0 and 1. We run experiments in 10 benchmark domains from the International Planning Competitions since 2000; we show that AsymRatio is a good indicator of SAT solver performance in 8 of these domains. We then examine carefully crafted synthetic planning domains that allow control of the amount of structure, and that are clean enough for a rigorous analysis of the combinatorial search space. The domains are parameterized by size, and by the amount of structure. The CNFs we examine are unsatisfiable, encoding one planning step less than the length of the optimal plan. We prove upper and lower bounds on the size of the best possible DPLL refutations, under different settings of the amount of structure, as a function of size. We also identify the best possible sets of branching variables (backdoors). With minimum AsymRatio, we prove exponential lower bounds, and identify minimal backdoors of size linear in the number of variables. With maximum AsymRatio, we identify logarithmic DPLL refutations (and backdoors), showing a doubly exponential gap between the two structural extreme cases. The reasons for this behavior -- the proof arguments -- illuminate the prototypical patterns of structure causing the empirical behavior observed in the competition benchmarks

CRIKEY! ― It's co-ordination in temporal planning

Temporal planning contains aspects of both planning and scheduling. Many temporal planners assume a loose coupling between these two sub-problems in the form of "blackbox" durative actions, where the state of the world is not known during the action's execution. This reduces the size of the search space and so simplifies the temporal planning problem, restricting what can be modelled. In particular, the simplification makes it impossible to model co-ordination, where actions must be executed concurrently to achieve a desired effect. Coordination results from logical and temporal constraints that must both be met, and for this reason, the planner and scheduler must communicate in order to find a valid temporal plan. This communication effectively increases the size of the search space, so must be done intelligently and as little as possible to limit this increase. This thesis contributes a comprehensive analysis of where temporal constraints appear in temporal planning problems. It introduces the notions of minimum and maximum temporal constraints, and with these isolates where the planning and scheduling are coupled together tightly, in the form of co-ordination, it characterises this with the new concepts of envelopes and contents. A new temporal planner written, called СRIKЕҮ, uses this theory to solve temporal problems involving co-ordination that other planners are unable to solve. However, it does this intelligently, using this theory to minimise the communication between the sub-solvers, and so does not expand the search space unnecessarily. The novel search space that CRIKEY uses docs not specify the timings of future events and this allows for the handling of duration inequalities, which again, few other temporal planners are able to solve. Results presented show СRIKЕҮ to be a competitive planner, whilst not making the same simplifying assumptions that other temporal planners make as to the nature of temporal planning problems

A general framework integrating techniques for scheduling under uncertainty

Ces dernières années, de nombreux travaux de recherche ont porté sur la planification de tâches et l'ordonnancement sous incertitudes. Ce domaine de recherche comprend un large choix de modèles, techniques de résolution et systèmes, et il est difficile de les comparer car les terminologies existantes sont incomplètes. Nous avons cependant identifié des familles d'approches générales qui peuvent être utilisées pour structurer la littérature suivant trois axes perpendiculaires. Cette nouvelle structuration de l'état de l'art est basée sur la façon dont les décisions sont prises. De plus, nous proposons un modèle de génération et d'exécution pour ordonnancer sous incertitudes qui met en oeuvre ces trois familles d'approches. Ce modèle est un automate qui se développe lorsque l'ordonnancement courant n'est plus exécutable ou lorsque des conditions particulières sont vérifiées. Le troisième volet de cette thèse concerne l'étude expérimentale que nous avons menée. Au-dessus de ILOG Solver et Scheduler nous avons implémenté un prototype logiciel en C++, directement instancié de notre modèle de génération et d'exécution. Nous présentons de nouveaux problèmes d'ordonnancement probabilistes et une approche par satisfaction de contraintes combinée avec de la simulation pour les résoudre. ABSTRACT : For last years, a number of research investigations on task planning and scheduling under uncertainty have been conducted. This research domain comprises a large number of models, resolution techniques, and systems, and it is difficult to compare them since the existing terminologies are incomplete. However, we identified general families of approaches that can be used to structure the literature given three perpendicular axes. This new classification of the state of the art is based on the way decisions are taken. In addition, we propose a generation and execution model for scheduling under uncertainty that combines these three families of approaches. This model is an automaton that develops when the current schedule is no longer executable or when some particular conditions are met. The third part of this thesis concerns our experimental study. On top of ILOG Solver and Scheduler, we implemented a software prototype in C++ directly instantiated from our generation and execution model. We present new probabilistic scheduling problems and a constraintbased approach combined with simulation to solve some instances thereof

GENERATING PLANS IN CONCURRENT, PROBABILISTIC, OVER-SUBSCRIBED DOMAINS

Planning in realistic domains typically involves reasoning under uncertainty, operating under time and resource constraints, and finding the optimal subset of goals to work on. Creating optimal plans that consider all of these features is a computationally complex, challenging problem. This dissertation develops an AO* search based planner named CPOAO* (Concurrent, Probabilistic, Over-subscription AO*) which incorporates durative actions, time and resource constraints, concurrent execution, over-subscribed goals, and probabilistic actions. To handle concurrent actions, action combinations rather than individual actions are taken as plan steps. Plan optimization is explored by adding two novel aspects to plans. First, parallel steps that serve the same goal are used to increase the plan’s probability of success. Traditionally, only parallel steps that serve different goals are used to reduce plan execution time. Second, actions that are executing but are no longer useful can be terminated to save resources and time. Conventional planners assume that all actions that were started will be carried out to completion. To reduce the size of the search space, several domain independent heuristic functions and pruning techniques were developed. The key ideas are to exploit dominance relations for candidate action sets and to develop relaxed planning graphs to estimate the expected rewards of states. This thesis contributes (1) an AO* based planner to generate parallel plans, (2) domain independent heuristics to increase planner efficiency, and (3) the ability to execute redundant actions and to terminate useless actions to increase plan efficiency

The 2011 International Planning Competition

After a 3 years gap, the 2011 edition of the IPC involved a total of 55 planners, some of them versions of the same planner, distributed among four tracks: the sequential satisficing track (27 planners submitted out of 38 registered), the sequential multicore track (8 planners submitted out of 12 registered), the sequential optimal track (12 planners submitted out of 24 registered) and the temporal satisficing track (8 planners submitted out of 14 registered). Three more tracks were open to participation: temporal optimal, preferences satisficing and preferences optimal. Unfortunately the number of submitted planners did not allow these tracks to be finally included in the competition. A total of 55 people were participating, grouped in 31 teams. Participants came from Australia, Canada, China, France, Germany, India, Israel, Italy, Spain, UK and USA. For the sequential tracks 14 domains, with 20 problems each, were selected, while the temporal one had 12 domains, also with 20 problems each. Both new and past domains were included. As in previous competitions, domains and problems were unknown for participants and all the experimentation was carried out by the organizers. To run the competition a cluster of eleven 64-bits computers (Intel XEON 2.93 Ghz Quad core processor) using Linux was set up. Up to 1800 seconds, 6 GB of RAM memory and 750 GB of hard disk were available for each planner to solve a problem. This resulted in 7540 computing hours (about 315 days), plus a high number of hours devoted to preliminary experimentation with new domains, reruns and bugs fixing. The detailed results of the competition, the software used for automating most tasks, the source code of all the participating planners and the description of domains and problems can be found at the competition’s web page: http://www.plg.inf.uc3m.es/ipc2011-deterministicThis booklet summarizes the participants on the Deterministic Track of the International Planning Competition (IPC) 2011. Papers describing all the participating planners are included

Improving delete relaxation heuristics through explicitly represented conjunctions

Heuristic functions based on the delete relaxation compute upper and lower bounds on the optimal delete-relaxation heuristic h+, and are of paramount importance in both optimal and satisficing planning. Here we introduce a principled and flexible technique for improving h+, by augmenting delete-relaxed planning tasks with a limited amount of delete information. This is done by introducing special fluents that explicitly represent conjunctions of fluents in the original planning task, rendering h+ the perfect heuristic h* in the limit. Previous work has introduced a method in which the growth of the task is potentially exponential in the number of conjunctions introduced. We formulate an alternative technique relying on conditional effects, limiting the growth of the task to be linear in this number. We show that this method still renders h+ the perfect heuristic h* in the limit. We propose techniques to find an informative set of conjunctions to be introduced in different settings, and analyze and extend existing methods for lower-bounding and upper-bounding h + in the presence of conditional effects. We evaluate the resulting heuristic functions empirically on a set of IPC benchmarks, and show that they are sometimes much more informative than standard delete-relaxation heuristics