In recent years research in the planning community has moved increasingly towards application of planners to realistic problems involving both time and many types of resources. For example, interest in planning demonstrated by the space research community has inspired work in observation scheduling, planetary rover exploration and spacecraft control domains. Other temporal and resource-intensive domains including logistics planning, plant control and manufacturing have also helped to focus the community on the modelling and reasoning issues that must be confronted to make planning technology meet the challenges of application. The International Planning Competitions have acted as an important motivating force behind the progress that has been made in planning since 1998. The third competition (held in 2002) set the planning community the challenge of handling time and numeric resources. This necessitated the development of a modelling language capable of expressing temporal and numeric properties of planning domains. In this paper we describe the language, pddl2.1, that was used in the competition. We describe the syntax of the language, its formal semantics and the validation of concurrent plans. We observe that pddl2.1 has considerable modelling power — exceeding the capabilities of current planning technology — and presents a number of important challenges to the research community.

While even STRIPS planners must search for plans of unbounded length, temporal planners must also cope with the fact that actions may start at any point in time. Most temporal planners cope with this challenge by restricting action start times to a small set of decision epochs, because this enables search to be carried out in state-space and leverages powerful state-based reachability heuristics, originally developed for classical planning. Indeed, decision-epoch planners won the International Planning Competition’s Temporal Planning Track in 2002, 2004 and 2006. However, decision-epoch planners have a largely unrecognized weakness: they are incomplete. In order to characterize the cause of incompleteness, we identify the notion of required concurrency, which separates expressive temporal action languages from simple ones. We show that decisionepoch planners are only complete for languages in the simpler class, and we prove that the simple class is ‘equivalent ’ to STRIPS! Surprisingly, no problems with required concurrency have been included in the planning competitions. We conclude by designing a complete state-space temporal planning algorithm, which we hope will be able to achieve high performance by leveraging the heuristics that power decision epoch planners. 1

The treatment of exogenous events in planning is practically important in many realworld domains where the preconditions of certain plan actions are affected by such events. In this paper we focus on planning in temporal domains with exogenous events that happen at known times, imposing the constraint that certain actions in the plan must be executed during some predefined time windows. When actions have durations, handling such temporal constraints adds an extra difficulty to planning. We propose an approach to planning in these domains which integrates constraint-based temporal reasoning into a graph-based planning framework using local search. Our techniques are implemented in a planner that took part in the 4th International Planning Competition (IPC-4). A statistical analysis of the results of IPC-4 demonstrates the effectiveness of our approach in terms of both CPU-time and plan quality. Additional experiments show the good performance of the temporal reasoning techniques integrated into our planner. 1.

Temporally expressive planning, an important class of temporal planning, has attracted much attention lately. Temporally expressive planning is difficult; few existing planners can solve them, as they have highly concurrent actions. We propose an optimal approach to temporally expressive planning based on a SAT formulation of the problem, finding solutions with the shortest time spans. Our experiments on several temporally expressive domains showed that our planner is able to optimally solve many instances in a reasonable amount of time, comparing favorably to existing temporally expressive planners. Our second result is a temporally expressive planning problem formulation of the Peer-to-Peer (P2P) network communications. In addition to demonstrating a better performance of our new method than the only existing temporally expressive planners on several temporally expressive problem domains, we apply our new planner to find optimal communication schedules for P2P networks. Our results will be potentially useful for designing efficient communication protocols in P2P networks.

We consider the problem of planning in domains with continuous linear numeric change. Such change cannot always be adequately modelled by discretisation and is a key facet of many interesting problems. We show how a forward-chaining temporal planner can be extended to reason with actions with continuous linear effects. We extend a temporal planner to handle numeric values using linear programming. We show how linear continuous change can be integrated into the same linear program and we discuss how a temporal-numeric heuristic can be used to provide the search guidance necessary to underpin continuous planning. We present results to show that the approach can effectively handle duration-dependent change and numeric variables subject to continuous linear change.

The primary revolution in automated planning in the last decade has been the very impressive scaleup in planner performance. A large part of the credit for this can be attributed squarely to the invention and deployment of powerful reachability heuristics. Most, if not all, modern reachability heuristics are based on a remarkably extensible data structure called the planning graph, which made its debut as a bit player in the success of GraphPlan, but quickly grew in prominence to occupy the center stage. Planning graphs are a cheap means to obtain informative look-ahead heuristics for search and have become ubiquitous in state of the art heuristic search planners. We present the foundations of planning graph heuristics in classical planning and explain how their flexibility lets them adapt to more expressive scenarios that consider action costs, goal utility, numeric resources, time, and uncertainty.

Work in partial satisfaction planning (PSP) has hither to assumed that goals are independent. This implies that that individual goals have additive utility values. In many real-world problems we cannot make this assumption and thus goal utility is not additive. In this paper, we motivate the need for representing and handling goal utility dependencies in PSP and we provide a framework for representing them using the General Additive Independence (GAI) model (Bacchus & Grove 1995). We then present an algorithm based on forward heuristic planning to solve this problem using heuristics derived from the planning graph. To show the effectiveness of our framework, we provide empirical results on benchmark planning domains.

Effective search control for numeric planning domains, in which appropriate numeric resource usage is critical to solving the problem, remains an open challenge in domainindependent planning. Most real-world problems rely on metric resources such as energy, money, fuel or materials. Despite the importance of numbers, few heuristics have been proposed to guide search in such domains. Hoffmann’s extended relaxation, implemented in Metric-FF, is one of the best general heuristics. We examine the behaviour of the Relaxed Planning Graph (RPG) heuristic, used by Metric-FF, in numeric problems. While effective in problems with simple numeric interactions, it has two weaknesses when numeric reasoning is a fundamental part of solving the problem. We present a new heuristic for use in strongly numeric domains, using a Linear Program to capture numeric constraints as an adjunct to a relaxed planning graph. We demonstrate that an intelligent combination of these two techniques offers greatly improved heuristic guidance.

Abstract. We are dealing with solving planning problems by the GraphPlan algorithm. We concentrate on solving a problem of finding supporting actions for a goal. This problem arises as a sub-problem many times during search for a solution. We showed in the paper that the supports problem is NP-complete. In order to improve the solving process of the supports problems we proposed a new global consistency technique which we call projection consistency. We present a polynomial algorithm for enforcing projection consistency. The projection consistency was implemented within our experimental planning system which we used for empirical evaluation. The empirical tests showed improvements in order of magnitudes compared to the standard GraphPlan (both in time and number of constraint checks). A significant improvement was also reached compared to the recent similar technique based on maintaining of arc-consistency.

The primary revolution in automated planning in the last decade has been the very impressive scaleup in planner performance. A large part of the credit for this can be attributed squarely to the invention and deployment of powerful reachability heuristics. Most, if not all, modern reachability heuristics are based on a remarkably extensible data structure called the planning graph, which made its debut as a bit player in the success of GraphPlan, but quickly grew in prominence to occupy the center stage. Planning graphs are a cheap means to obtain informative look-ahead heuristics for search and have become ubiquitous in state-of-the-art heuristic search planners. We present the foundations of planning graph heuristics in classical planning and explain how their flexibility lets them adapt to more expressive scenarios that consider action costs, goal utility, numeric resources, time, and uncertainty.