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Complexity Results for SAS+ Planning
Abstract
We have previously reported a number of tractable planning problems defined in the SAS + formalism. This report complements these results by providing a complete map over the complexity of SAS + planning under all combinations of the previously considered restrictions. We analyze the complexity both of finding a minimal plan and of finding any plan. In contrast to other complexity surveys of planning we study not only the complexity of the decision problems but also of the generation problems. We prove that the SAS + -PUS problem is the maximal tractable problem under the restrictions we have considered if we want to generate minimal plans. If we are satisfied with any plan, then we can generalize further to the SAS + -US problem, which we prove to be the maximal tractable problem in this case. This research was supported by the Swedish National Board for the Engineering Sciences (TFR) under grant Dnr. 92-143, by the German Ministry for Research and Technology (BMFT) under gr...
... The main modules of TFLAP are kept practically intact: • Initially, the domain and problem files of the planning task are sent to the parser module. Then, the information is preprocessed, grounded and translated to the SAS+ formalism [4], which is a formalism that is used in automated planning and scheduling systems to represent planning problems using multi-valued state variables instead of propositional facts. ...
... ▷ Fluents scheduled to be inserted 4: ▷ Get the scheduled fluent with smallest level value 12: f ← argmin(level( f i )), ∀ f i ∈ f l 13: f l ← f l − { f } ▷ Remove it not to be added again 14: ▷ Unreached actions with f as precondition 15: for each a ∈ O ′ /level(a) = ∞ ∧ f ∈ prec(a) do 16: ▷ Check if all action preconditions are met 17: if level( f i ) <= level( f ), ∀ f i ∈ prec(a) then 18: level(a) ← level( f ) ▷ Action level updated 19: ▷ Level for the action effects 20: e_level ← level(a) + δ(a, π) 21: ...
... 4. A finite set of hard goals G; each g ∈ G is a fluent that the planner must achieve.Hence for our purposes, a domain is a tuple Dom = (T, V, OP), and problem is a quadruple Prob = (O, I, TILs, G). ...
While executing its plan in a dynamic environment where multiple agents are operating, an autonomous agent may suffer a failure due to discrepancies between the expected and actual context and thus must replace its obsolete plan. In its endeavour to fix the failure and reach its original goals, the agent may unknowingly disrupt other agents executing their plans in the same environment. We present a property for plan repair called plan commitment to ensure a responsible repair policy among agents that aims to minimise the negative impact on others. We present arguments to support the claim that plan commitment is a valuable property when an agent may have made bookings and commitments to others. We then propose C-TFLAP, an implementation of a plan repair heuristic that allows adapting a failed plan to the new context while committing as much as possible to the original plan. We demonstrate empirically that: (1) our plan repair achieves more committed plans than plan-stability repair when an agent has made bookings and commitments to others, and (2) compared to typical replanning and plan-stability repair, it can reduce the revisions among agents when failures are avoidable and can decrease the time-loss otherwise. In addition, to demonstrate extensibility, we integrate context-aware knowledge extension with committed repairing to increase the agent’s chances of repairing.
... In this thesis, we consider classical planning domains and tasks that are characterized by the SAS + formalism (Bäckström and Nebel 1995). ...
... More precisely, the bounded plan existence problem of planning is the problem of deciding for a given planning task Π whether there exists a plan. It was shown that this problem is PSPACE-complete for STRIPS (Bylander 1997) and SAS + planning tasks (Bäckström and Nebel 1995). ...
... -Albert Einstein (1950) Core Publication of this Chapter In classical planning, Boolean or finite domain variables are used to describe the states of the world, the preconditions and the effects of actions, and the goal description (Bäckström and Nebel 1995;Fikes and Nilsson 1971). For many real-world problems, however, complex action preconditions or goals are desirable or even necessary for a compact problem description (Thiébaux, Hoffmann, and Nebel 2005). ...
In classical planning, the goal is to derive a course of actions that allows an intelligent agent to move from any situation it finds itself in to one that satisfies its goals. Classical planning is considered domain-independent, i.e., it is not limited to a particular application and can be used to solve different types of reasoning problems. In practice, however, some properties of a planning problem at hand require an expressive extension of the standard classical planning formalism to capture and model them. Although the importance of many of these extensions is well known, most planners, especially optimal planners, do not support these extended planning formalisms. The lack of support not only limits the use of these planners for certain problems, but even if it is possible to model the problems without these extensions, it often leads to increased effort in modeling or makes modeling practically impossible as the required problem encoding size increases exponentially. In this thesis, we propose to use symbolic search for cost-optimal planning for different expressive extensions of classical planning, all capturing different aspects of the problem. In particular, we study planning with axioms, planning with state-dependent action costs, oversubscription planning, and top-k planning. For all formalisms, we present complexity and compilability results, highlighting that it is desirable and even necessary to natively support the corresponding features. We analyze symbolic heuristic search and show that the search performance does not always benefit from the use of a heuristic and that the search performance can exponentially deteriorate even under the best possible circumstances, namely the perfect heuristic. This reinforces that symbolic blind search is the dominant symbolic search strategy nowadays, on par with other state-of-the-art cost-optimal planning strategies...
... In this thesis, we consider classical planning domains and tasks that are characterized by the SAS + formalism (Bäckström and Nebel 1995). ...
... More precisely, the bounded plan existence problem of planning is the problem of deciding for a given planning task Π whether there exists a plan. It was shown that this problem is PSPACE-complete for STRIPS (Bylander 1997) and SAS + planning tasks (Bäckström and Nebel 1995). ...
... -Albert Einstein (1950) Core Publication of this Chapter In classical planning, Boolean or finite domain variables are used to describe the states of the world, the preconditions and the effects of actions, and the goal description (Bäckström and Nebel 1995;Fikes and Nilsson 1971). For many real-world problems, however, complex action preconditions or goals are desirable or even necessary for a compact problem description (Thiébaux, Hoffmann, and Nebel 2005). ...
In classical planning, the goal is to derive a course of actions that allows an intelligent agent to move from any situation it finds itself in to one that satisfies its goals. Classical planning is considered domain-independent, i.e., it is not limited to a particular application and can be used to solve different types of reasoning problems. In practice, however, some properties of a planning problem at hand require an expressive extension of the standard classical planning formalism to capture and model them. Although the importance of many of these extensions is well known, most planners, especially optimal planners, do not support these extended planning formalisms. The lack of support not only limits the use of these planners for certain problems, but even if it is possible to model the problems without these extensions, it often leads to increased effort in modeling or makes modeling practically impossible as the required problem encoding size increases exponentially.
In this thesis, we propose to use symbolic search for cost-optimal planning for different expressive extensions of classical planning, all capturing different aspects of the problem. In particular, we study planning with axioms, planning with state-dependent action costs, oversubscription planning, and top-k planning. For all formalisms, we present complexity and compilability results, highlighting that it is desirable and even necessary to natively support the corresponding features. We analyze symbolic heuristic search and show that the search performance does not always benefit from the use of a heuristic and that the search performance can exponentially deteriorate even under the best possible circumstances, namely the perfect heuristic. This reinforces that symbolic blind search is the dominant symbolic search strategy nowadays, on par with other state-of-the-art cost-optimal planning strategies. Based on this observation and the lack of good heuristics for planning formalisms with expressive extensions, symbolic search turns out to be a strong approach. We introduce symbolic search to support each of the formalisms individually and in combination, resulting in optimal, sound, and complete planning algorithms that empirically compare favorably with other approaches.
... Given that Alice is able to successively perform each of these actions, the sequence (1), (2), (3) is a plan. In the following, we will show how to formalize situations like these using the SAS+ framework (Bäckström and Nebel, 1995). Specifically, we will show how to formalize states, actions and plans. ...
... Now that we have introduced how to formally represent planning tasks, we describe methods of solving them. In general, finding a solution, optimal or not, to a classical planning task is PSPACE-complete (Bäckström and Nebel, 1995;Bylander, 1994). Nevertheless, various techniques have been developed to solve a wide variety of planning tasks efficiently. ...
In privacy-preserving planning, multiple agents engage in a distributed planning process in order to solve a given problem cooperatively. They communicate with one another to exchange information and to coordinate their actions and they do so while maintaining private information.
In this thesis, we present a new algorithmic framework for the specification of privacy-preserving planning algorithms, called DMT. We discuss theoretical properties, like privacy preservation, soundness, and completeness, and empirically evaluate the presented approach, comparing it to a multi-agent forward search baseline. We develop a technique that extends search by explorative trials, and show that it significantly improves search performance. This technique is also transferred to multi-agent forward search and likewise increased the search performance considerably.
To further improve privacy-preserving planning algorithms and the presented search approaches, in particular, we develop a partial order reduction technique based on stubborn sets. Again, we discuss theoretical properties and evaluate the approach empirically. The evaluation shows that stubborn sets pruning can have a profound positive effect on the number of problems that a solution algorithm solves.
... The first aspect also follows from well-known computational complexity studies on planning problem generators (Bäckström & Nebel, 1995), and the second was confirmed by the results reported above. The comments reported by users involved in the training activity and the errors they found were crucial for identifying problems and solving them: In some situations, there was a discrepancy between the actual difficulty of exercises and the level for which they were proposed. ...
... The modelling approach in this work is not based on a standardized format, e.g., classical PDDL, which is too limited for the approach. Instead, it uses the native SAS+ format (Bäckström and Nebel, 1995). Despite the improvements suggested by Geißer et al., these conversions will in the worst case grow exponentially. ...
Modern industrial robots are increasingly deployed in dynamic environments, where unpredictable events are expected to impact the robot’s operation. Under these conditions, runtime task replanning is required to avoid failures and unnecessary stops, while keeping up productivity. Task replanning is a long-sighted complement to path replanning, which is mostly concerned with avoiding unexpected obstacles that can lead to potentially unsafe situations. This paper focuses on task replanning as a way to dynamically adjust the robot behaviour to the continuously evolving environment in which it is deployed. Analogously to probabilistic roadmaps used in path planning, we propose the concept of Task roadmaps as a method to replan tasks by leveraging an offline generated search space. A graph-based model of the robot application is converted to a task scheduling problem to be solved by a proposed Branch and Bound (B&B) approach and two benchmark approaches: Mixed Integer Linear Programming (MILP) and Planning Domain Definition Language (PDDL). The B&B approach is proposed to compute the task roadmap, which is then reused to replan for unforeseeable events. The optimality and efficiency of this replanning approach are demonstrated in a simulation-based experiment with a mobile manipulator in a kitting application. In this study, the proposed B&B Task Roadmap replanning approach is significantly faster than a MILP solver and a PDDL based planner.
... Fast Downward [10] is the most well-known, supported and reused state-of-the-art planner. Its preprocessing module performs sophisticated transformations from PDDL to the more solver-amenable SAS+ format [2]. This preprocessor is currently used by many of the state-of-the-art planners. ...
Plotting is a tile-matching puzzle video game published by Taito in 1989. Its objective is to reduce a given grid of coloured blocks down to a goal number or fewer. This is achieved by the avatar character repeatedly shooting the block it holds into the grid. Plotting is an example of a planning problem: given a model of the environment, a planning problem asks us to find a sequence of actions that can lead from an initial state of the environment to a given goal state while respecting some constraints. The key difficulty in modelling Plotting is in capturing the way the puzzle state changes after each shot. A single shot can affect multiple tiles directly, and the grid is affected by gravity so numerous other tiles can be affected indirectly. We present and evaluate a constraint model of the Plotting problem that captures this complexity. We also discuss the difficulties and inefficiencies of modelling Plotting in PDDL, the standard language used for input to specialised AI planners. We conclude by arguing that AI planning could benefit from a richer modelling language.
... Classical planning has been well analyzed over the years (Bäckström and Nebel, 1995;Bylander, 1994), and finding a solution is in general PSPACE-2 Chapter 1. Introduction hard. However, applying heuristic search yields satisfying results to many domains. ...
Automated planning is the field of research with the goal of enabling agents
to act in an intelligent way to reach a certain goal. In business applications,
this corresponds to generating workflows, describing how objectives are to
be reached. In this thesis, a method for creating such workflows automatically,
from formal data specifications with the help of planning is described.
Even though, this provides functional workflows for the developed digital
preservation system, it lacks functionality considering usability issues, essential
for human computer interaction. These usability constraints can be modeled
using soft goals, which add optional constraints to the resulting plan.
These constraints do not need to be fulfilled by the plan, however increase
the quality of the result. A method for dealing with these soft constraints
in classical planning is introduced, using conditional effects for tracking the
constraints, and state-dependent action costs for guiding the search.
A prominent approach for solving such planning problems is heuristic search,
which uses so called heuristic estimates to guide the search towards achieving
the goal condition. When combining state-dependent action costs with
conditional effects, some problems arise, which leads to the heuristic functions
becoming relatively uninformed, providing inferior guidance. Therefore,
a theory on treating both state-dependent action costs and conditional
effects combined is introduced, which reduced the problems when dealing
with them independently. This approach is based on an edge-valued multivalued
decision diagram (EVMDD) representation of the cost function and
the conditional effects. Here, the existing theory of EVMDDs over arithmetic
functions is generalized to EVMDDs over monoids, as to be able to represent
the cost functions and conditional effects in one EVMDD combined.
As workflows involving human users, can consist of actions for which the
outcome is not a priory known, soft trajectory constraints are introduced
to the fully observable nondeterministic setting. This thesis provides a basic
understanding on how these constraints can be interpreted in this setting,
and how existing heuristic functions can be augmented, as to guide the
search towards a goal, fulfilling the constraints.
... More recent planning systems are usually not restricted to propositional state variables. Instead they use the SAS + formalism [BN93], which allows for (finitedomain) multi-valued variables. Here, the counterpart of a "delete relaxation" is a relaxation which replaces the domains of variables in the relaxation by a set of reachable values. ...
Ein wichtiges Merkmal von intelligenten Agenten ist, das sie denken bevor sie handeln. Handlungsplanung ist das Teilgebiet der Künstlichen Intelligenz, welches sich mit dieser Art von Denken beschäftigt. Das Ergebnis eines solchen Denkprozesses ist eine Handlungsanweisung für die Schritte des Agenten. Gegeben ein durch Zustände und Aktionen beschriebenes Modell der Welt, ist ein Plan eine Sequenz von Aktionen, welche einen initialen Weltzustand in einen Zustand überführt, in welchem eine gewünschte Zielbedingung erfüllt ist.
Im klassischen Planen werden die Zustände der Welt durch Variablen mit beschränktem Wertebereich beschrieben. Allerdings ist dieser Formalismus für viele reale Anwendungsbereiche nicht ausdrucksstark genug. Um etwa Ressourcen (z.B. die verbleibende Menge Benzin im Tank) oder physikalsiche Größen (z.B. die aktuelle Geschwindigkeit eines Autos) zu modellieren, werden numerische Variablen benötigt. In dieser Arbeit beschäftigen wir uns mit numerischer Handlungsplanung bei welcher Variablen auch kontinuierliche Werte zugewiesen werden können.
Im Allgemeinen ist die Existenz einer Lösung eines numerischen Planungsproblems unentscheidbar. Daher untersuchen wir Näherungslösungen für numerische Planungsprobleme, welche die Kosten von bestimmten numerischen Fakten abschätzen, insbesondere solche, die zum erreichen eines Ziels benötigt werden. Im Fokus dieser Arbeit stehen hierbei Intervall-basierte Relaxiserungsheuristiken, da diese auf viele numerische Probleme angewendet werden können, insbesondere auch auf Probleme mit nicht-linearen Änderungen. Bei einigen Problemen bieten die vorgestellten Relaxierungsheuristiken eine gute Orientierungshilfe, aber selbst in Fällen bei denen die Informationsqualität schwach ist, ermöglichen Relaxierungsheuristiken eine grundlegende Orientierung für Probleme in welchen spezialisierte Lösungen nicht verfügbar sind.
... All results in this article will be stated using propositional STRIPS. In particular, we will use propositional STRIPS with negative goals (PSN) [8], which can alternatively be viewed as SAS + [6] restricted to boolean (i.e. two-valued) variable domains. ...
The use of computational complexity in planning, and in AI in general, has always been a disputed topic. A major problem with ordinary worst-case analyses is that they do not provide any quantitative information: they do not tell us much about the running time of concrete algorithms, nor do they tell us much about the running time of optimal algorithms. We address problems like this by presenting results based on the exponential time hypothesis (ETH), which is a widely accepted hypothesis concerning the time complexity of 3-SAT. By using this approach, we provide, for instance, almost matching upper and lower bounds onthe time complexity of propositional planning.
For applying symbolic planning, an agent acting in an environment needs to know its symbolic state, and an abstract model of the environment dynamics. However, in the real world, an agent has low-level perceptions of the environment (e.g. its position given by a GPS sensor), rather than symbolic observations representing its current state. Furthermore, in many real-world scenarios, it is not feasible to provide an agent with a complete and correct model of the environment, e.g., when the environment is (partially) unknown a priori. Therefore, agents need to dynamically learn/adapt/extend their perceptual abilities online, in an autonomous way, by exploring and interacting with the environment where they operate. In this paper, we provide a general architecture of a planning, learning, and acting agent. Moreover, we propose solutions to the problems of automatically training a neural network to recognize object properties, learning the situations where such properties are better perceivable, and planning to get into such situations. We experimentally show the effectiveness of our approach in simulated and complex environments, and we empirically demonstrate the feasibility of our approach in a real-world scenario that involves noisy perceptions and noisy actions on a real robot.
Research in automated planning traditionally focuses on model-based approaches that often sacrifice expressivity for computational efficiency. For artificial agents that operate in complex environments, however, frequently the agent needs to reason about the beliefs of other agents and be capable of handling uncertainty. We present Spectra, a STRIPS-inspired AI planner built atop automated reasoning. Our system is expressive, in that we allow for state spaces to be defined as arbitrary formulae. Spectra is also designed to be logic-agnostic, as long as an automated reasoner exists that can perform entailment and question-answering over it. Spectra can handle environments of unbounded uncertainty; and with certain non-classical logics, our system can create plans under epistemic beliefs. We highlight all of these features using the cognitive calculus . Lastly, we discuss that under this framework, in order to fully plan under uncertainty, a defeasible (= non-monotonic) logic can be used in conjunction with our planner.
Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze normative ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr’s three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the moral tractability thesis.
Goal recognition is an important problem in many application domains (e.g., pervasive computing, intrusion detection, computer games, etc.). In many application scenarios, it is important that goal recognition algorithms can recognize goals of an observed agent as fast as possible. However, many early approaches in the area of Plan Recognition As Planning, require quite large amounts of computation time to calculate a solution. Mainly to address this issue, recently, Pereira et al. developed an approach that is based on planning landmarks and is much more computationally efficient than previous approaches. However, the approach, as proposed by Pereira et al., considers trivial landmarks (i.e., facts that are part of the initial state and goal description are landmarks by definition) for goal recognition. In this paper, we show that it does not provide any benefit to use landmarks that are part of the initial state in a planning landmark based goal recognition approach. The empirical results show that omitting initial state landmarks for goal recognition improves goal recognition performance.
In this work, we propose a new approach for coordinating generated agents’ plans dynamically. The purpose is to take into consideration new conflicts introduced in new versions of agents’ plans. The approach consists in finding the best combination which contains one plan for each agent among its set of possible plans whose execution does not entail any conflict. This combination of plans is reconstructed dynamically, each time agents decide to change their plans to take into account unpredictable changes in the environment. This not only ensures that new conflicts are likely to be introduced in the new plans that are taken into account but also it allows agents to deal, solely, with the execution of their actions and not with the resolution of conflicts. For this, we use genetic algorithms where the proposed fitness function is defined based on the number of conflicts that agents can experience in each combination of plans. As part of our work, we used a concrete case to illustrate and show the usefulness of our approach.
There any many different access-control systems, yet a commonality is that they provide flexible mechanisms to enforce different access levels. Their importance in organisations to adequately restrict resources, coupled with their use in a dynamic environment, mandates the need to routinely perform policy analysis. The aim of performing analysis is often to identify potential problematic permissions, which have the potential to be exploited and could result in data theft and unintended modification. There is a vast body of published literature on analysing access-control systems, yet as performing analysis has a strong end-user motivation and is grounded in security challenges faced in real-world systems, it is important to understand how research is developing, what are the common themes of interest, and to identify key challenges that should be addressed in future work. To the best of the authors’ knowledge, no survey has been performed to gain an understanding of empirical access-control analysis, focussing on how techniques are evaluated and how they align to the needs of real-world analysis tasks. This article provides a systematic literature review, identifying and summarising key works. Key findings are identified and discussed as areas of future work.
Robotic planning in real-world scenarios typically requires joint optimization of logic and continuous variables. A core challenge to combine the strengths of logic planners and continuous solvers is the design of an efficient interface that informs the logical search about continuous infeasibilities. In this paper we present a novel iterative algorithm that connects logic planning with nonlinear optimization through a bidirectional interface, achieved by the detection of minimal subsets of nonlinear constraints that are infeasible. The algorithm continuously builds a database of graphs that represent (in)feasible subsets of continuous variables and constraints, and encodes this knowledge in the logical description. As a foundation for this algorithm, we introduce
Planning with Nonlinear Transition Constraints (PNTC)
, a novel planning formulation that clarifies the exact assumptions our algorithm requires and can be applied to model Task and Motion Planning (TAMP) efficiently. Our experimental results show that our framework significantly outperforms alternative optimization-based approaches for TAMP.
Answer Set Planning refers to the use of Answer Set Programming (ASP) to compute plans , that is, solutions to planning problems, that transform a given state of the world to another state. The development of efficient and scalable answer set solvers has provided a significant boost to the development of ASP-based planning systems. This paper surveys the progress made during the last two and a half decades in the area of answer set planning, from its foundations to its use in challenging planning domains. The survey explores the advantages and disadvantages of answer set planning. It also discusses typical applications of answer set planning and presents a set of challenges for future research.
In this paper, we study the computational complexity of action-based temporal planning interpreted over dense time. When time is assumed to be discrete, the problem is known to be EXPSPACE-complete. However, the official PDDL 2.1 semantics and many implementations interpret time as a dense domain. This work provides several results about the complexity of the problem, focusing on some particularly interesting cases: whether a minimum amount ε of separation between mutually exclusive events is given, in contrast to the separation being simply required to be non-zero, and whether or not actions are allowed to overlap already running instances of themselves. We prove the problem to be PSPACE-complete when self-overlap is forbidden, whereas, when it is allowed, it becomes EXPSPACE-complete with ε-separation and even undecidable with non-zero separation. These results clarify the computational consequences of different choices in the definition at the core of the PDDL 2.1 semantics, which have been vague until now.
Attribute-based access control (ABAC) models are widely used to provide fine-grained and adaptable authorization based on the attributes of users, resources, and other relevant entities. Hierarchial group and attribute based access control (HGABAC) model was recently proposed which introduces the novel notion of attribute inheritance through group membership. GURA\textsubscript{G} was subsequently proposed to provide an administrative model for user attributes in HGABAC, building upon the ARBAC97 and GURA administrative models. The GURA model uses administrative roles to manage user attributes. The reachability problem for the GURA model is to determine what attributes a particular user can acquire, given a predefined set of administrative rules. This problem has been previously analyzed in the literature. In this paper, we study the user attribute reachability problem based on directly assigned attributes of the user and attributes inherited via group memberships. We first define a restricted form of GURA\textsubscript{G}, called rGURA\textsubscript{G} scheme, as a state transition system with multiple instances having different preconditions and provide reachability analysis for each of these schemes. In general, we show PSPACE-complete complexity for all rGURA\textsubscript{G} schemes. We further present polynomial time algorithms with empirical experimental evaluation to solve special instances of rGURA\textsubscript{G} schemes under restricted conditions.
View Video Presentation: https://doi.org/10.2514/6.2022-1412.vid Future long-duration missions will require astronauts to act more autonomously, manage their schedules, and replan timelines as anomalies and discoveries occur. Astronauts are not professional planners, however, and the complexity of schedules that novice planners can complete successfully is not fully understood. To identify the primary factors which contribute to scheduling task complexity, we conducted a human-in-the-loop study and developed planning algorithms to investigate how the type and amount of constraints affect the difficulty of scheduling and rescheduling. We created rankings of difficulty using a combination of human performance metrics from experimental planning tasks and metrics describing the final plans that participants scheduled. Using the results of our scheduling and rescheduling algorithm algorithms, we created a similar ranking with which to compare. We created rankings which compared well between the experimental and algorithm results for the scheduling task, but the rescheduling task proved more difficult to estimate.
ion has been used in combinatorial search and action planning from the very beginning of AI. Many different methods and formalisms for state abstraction have been proposed in the literature, but they have been designed from various points of view and with varying purposes. Hence, these methods have been notoriously difficult to analyse and compare in a structured way. In order to improve upon this situation, we present a coherent and flexible framework for modelling abstraction (and abstraction-like) methods based on graph transformations. The usefulness of the framework is demonstrated by applying it to problems in both search and planning. We model six different abstraction methods from the planning literature and analyse their intrinsic properties. We show how to capture many search abstraction concepts (such as avoiding backtracking between levels) and how to put them into a broader context. We also use the framework to identify and investigate connections between refinement and heuristics—two concepts that have usually been considered as unrelated in the literature. This provides new insights into various topics, e.g. Valtorta's theorem and spurious states. We finally extend the framework with composition of transformations to accomodate for abstraction hierarchies, and other multi-level concepts. We demonstrate the latter by modelling and analysing the merge-and-shrink abstraction method.
In AI research, synthesizing a plan of action has typically used descriptive models of the actions that abstractly specify what might happen as a result of an action, and are tailored for efficiently computing state transitions. However, executing the planned actions has needed operational models, in which rich computational control structures and closed-loop online decision-making are used to specify how to perform an action in a nondeterministic execution context, react to events and adapt to an unfolding situation. Deliberative actors, which integrate acting and planning, have typically needed to use both of these models together—which causes problems when attempting to develop the different models, verify their consistency, and smoothly interleave acting and planning.
As an alternative, we define and implement an integrated acting and planning system in which both planning and acting use the same operational models. These rely on hierarchical task-oriented refinement methods offering rich control structures. The acting component, called Reactive Acting Engine (RAE), is inspired by the well-known PRS system. At each decision step, RAE can get advice from a planner for a near-optimal choice with respect to an utility function. The anytime planner uses a UCT-like Monte Carlo Tree Search procedure, called UPOM, whose rollouts are simulations of the actor's operational models. We also present learning strategies for use with RAE and UPOM that acquire, from online acting experiences and/or simulated planning results, a mapping from decision contexts to method instances as well as a heuristic function to guide UPOM. We demonstrate the asymptotic convergence of UPOM towards optimal methods in static domains, and show experimentally that UPOM and the learning strategies significantly improve the acting efficiency and robustness.
The problem of planning for a robot that operates in environments containing a large number of objects, taking actions to move itself through the world as well as to change the state of the objects, is known as task and motion planning (TAMP). TAMP problems contain elements of discrete task planning, discrete–continuous mathematical programming, and continuous motion planning and thus cannot be effectively addressed by any of these fields directly. In this article, we define a class of TAMP problems and survey algorithms for solving them, characterizing the solution methods in terms of their strategies for solving the continuous-space subproblems and their techniques for integrating the discrete and continuous components of the search.
Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 4 is May 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
Research in classical planning so far has been mainly concerned with generating a satisficing or an optimal plan. However, if such systems are used to make decisions that are relevant to humans, one should also consider the ethical consequences generated plans can have. Traditionally, ethical principles are formulated in an action-based manner, allowing to judge the execution of one action. We show how such a judgment can be generalized to plans. Further, we study the computational complexity of making ethical judgment about plans.
In this chapter, we proposeSabbadin, Régis a non-exhaustive review of past works of the AI community on classical planning and planning underTeichteil-Königsbuch, Florent uncertainty. We first present the classical propositional STRIPS planning language. Its extensions, based on the problem description language PDDL have become a standard in the community. We briefly deal with the structural analysis of planning problems, which has initiated theVidal, Vincent development of efficient planning algorithms and associated planners. Then, we describe the Markov Decision Processes framework (MDP), initially proposed in the Operations Research community before the AI community adopted it as a framework for planning under uncertainty. Eventually, we will describe innovative (approximate or exact) MDP solution algorithms as well as recent progresses in AI in terms of knowledge representation (logics, Bayesian networks) which have been used to increase the power of expression of the MDP framework.
We present a list of parameterized problems together with a complexity classification of whether they allow a fixed-parameter tractable reduction to SAT or not. These problems are parameterized versions of problems whose complexity lies at the second level of the Polynomial Hierarchy or higher.
Multi-Agent Planning deals with the task of generating a plan for/by a set of agents that jointly solve a planning problem. One of the biggest challenges is how to handle interactions arising from agents’ actions. The first contribution of the paper is Plan Merging by Reuse, pmr, an algorithm that automatically adjusts its behaviour to the level of interaction. Given a multi-agent planning task, pmr assigns goals to specific agents. The chosen agents solve their individual planning tasks and the resulting plans are merged. Since merged plans are not always valid, pmr performs planning by reuse to generate a valid plan. The second contribution of the paper is rrpt-plan, a stochastic plan-reuse planner that combines plan reuse, standard search and sampling. We have performed extensive sets of experiments in order to analyze the performance of pmr in relation to state of the art multi-agent planning techniques.
Temporal planning is a research discipline that addresses the problem of generating a totally or a partially ordered sequence of actions that transform the environment from some initial state to a desired goal state, while taking into account time constraints and actions' duration. For its ability to describe and address temporal constraints, temporal planning is of critical importance for a wide range of real‐world applications. Predicting the performance of temporal planners can lead to significant improvements in the area, as planners can then be combined in order to boost the performance on a given set of problem instances.
This paper investigates the predictability of the state‐of‐the‐art temporal planners by introducing a new set of temporal‐specific features and exploiting them for generating classification and regression empirical performance models (EPMs) of considered planners. EPMs are also tested with regard to their ability to select the most promising planner for efficiently solving a given temporal planning problem.
Our extensive empirical analysis indicates that the introduced set of features allows to generate EPMs that can effectively perform algorithm selection, and the use of EPMs is therefore a promising direction for improving the state of the art of temporal planning, hence fostering the use of planning in real‐world applications.
Discoplan is a durable and efficient system for inferring state constraints (invariants) in planning domains, specified in the PDDL language. It is exceptional in the range of constraint types it can discover and verify, and it directly allows for conditional effects in action operators. However, although various aspects of Discoplan have been previously described and its utility in planning demonstrated, the underlying methodology, the algorithms for the discovery and inductive verification of constraints, and the proofs of correctness of the algorithms and their complexity analysis have never been laid out in adequate detail. The purpose of this paper is to remedy these lacunae.
In the field of automated planning, the central research focus is on domain‐independent planning engines that accept planning tasks (domain models and problem descriptions) in a description language, such as Planning Domain Definition Language, and return solution plans. The performance of planning engines can be improved by gathering additional knowledge about specific planning domain models/tasks (such as control rules) that can narrow the search for a solution plan. Such knowledge is often learned from training plans and solutions of simple tasks. Using techniques to reformulate the given planning task to incorporate additional knowledge, while keeping to the same input language, allows to exploit off‐the‐shelf planning engines. In this paper, we present inner entanglements that are relations between pairs of operators and predicates that represent the exclusivity of predicate achievement or requirement between the given operators. Inner entanglements can be encoded into a planner's input language by transforming the original planning task; hence, planning engines can exploit them. The contribution of this paper is to provide an in‐depth analysis and evaluation of inner entanglements, covering theoretical aspects such as complexity results, and an extensive empirical study using International Planning Competition benchmarks and state‐of‐the‐art planning engines.
A* is a best-first search algorithm for finding optimal-cost paths in graphs. A* benefits significantly from parallelism because in many applications, A* is limited by memory usage, so distributed memory implementations of A* that use all of the aggregate memory on the cluster enable us to solve problems that can not be solved by serial, single-machine implementations. We survey approaches to parallel A*, focusing on decentralized approaches to A* which partition the state space among processors. We also survey approaches to parallel, limited-memory variants of A* such as parallel IDA*. © Springer International Publishing AG, part of Springer Nature 2018. All rights reserved.
Multi-agent planning (MAP) deals with planning systems that reason on long-term goals by multiple collaborative agents which want to maintain privacy on their knowledge. Recently, new MAP techniques have been devised to provide efficient solutions. Most approaches expand distributed searches using modified planners, where agents exchange public information. They present two drawbacks: they are planner-dependent; and incur a high communication cost. Instead, we present two algorithms whose search processes are monolithic (no communication while individual planning) and MAP tasks are compiled such that they are planner-independent (no programming effort needed when replacing the base planner). Our two approaches first assign each public goal to a subset of agents. In the first distributed approach, agents iteratively solve problems by receiving plans, goals and states from previous agents. After generating new plans by reusing previous agents’ plans, they share the new plans and some obfuscated private information with the following agents. In the second centralized approach, agents generate an obfuscated version of their problems to protect privacy and then submit it to an agent that performs centralized planning. The resulting approaches are efficient, outperforming other state-of-the-art approaches.
We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems where there are k different target sets, and the problems are as follows: (a) the coverage problem asks whether there is a plan for each individual target set, and (b) the sequential target reachability problem asks whether the targets can be reached in sequence. For the coverage problem, we present a linear-time algorithm for graphs and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs and for the sequential reachability problem games on graphs are harder than MDPs and graphs; (ii) objective-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.
A main focus of machine learning research has been improving the generalization accuracy and efficiency of prediction models. However, what emerges as missing in many applications is actionability, i.e., the ability to turn prediction results into actions. Existing effort in deriving such actionable knowledge is few and limited to simple action models while in many real applications those models are often more complex and harder to extract an optimal solution. In this paper, we propose a novel approach that achieves actionability by combining learning with planning, two core areas of AI. In particular, we propose a framework to extract actionable knowledge from random forest, one of the most widely used and best off-the-shelf classifiers. We formulate the actionability problem to a sub-optimal action planning (SOAP) problem, which is to find a plan to alter certain features of a given input so that the random forest would yield a desirable output, while minimizing the total costs of actions. Technically, the SOAP problem is formulated in the SAS+ planning formalism, and solved using a Max-SAT based approach. Our experimental results demonstrate the effectiveness and efficiency of the proposed approach on a personal credit dataset and other benchmarks. Our work represents a new application of automated planning on an emerging and challenging machine learning paradigm.
This paper presents a general-purpose formulation of a large class of discrete-time planning problems, with hybrid state and control-spaces, as factored transition systems. Factoring allows state transitions to be described as the intersection of several constraints each affecting a subset of the state and control variables. Robotic manipulation problems with many movable objects involve constraints that only affect several variables at a time and therefore exhibit large amounts of factoring. We develop a theoretical framework for solving factored transition systems with sampling-based algorithms. The framework characterizes conditions on the submanifold in which solutions lie, leading to a characterization of robust feasibility that incorporates dimensionality-reducing constraints. It then connects those conditions to corresponding conditional samplers that can be composed to produce values on this submanifold. We present two domain-independent, probabilistically complete planning algorithms that take, as input, a set of conditional samplers. We demonstrate the empirical efficiency of these algorithms on a set of challenging task and motion planning problems involving picking, placing, and pushing.
State space search is a basic method for analyzing reachability in discrete transition systems. To tackle large compactly described transition systems – the state space explosion – a wealth of techniques (e.g., partial-order reduction) have been developed that reduce the search space without affecting the existence of (optimal) solution paths. Focusing on classical AI planning, where the compact description is in terms of a vector of state variables, an initial state, a goal condition, and a set of actions, we add another technique, that we baptize star-topology decoupling, into this arsenal. A star topology partitions the state variables into components so that a single center component directly interacts with several leaf components, but the leaves interact only via the center. Many applications explicitly come with such structure; any classical planning task can be viewed in this way by selecting the center as a subset of state variables separating connected leaf components.
Our key observation is that, given such a star topology, the leaves are conditionally independent given the center, in the sense that, given a fixed path of transitions by the center, the possible center-compliant paths are independent across the leaves. Our decoupled search hence branches over center transitions only, and maintains the center-compliant paths for each leaf separately. As we show, this method has exponential separations to all previous search reduction techniques, i.e., examples where it results in exponentially less effort. One can, in principle, prune duplicates in a way so that the decoupled state space can never be larger than the original one. Standard search algorithms remain applicable using simple transformations. Our experiments exhibit large improvements on standard AI planning benchmarks with a pronounced star topology.
PDDL4J (Planning Domain Description Library for Java) is an open source toolkit for Java cross-platform developers meant (1) to provide state-of-the-art planners based on the Pddl language, and (2) to facilitate research works on new planners. In this article, we present an overview of the Automated Planning concepts and languages. We present some planning systems and their most significant applications. Then, we detail the Pddl4j toolkit with an emphasis on the available informative structures, heuristics and search algorithms.
Action planning deals with the problem of finding a sequence of actions transferring the world from a given state to a desired (goal) state. This problem is important in various areas such as robotics, manufacturing, transportation, autonomic computing, computer games, etc. Action planning is a form of a reachability problem in a huge state space so it is critical to efficiently represent world states and actions (transitions between states).In this paper we present a modeling framework for planning problems based on tabled logic programming that exploits a planner module in the Picat language. In particular, we suggest techniques for structured representation of states and for including control knowledge in the description of actions. We demonstrate these techniques using the complex planning domain Cave Diving from the International Planning Competition. Experimentally, we show properties of the model for different search approaches and we compare the performance of the proposed approach with state-of-the-art automated planners. The focus of this paper is on providing guidelines for manual modeling of planning domains rather than on automated reformulation of models.
A main focus of machine learning research has been improving the generalization accuracy and efficiency of prediction models. Many models such as SVM, random forest, and deep neural nets have been proposed and achieved great success. However, what emerges as missing in many applications is actionability, i.e., the ability to turn prediction results into actions. For example, in applications such as customer relationship management, clinical prediction, and advertisement, the users need not only accurate prediction, but also actionable instructions which can transfer an input to a desirable goal (e.g., higher profit repays, lower morbidity rates, higher ads hit rates). Existing effort in deriving such actionable knowledge is few and limited to simple action models which restricted to only change one attribute for each action. The dilemma is that in many real applications those action models are often more complex and harder to extract an optimal solution. In this paper, we propose a novel approach that achieves actionability by combining learning with planning, two core areas of AI. In particular, we propose a framework to extract actionable knowledge from random forest, one of the most widely used and best off-the-shelf classifiers. We formulate the actionability problem to a sub-optimal action planning (SOAP) problem, which is to find a plan to alter certain features of a given input so that the random forest would yield a desirable output, while minimizing the total costs of actions. Technically, the SOAP problem is formulated in the SAS+ planning formalism, and solved using a Max-SAT based approach. Our experimental results demonstrate the effectiveness and efficiency of the proposed approach on a personal credit dataset and other benchmarks. Our work represents a new application of automated planning on an emerging and challenging machine learning paradigm.
Mobile manipulation problems involving many objects are challenging to solve due to the high dimensionality and multi-modality of their hybrid configuration spaces. Planners that perform a purely geometric search are prohibitively slow for solving these problems because they are unable to factor the configuration space. Symbolic task planners can efficiently construct plans involving many variables but cannot represent the geometric and kinematic constraints required in manipulation. We present the FFRob algorithm for solving task and motion planning problems. First, we introduce Extended Action Specification (EAS) as a general purpose planning representation that supports arbitrary predicates as conditions. We adapt heuristic search ideas for solving \proc{strips} planning problems, particularly delete-relaxations, to solve EAS problem instances. We then apply the EAS representation and planners to manipulation problems resulting in FFRob. FFRob iteratively discretizes task and motion planning problems using batch sampling of manipulation primitives and a multi-query roadmap structure that can be conditionalized to evaluate reachability under different placements of movable objects. This structure enables the EAS planner to efficiently compute heuristics that incorporate geometric and kinematic planning constraints to give a tight estimate of the distance to the goal. Additionally, we show FFRob is probabilistically complete and has finite expected runtime. Finally, we empirically demonstrate FFRob's effectiveness on complex and diverse task and motion planning tasks including rearrangement planning and navigation among movable objects.
This paper formally presents a class of planning problems which allows non-binary state variables and parallel execution of actions. The class is proven to be tractable, and we provide a sound and complete polynomial time algorithm for planning within this class. This result means that we are getting closer to tackling realistic planning problems in sequential control, where a restricted problem representation is often sufficient, but where the size of the problems make tractability an important issue. 1 Introduction A large proportion of earlier papers about planning focus either on implementation of planners, or on representation problems, using logic or otherwise, and do not address computational issues at all. Among earlier work on planning complexity, Chapman [ 1987 ] has designed an algorithm, called TWEAK, which captures the essentials of constraint-posting nonlinear planners. TWEAK is proven correct, but does not always terminate. Chapman has proven that the class of problems...
Of all hard- and software developed for industrial control purposes, the majority is devoted to sequential, or binary valued, control and only a minor part to classical linear control. Typically, the sequential parts of the controller are invoked during startup and shut-down to bring the system into its normal operating region and into some safe standby region, respectively. Despite its importance, fairly little theoretical research has been devoted to this area, and sequential control programs are therefore still created manually without much theoretical support to obtain a systematic approach. We propose a method to create sequential control programs automatically. The main idea is to spend some effort off-line modelling the plant, and from this model generate the control strategy, that is the plan. The plant is modelled using action structures, thereby concentrating on the actions instead of the states of the plant. In general the planning problem shows exponential complexity in the...
I analyze the computational complexity of extended propositional STRIPS planning, i.e., propositional STRIPS planning augmented with a propositional domain theory for inferring additional effects. The difficulties of formalizing the extended STRIPS assumption are finessed by requiring a preference ordering of all literals; roughly, if two literals are true of the previous state, and if it is inconsistent to assert both in the next state, then the ordering indicates which literal remains true. My primary result is that planning with definite Horn domain theories is PSPACE-complete even if operators are limited to zero preconditions and one postcondition. I also analyze the complexity of planning with Krom theories. These results in combination with previous analyses are not encouraging for domain-independent planning.
Research efforts in case-based reasoning have made advances in various problem domains, but general principles and domain-independent algorithms have been slower to emerge. We seek to explore the theoretical foundations of case-based planning, in particular to characterize the fundamental tradeoffs that govern the process of plan adaptation. To do so we view the planning process as a search through a graph of partial plans: plan generation starts at the graph's root and adds constraints, plan adaptation starts at an arbitrary place in the graph and can either add or delete constraints.
This paper describes a polynomial-time, O(n
3), planning algorithm for a limited class of planning problems. Compared to previous work on complexity of algorithms for knowledge-based or logic-based planning, our algorithm achieves computational tractability, but at the expense of only applying to a significantly more limited class of problems. Our algorithm is proven correct and complete, and it always returns a minimal plan if there is a plan at all.
The ability to modify existing plans to accommodate a variety of externally imposed constraints (such as changes in the problem specification, the expected world state, or the structure of the plan) is a valuable tool for improving efficiency of planning by avoiding repetition of planning effort. In this paper, we present a theory of incremental plan modification suitable for hierarchical nonlinear planning, and describe its implementation in a system called PRIAR. In this theory, the causal and teleological structure of the plans generated by a planner are represented in the form of an explanation of correctness called the “validation structure”. Individual planning decisions are justified in terms of their relation to the validation structure. Plan modification is formalized as a process of removing inconsistencies in the validation structure of a plan when it is being reused in a new or changed planning situation. The repair of these inconsistencies involves removing unnecessary parts of the plan and adding new nonprimitive tasks to the plan to establish missing or failing validations. The result is a partially reduced plan with a consistent validation structure, which is then sent to the planner for complete reduction. We discuss this theory, present an empirical evaluation of the resulting plan modification system, and characterize the coverage, efficiency and limitations of the approach.
One kind of temporal reasoning is temporal projection—the computation of the consequences of a set of events. This problem is related to a number of other temporal reasoning tasks such as plan validation and planning. We show that one particular, simple case of temporal projection on partially ordered events turns out to be harder than previously conjectured, while planning is easy under the same restrictions. Additionally, we show that plan validation is tractable for an even larger class of plans—the unconditional plans—for which temporal projection is NP-hard, thus indicating that temporal projection may not be a necessary ingredient in planning and plan validation. Analyzing the partial decision procedure for the temporal projection problem that has been proposed by other authors, we notice that it fails to be complete for unconditional plans, a case where we have shown plan validation tractable.
In this paper, we show that in the best-known version of the blocks world (and several related versions), planning is difficult, in the sense that finding an optimal plan is NP-hard. However, the NP-hardness is not due to deleted-condition interactions, but instead due to a situation which we call a deadlock. For problems that do not contain deadlocks, there is a simple hill-climbing strategy that can easily find an optimal plan, regardless of whether or not the problem contains any deleted-condition interactions.The above result is rather surprising, since one of the primary roles of the blocks world in the planning literature has been to provide examples of deleted-condition interactions such as creative destruction and Sussman's anomaly. However, we can explain why deadlocks are hard to handle in terms of a domain-independent goal interaction which we call an enabling-condition interaction, in which an action invoked to achieve one goal has a side-effect of making it easier to achieve other goals. If different actions have different useful side-effects, then it can be difficult to determine which set of actions will produce the best plan.
The problem of achieving conjunctive goals has been central to domain-independent planning research; the nonlinear constraint-posting approach has been most successful. Previous planners of this type have been complicated, heuristic, and ill-defined. I have combined and distilled the state of the art into a simple, precise, implemented algorithm (TWEAK) which I have proved correct and complete. I analyze previous work on domain-independent conjunctive planning; in retrospect it becomes clear that all conjunctive planners, linear and nonlinear, work the same way. The efficiency and correctness of these planners depends on the traditional add/delete-list representation for actions, which drastically limits their usefulness. I present theorems that suggest that efficient general purpose planning with more expressive action representations is impossible, and suggest ways to avoid this problem.
We describe a new problem solver called STRIPS that attempts to find a sequence of operators in a space of world models to transform a given initial world model in which a given goal formula can be proven to be true. STRIPS represents a world model as an arbitrary collection in first-order predicate calculus formulas and is designed to work with models consisting of large numbers of formula. It employs a resolution theorem prover to answer questions of particular models and uses means-ends analysis to guide it to the desired goal-satisfying model.
This paper describes a class of temporal reasoning problems involving events whose order is not completely known. We examine the complexity of such problems and show that for all but trivial cases these problems are likely to be intractable. As an alternative to a complete, but potentially exponential-time decision procedure, we provide a partial decision procedure that reports useful results and runs in polynomial time. © 1990 Copyright © 1990 Morgan Kaufmann Publishers, Inc. Published by Elsevier Inc. All rights reserved.
In this paper, we examine how the complexity of domain-independent planning with strips-style operators depends on the nature of the planning operators. We show how the time complexity varies depending on a wide variety of conditions: • whether or not delete lists are allowed; • whether or not negative preconditions are al- lowed; • whether or not the predicates are restricted to be propositions (i.e., 0-ary); • whether the planning operators are given as part of the input to the planning problem, or instead are fixed in advance.
Korf (1985) presents a method for learning macro-operators and shows that the method is applicable to serially decomposable problems. In this paper I analyze the computational complexity of serial decomposability. Assuming that operators take polynomial time, it is NP-complete. to determine if an operator (or set of operators) is not serially decomposable, whether or not an ordering of state variables is given. In addition to serial decomposability of operators, a serially decomposable problem requires that the set of solvable states is closed under the operators. It is PSPACE-complete to determine if a given "finite state-variable problem" is serially decomposable. In fact, every solvable instance of a PSPACE problem can be converted to a serially decomposable problem. Furthermore, given a bound on the size of the input, every problem in PSPACE can be transformed to a problem that is nearly serially-decomposable, i.e., the problem is serially decomposable except for closure of solvable states or a unique goal state.
I describe several computational complexity results for planning, some of which identify tractable planning problems. The model of planning, called "propositional planning," is simple—conditions within operators are literals with no variables allowed. The different plan ning problems are defined by different restric- tions on the preconditions and postconditions of operators. The main results are: Proposi tional planning is PSPACE-complete, even if operators are restricted to two positive (non- negated) preconditions and two postconditions, or if operators are restricted to one postcondi tion (with any number of preconditions ). It is NP-complete if operators are restricted to positive postconditions, even if operators are restricted to one precondition and one posi tive postcondition. It is tractable in a few re stricted cases, one of which is if each opera tor is restricted to positive preconditions and one postcondition. The blocks-world problem, slightly modified, is a subproblem of this re stricted planning problem.
We present the thesis that planning can be viewed as problem-solving search using subgoals, macro-operators, and abstraction as knowledge sources. Our goal is to quantify problem-solving performance using these sources of knowledge. New results include the identification of subgoal distance as a fundamental measure of problem difficulty, a multiplicative time-space tradeoff for macro-operators, and an analysis of abstraction which concludes that abstraction hierarchies can reduce exponential problems to linear complexity.
This article describes a polynomial-time, O(n3), planning algorithm for a limited class of planning problems. Compared to previous work on complexity of algorithms for knowledge-based or logic-based planning, our algorithm achieves computational tractability, but at the expense of only applying to a significantly more limited class of problems. Our algorithm is proven correct, and it always returns a parallel minimal plan if there is a plan at all.
Cet article décrit un algorithme de planification de temps polynomial O(n3) pour une classe restreinte de problemes de planification. Contrairement aux travaux précédents sur la complexité des algorithmes pour la planification basée sur la logique ou les connaissances, l' algorithme dont il est question dans cet article permet d' obtenir la tractabilityé computationnelle; cependant, il ne peut ětre appliqué qu'à une catégorie beaucoup plus restreinte de problèmes. Cet algorithme s'est done révélé correct et il génère toujours un plan minimal en parallèle lorsqu'il y en a un.
Most tractable planning problems reported in the literature have been defined by syntactical restrictions. To better exploit the inherent structure of problems, however, it is probably necessary to study also structural restrictions on the state-transition graph. We present an exhaustive map of complexity results for state-variable planning under all combinations of our previously analysed syntactical (P, U, B, S) and structural (I, A, O) restrictions in combination with two new restrictions (A + , A Gamma ). The complexity map considers both optimal and non-optimal plan generation. This research was sponsored by the Swedish Research Council for the Engineering Sciences (TFR) under grants Dnr. 92-143 and Dnr. 93-00291. A short version of this report appears in the Proceedings of the 6th International Conference on Artificial Intelligence: Methodology, Systems, Applications (AIMSA-94), Sofia, Bulgaria, September 1994, pp. 205--213. It was also presented at the workshop on Algo...
So far, tractable planning problems reported in the literature have been defined by syntactical restrictions. To better exploit the inherent structure in problems, however, it is probably necessary to study also structural restrictions on the state-transition graph. Such restrictions are typically computationally hard to test, though, since this graph is of exponential size. Hence, we take an intermediate approach, using a statevariable model for planning and restricting the state-transition graph implicitly by restricting the transition graph for each state variable in isolation. We identify three such restrictions which are tractable to test and we present a planning algorithm which is correct and runs in polynomial time under these restrictions. Introduction Many planning problems in manufacturing and process industry are believed to be highly structured, thus allowing for efficient planning if exploiting this structure. However, a `blind' domain-independent planner...
Systematic adaption for case-based planning A catalog of complexity classes
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Computational Complexity of Reasoning about Plans Doctoral dissertation BACKSTR~M, C. 1992b. Equivalence and tractability results for SAS' planning
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A representation of coordinated actions characterized by interval valued conditions
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