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Artificial intelligence |
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**Automated planning and scheduling**, sometimes denoted as simply **AI planning**,^{ [1] } is a branch of artificial intelligence that concerns the realization of strategies or action sequences, typically for execution by intelligent agents, autonomous robots and unmanned vehicles. Unlike classical control and classification problems, the solutions are complex and must be discovered and optimized in multidimensional space. Planning is also related to decision theory.

In computer science, **artificial intelligence** (**AI**), sometimes called **machine intelligence**, is intelligence demonstrated by machines, in contrast to the **natural intelligence** displayed by humans. Colloquially, the term "artificial intelligence" is often used to describe machines that mimic "cognitive" functions that humans associate with the human mind, such as "learning" and "problem solving".

**Strategy** is a high level plan to achieve one or more goals under conditions of uncertainty. In the sense of the "art of the general," which included several subsets of skills including tactics, siegecraft, logistics etc., the term came into use in the 6th century C.E. in East Roman terminology, and was translated into Western vernacular languages only in the 18th century. From then until the 20th century, the word "strategy" came to denote "a comprehensive way to try to pursue political ends, including the threat or actual use of force, in a dialectic of wills" in a military conflict, in which both adversaries interact.

In artificial intelligence, an **intelligent agent** (**IA**) refers to an autonomous entity which acts, directing its activity towards achieving goals, upon an environment using observation through sensors and consequent actuators. Intelligent agents may also learn or use knowledge to achieve their goals. They may be very simple or very complex. A reflex machine, such as a thermostat, is considered an example of an intelligent agent.

- Overview
- Domain independent planning
- Planning domain modelling languages
- Algorithms for planning
- Classical planning
- Reduction to other problems
- Temporal planning
- Probabilistic planning
- Preference-based planning
- Conditional planning
- Deployment of planning systems
- See also
- References
- Further reading
- External links

In known environments with available models, planning can be done offline. Solutions can be found and evaluated prior to execution. In dynamically unknown environments, the strategy often needs to be revised online. Models and policies must be adapted. Solutions usually resort to iterative trial and error processes commonly seen in artificial intelligence. These include dynamic programming, reinforcement learning and combinatorial optimization. Languages used to describe planning and scheduling are often called action languages.

**Trial and error** is a fundamental method of problem solving. It is characterised by repeated, varied attempts which are continued until success, or until the practicer stops trying.

**Dynamic programming** is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively. Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have optimal substructure.

**Reinforcement learning** (**RL**) is an area of machine learning concerned with how software agents ought to take actions in an environment so as to maximize some notion of cumulative reward. Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning.

Given a description of the possible initial states of the world, a description of the desired goals, and a description of a set of possible actions, the planning problem is to synthesise a plan that is guaranteed (when applied to any of the initial states) to generate a state which contains the desired goals (such a state is called a goal state).

The difficulty of planning is dependent on the simplifying assumptions employed. Several classes of planning problems can be identified depending on the properties the problems have in several dimensions.

- Are the actions deterministic or nondeterministic? For nondeterministic actions, are the associated probabilities available?
- Are the state variables discrete or continuous? If they are discrete, do they have only a finite number of possible values?
- Can the current state be observed unambiguously? There can be full observability and partial observability.
- How many initial states are there, finite or arbitrarily many?
- Do actions have a duration?
- Can several actions be taken concurrently, or is only one action possible at a time?
- Is the objective of a plan to reach a designated goal state, or to maximize a reward function?
- Is there only one agent or are there several agents? Are the agents cooperative or selfish? Do all of the agents construct their own plans separately, or are the plans constructed centrally for all agents?

The simplest possible planning problem, known as the Classical Planning Problem, is determined by:

- a unique known initial state,
- durationless actions,
- deterministic actions,
- which can be taken only one at a time,
- and a single agent.

Since the initial state is known unambiguously, and all actions are deterministic, the state of the world after any sequence of actions can be accurately predicted, and the question of observability is irrelevant for classical planning.

Further, plans can be defined as sequences of actions, because it is always known in advance which actions will be needed.

With nondeterministic actions or other events outside the control of the agent, the possible executions form a tree, and plans have to determine the appropriate actions for every node of the tree.

Discrete-time Markov decision processes (MDP) are planning problems with:

A **Markov decision process** (**MDP**) is a discrete time stochastic control process. It provides a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker. MDPs are useful for studying optimization problems solved via dynamic programming and reinforcement learning. MDPs were known at least as early as the 1950s; a core body of research on Markov decision processes resulted from Ronald Howard's 1960 book, *Dynamic Programming and Markov Processes*. They are used in many disciplines, including robotics, automatic control, economics and manufacturing. The name of MDPs comes from the Russian mathematician Andrey Markov.

- durationless actions,
- nondeterministic actions with probabilities,
- full observability,
- maximization of a reward function,
- and a single agent.

When full observability is replaced by partial observability, planning corresponds to partially observable Markov decision process (POMDP).

A **partially observable Markov decision process** (**POMDP**) is a generalization of a Markov decision process (MDP). A POMDP models an agent decision process in which it is assumed that the system dynamics are determined by an MDP, but the agent cannot directly observe the underlying state. Instead, it must maintain a probability distribution over the set of possible states, based on a set of observations and observation probabilities, and the underlying MDP.

If there are more than one agent, we have multi-agent planning, which is closely related to game theory.

In computer science **multi-agent planning** involves coordinating the resources and activities of multiple "agents".

**Game theory** is the study of mathematical models of strategic interaction in between rational decision-makers. It has applications in all fields of social science, as well as in logic and computer science. Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

In AI planning, planners typically input a domain model (a description of a set of possible actions which model the domain) as well as the specific problem to be solved specified by the initial state and goal, in contrast to those in which there is no input domain specified. Such planners are called "domain independent" to emphasis the fact that they can solve planning problems from a wide range of domains. Typical examples of domains are block stacking, logistics, workflow management, and robot task planning. Hence a single domain independent planner can be used to solve planning problems in all these various domains. On the other hand, a route planner is typical of a domain specific planner.

The most commonly used languages for representing planning domains and specific planning problems, such as STRIPS and PDDL for Classical Planning, are based on state variables. Each possible state of the world is an assignment of values to the state variables, and actions determine how the values of the state variables change when that action is taken. Since a set of state variables induce a state space that has a size that is exponential in the set, planning, similarly to many other computational problems, suffers from the curse of dimensionality and the combinatorial explosion.

The **Stanford****Research****Institute****Problem****Solver**, known by its acronym **STRIPS**, is an automated planner developed by Richard Fikes and Nils Nilsson in 1971 at SRI International. The same name was later used to refer to the formal language of the inputs to this planner. This language is the base for most of the languages for expressing automated planning problem instances in use today; such languages are commonly known as action languages. This article only describes the language, not the planner.

The **Planning Domain Definition Language** (**PDDL**) is an attempt to standardize Artificial Intelligence (AI) planning languages. It was first developed by Drew McDermott and his colleagues in 1998 mainly to make the 1998/2000 International Planning Competition (IPC) possible, and then evolved with each competition. *"The adoption of a common formalism for describing planning domains fosters far greater reuse of research and allows more direct comparison of systems and approaches, and therefore supports faster progress in the field. A common formalism is a compromise between expressive power and the progress of basic research. The role of a common formalism as a communication medium for exchange demands that it is provided with a clear semantics."*

**The curse of dimensionality** refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming.

An alternative language for describing planning problems is that of hierarchical task networks, in which a set of tasks is given, and each task can be either realized by a primitive action or decomposed into a set of other tasks. This does not necessarily involve state variables, although in more realistic applications state variables simplify the description of task networks.

- forward chaining state space search, possibly enhanced with heuristics
- backward chaining search, possibly enhanced by the use of state constraints (see STRIPS, graphplan)
- partial-order planning

- reduction to the propositional satisfiability problem (satplan).
- reduction to Model checking - both are essentially problems of traversing state spaces, and the classical planning problem corresponds to a subclass of model checking problems.

Temporal planning can be solved with methods similar to classical planning. The main difference is, because of the possibility of several, temporally overlapping actions with a duration being taken concurrently, that the definition of a state has to include information about the current absolute time and how far the execution of each active action has proceeded. Further, in planning with rational or real time, the state space may be infinite, unlike in classical planning or planning with integer time. Temporal planning is closely related to scheduling problems. Temporal planning can also be understood in terms of timed automata.

Probabilistic planning can be solved with iterative methods such as value iteration and policy iteration, when the state space is sufficiently small. With partial observability, probabilistic planning is similarly solved with iterative methods, but using a representation of the value functions defined for the space of beliefs instead of states.

In preference-based planning, the objective is not only to produce a plan but also to satisfy user-specified preferences. A difference to the more common reward-based planning, for example corresponding to MDPs, preferences don't necessarily have a precise numerical value.

Deterministic planning was introduced with the STRIPS planning system, which is a hierarchical planner. Action names are ordered in a sequence and this is a plan for the robot. Hierarchical planning can be compared with an automatic generated behavior tree.^{ [2] } The disadvantage is, that a normal behavior tree is not so expressive like a computer program. That means, the notation of a behavior graph contains action commands, but no loops or if-then-statements. Conditional planning overcomes the bottleneck and introduces an elaborated notation which is similar to a control flow, known from other programming languages like Pascal. It is very similar to program synthesis, that means a planner generates sourcecode which can be executed by an interpreter.^{ [3] }

An early example of a conditional planner is “Warplan-C” which was introduced in the mid 1970s.^{ [4] } Until now, the question was not answered what the difference is between a normal sequence and a complicated plan, which contains if-then-statements. It has to do with uncertainty at runtime of a plan. The idea is, that a plan can react to sensor signals which are unknown for the planner. The planner generates two choices in advance. For example, if an object was detected, then action A is executed, if an object is missing, then action B is executed.^{ [5] } A major advantage of conditional planning is the ability to handle partial plans.^{ [6] } An agent is not forced to plan everything from start to finish but can divide the problem into chunks. This helps to reduce the state space and solves much more complex problems.

We speak of "contingent planning" when the environment is observable through sensors, which can be at faulty. It is thus a situation where the planning agent acts under incomplete information. For a contingent planning problem, a plan is no longer a sequence of actions but a decision tree because each step of the plan is represented by a set of states rather than a single perfectly observable state, as in the case of classical planning.^{ [7] } The selected actions depend on the state of the system. For example, if it rains, the agent chooses to take the umbrella, and if it doesn't, they may choose not to take it.

Mikael L. Littman showed in 1998 that with branching actions, the planning problem becomes EXPTIME-complete.^{ [8] }^{ [9] } A particular case of contiguous planning is represented by FOND problems - for "fully-observable and non-deterministic". If the goal is specified in LTLf (linear time logic on finite trace) then the problem is always EXPTIME-complete^{ [10] } and 2EXPTIME-complete if the goal is specified with LDLf.

Conformant planning is when the agent is uncertain about the state of the system, and it cannot make any observations. The agent then has beliefs about the real world, but cannot verify them with sensing actions, for instance. These problems are solved by techniques similar to those of classical planning,^{ [11] }^{ [12] } but where the state space is exponential in the size of the problem, because of the uncertainty about the current state. A solution for a conformant planning problem is a sequence of actions. Haslum and Jonsson have demonstrated that the problem of conformant planning is EXPSPACE-complete,^{ [13] } and 2EXPTIME-complete when the initial situation is uncertain, and there is non-deternimism in the actions outcomes.^{ [9] }

- The Hubble Space Telescope uses a short-term system called SPSS and a long-term planning system called Spike.

- Action description language
- Actor model
- Applications of artificial intelligence
- Constraint satisfaction problem
- Reactive planning
- Scheduling (computing)
- Strategy (game theory)

- Lists

In computational complexity theory, **NP** is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time.

In computational complexity theory, the complexity class **EXPTIME** is the set of all decision problems that have **exponential runtime**, i.e., that are solvable by a deterministic Turing machine in O(2^{p}) time, where *p*(*n*) is a polynomial function of *n*.

In computational complexity theory, **DTIME** is the computational resource of computation time for a deterministic Turing machine. It represents the amount of time that a "normal" physical computer would take to solve a certain computational problem using a certain algorithm. It is one of the most well-studied complexity resources, because it corresponds so closely to an important real-world resource.

In computational complexity theory, **SL** is the complexity class of problems log-space reducible to **USTCON**, which is the problem of determining whether there exists a path between two vertices in an undirected graph, otherwise described as the problem of determining whether two vertices are in the same connected component. This problem is also called the **undirected reachability problem**. It does not matter whether many-one reducibility or Turing reducibility is used. Although originally described in terms of symmetric Turing machines, that equivalent formulation is very complex, and the reducibility definition is what is used in practice.

In artificial intelligence, **hierarchical task network (HTN) planning** is an approach to automated planning in which the dependency among actions can be given in the form of hierarchically structured networks.

In computational complexity theory, **NL-complete** is a complexity class containing the languages that are complete for **NL**, the class of decision problems that can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space. The NL-complete languages are the most "difficult" or "expressive" problems in **NL**. If a method exists for solving any one of the NL-complete problems in logarithmic memory space, then **NL** = **L**.

In artificial intelligence, **action description language** (**ADL**) is an automated planning and scheduling system in particular for robots. It is considered an advancement of STRIPS. Edwin Pednault proposed this language in 1987. It is an example of an action language.

In computational complexity theory, the complexity class **2-EXPTIME** is the set of all decision problems solvable by a deterministic Turing machine in O(2^{2p}) time, where *p*(*n*) is a polynomial function of *n*.

A **hyper-heuristic** is a heuristic search method that seeks to automate, often by the incorporation of machine learning techniques, the process of selecting, combining, generating or adapting several simpler heuristics to efficiently solve computational search problems. One of the motivations for studying hyper-heuristics is to build systems which can handle classes of problems rather than solving just one problem.

In probability theory, a **Markov model** is a stochastic model used to model randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it. Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable. For this reason, in the fields of predictive modelling and probabilistic forecasting, it is desirable for a given model to exhibit the Markov property.

In artificial intelligence and computer programming, **state space planning** is a process used in designing programs to search for data or solutions to problems. In a computer algorithm that searches a data structure for a piece of data, for example a program that looks up a word in a computer dictionary, the *state space* is a collective term for all the data to be searched. Similarly, artificial intelligence programs often employ a process of searching through a finite universe of possible procedures for reaching a goal, to find a procedure or the best procedure to achieve the goal. The universe of possible solutions to be searched is called the state space. *State space planning* is the process of deciding which parts of the state space the program will search, and in what order.

**Partial-order planning** is an approach to automated planning that maintains a partial ordering between actions and only commits ordering between actions when forced to i.e, ordering of actions is partial.Also this planning doesn't specify which action will come out first when two actions are processed. By contrast, **total-order planning** maintains a total ordering between all actions at every stage of planning. Given a problem in which some sequence of actions is required in order to achieve a goal, a **partial-order plan** specifies all actions that need to be taken, but specifies an ordering between actions only where necessary.

In artificial intelligence, **preference-based planning** is a form of automated planning and scheduling which focuses on producing plans that additionally satisfy as many user-specified preferences as possible. In many problem domains, a task can be accomplished by various sequences of actions. These plans can vary in quality: there can be many ways to solve a problem but one generally prefers a way that is, e.g., cost-effective, quick and safe.

**Action model learning** is an area of machine learning concerned with creation and modification of software agent's knowledge about *effects* and *preconditions* of the *actions* that can be executed within its *environment*. This knowledge is usually represented in logic-based action description language and used as the input for automated planners.

This **glossary of artificial intelligence** terms is about artificial intelligence, its sub-disciplines, and related fields.

- ↑ Ghallab, Malik; Nau, Dana S.; Traverso, Paolo (2004),
*Automated Planning: Theory and Practice*, Morgan Kaufmann, ISBN 1-55860-856-7 - ↑ Neufeld, Xenija and Mostaghim, Sanaz and Sancho-Pradel, Dario and Brand, Sandy (2017). "Building a Planner: A Survey of Planning Systems Used in Commercial Video Games".
*IEEE Transactions on Games*. IEEE.CS1 maint: multiple names: authors list (link) - ↑ Sanelli, Valerio and Cashmore, Michael and Magazzeni, Daniele and Iocchi, Luca (2017).
*Short-term human robot interaction through conditional planning and execution*. Proc. of International Conference on Automated Planning and Scheduling (ICAPS).CS1 maint: multiple names: authors list (link) - ↑ Peot, Mark A and Smith, David E (1992).
*Conditional nonlinear planning*(PDF). Artificial Intelligence Planning Systems. Elsevier. pp. 189–197.CS1 maint: multiple names: authors list (link) - ↑ Karlsson, Lars (2001).
*Conditional progressive planning under uncertainty*(PDF). IJCAI. pp. 431–438. - ↑ Liu, Daphne Hao (2008).
*A survey of planning in intelligent agents: from externally motivated to internally motivated systems*(Technical report). Technical Report TR-2008-936, Department of Computer Science, University of Rochester. - ↑ Alexandre Albore; Hector Palacios; Hector Geffner.
*A Translation-Based Approach to Contingent Planning*. International Joint Conference of Artificial Intelligence (IJCAI). Pasadena, CA: AAAI. - ↑ Littman, Michael L. (1997).
*Probabilistic Propositional Planning: Representations and Complexity*. Fourteenth National Conference on Artificial Intelligence. MIT Press. pp. 748–754. Retrieved 2019-02-10. - 1 2 Jussi Rintanen (2004).
*Complexity of Planning with Partial Observability*(PDF). Int. Conf. Automated Planning and Scheduling. AAAI. - ↑ De Giacomo, Giuseppe; Rubin, Sasha (2018).
*Automata-Theoretic Foundations of FOND Planning for LTLf and LDLf Goals*. IJCAI. Retrieved 2018-07-17. - ↑ Palacios, Hector; Geffner, Hector (2009). "Compiling uncertainty away in conformant planning problems with bounded width".
*Journal of Artificial Intelligence Research*.**35**: 623–675. - ↑ Albore, Alexandre; Ramírez, Miquel; Geffner, Hector (2011).
*Effective heuristics and belief tracking for planning with incomplete information*. Twenty-First International Conference on Automated Planning and Scheduling (ICAPS). - ↑ Haslum, Patrik; Jonsson, Peter (2000). "Some Results on the Complexity of Planning with Incomplete Information".
*Recent Advances in AI Planning*. Lecture Notes in Computer Science. Springer Berlin Heidelberg: 308–318. doi:10.1007/10720246_24. ISBN 9783540446576 . Retrieved 2019-02-10.

- Vlahavas, I. "Planning and Scheduling".
*EETN*. Archived from the original on 2013-12-22.Cite uses deprecated parameter`|deadurl=`

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