State-space search
State-space search is a process used in the field of computer science, including artificial intelligence (AI), in which successive configurations or states of an instance are considered, with the intention of finding a goal state with the desired property.
Problems are often modelled as a state space, a set of states that a problem can be in. The set of states forms a graph where two states are connected if there is an operation that can be performed to transform the first state into the second.
State-space search often differs from traditional computer science search methods because the state space is implicit: the typical state-space graph is much too large to generate and store in memory. Instead, nodes are generated as they are explored, and typically discarded thereafter. A solution to a combinatorial search instance may consist of the goal state itself, or of a path from some initial state to the goal state.
Representation
[edit]In state-space search, a state space is formally represented as a tuple , in which:
- is the set of all possible states;
- is the set of possible actions, not related to a particular state but regarding all the state space;
- is the function that establishes which action is possible to perform in a certain state;
- is the function that returns the state reached performing action in state ;
- is the cost of performing an action in state . In many state spaces, is a constant, but this is not always true.
Examples of state-space search algorithms
[edit]Uninformed search
[edit]According to Poole and Mackworth, the following are uninformed state-space search methods, meaning that they do not have any prior information about the goal's location.[1]
- Traditional depth-first search
- Breadth-first search
- Iterative deepening
- Lowest-cost-first search / Uniform-cost search (UCS)
Informed search
[edit]These methods take the goal's location in the form of a heuristic function.[2] Poole and Mackworth cite the following examples as informed search algorithms:
- Informed/Heuristic depth-first search
- Greedy best-first search
- A* search
See also
[edit]- State space
- State-space planning
- Branch and bound – Method for making state-space search more efficient by pruning subsets of it
References
[edit]- ^ Poole, David; Mackworth, Alan. "3.5 Uninformed Search Strategies‣ Chapter 3 Searching for Solutions ‣ Artificial Intelligence: Foundations of Computational Agents, 2nd Edition". artint.info. Retrieved 7 December 2017.
- ^ Poole, David; Mackworth, Alan. "3.6 Heuristic Search‣ Chapter 3 Searching for Solutions ‣ Artificial Intelligence: Foundations of Computational Agents, 2nd Edition". artint.info. Retrieved 7 December 2017.
- Stuart J. Russell and Peter Norvig (1995). Artificial Intelligence: A Modern Approach. Prentice Hall.