Editing Search algorithm (section)

===For virtual search spaces===
{{see also|Solver}}

Algorithms for searching virtual spaces are used in the [[constraint satisfaction problem]], where the goal is to find a set of value assignments to certain variables that will satisfy specific mathematical [[equation]]s and [[inequation]]s / equalities.  They are also used when the goal is to find a variable assignment that will [[discrete optimization|maximize or minimize]] a certain function of those variables.  Algorithms for these problems include the basic [[brute-force search]] (also called  "naïve" or "uninformed" search), and a variety of [[heuristic function|heuristic]]s that try to exploit partial knowledge about the structure of this space, such as linear relaxation, constraint generation, and [[Local consistency|constraint propagation]].

An important subclass are the [[Local search (optimization)|local search]] methods, that view the elements of the search space as the [[vertex (graph theory)|vertices]] of a graph, with edges defined by a set of heuristics applicable to the case; and scan the space by moving from item to item along the edges, for example according to the [[gradient descent|steepest descent]] or [[best-first search|best-first]] criterion, or in a [[Stochastic optimization|stochastic search]].  This category includes a great variety of general [[metaheuristic]] methods, such as [[simulated annealing]], [[tabu search]], A-teams, and [[genetic programming]], that combine arbitrary heuristics in specific ways. The opposite of local search would be global search methods. This method is applicable when the search space is not limited and all aspects of the given network are available to the entity running the search algorithm.<ref>{{Cite journal|last1=Hunter|first1=A.H.|last2=Pippenger|first2=Nicholas|date=4 July 2013|title=Local versus global search in channel graphs|journal=Networks: An International Journey|arxiv=1004.2526}}</ref>

This class also includes various [[Tree traversal|tree search algorithm]]s, that view the elements as vertices of a [[tree (graph theory)|tree]], and traverse that tree in some special order.  Examples of the latter include the exhaustive methods such as [[depth-first search]] and [[breadth-first search]], as well as various heuristic-based [[Pruning (decision trees)|search tree pruning]] methods such as [[backtracking]] and [[branch and bound]].  Unlike general metaheuristics, which at best work only in a probabilistic sense, many of these tree-search methods are guaranteed to find the exact or optimal solution, if given enough time. This is called "[[Completeness (logic)|completeness]]".

Another important sub-class consists of algorithms for exploring the [[game tree]] of multiple-player games, such as [[chess]] or [[backgammon]], whose nodes consist of all possible game situations that could result from the current situation.  The goal in these problems is to find the move that provides the best chance of a win, taking into account all possible moves of the opponent(s).  Similar problems occur when humans or machines have to make successive decisions whose outcomes are not entirely under one's control, such as in [[robot]] guidance or in [[marketing]], [[finance|financial]], or [[military]] strategy planning.  This kind of problem — [[combinatorial search]] — has been extensively studied in the context of [[artificial intelligence]]. Examples of algorithms for this class are the [[Minimax|minimax algorithm]], [[alpha–beta pruning]], and the [[A* search algorithm|A* algorithm]] and its variants.