HEURISTIC Good enough is perfect

Example The most fundamental heuristic is trial and error, which can be used in everything from matching nuts and bolts to finding the values of variables in algebra problems.trial and error 2

How to Solve It Here are a few other commonly used heuristics, from George Pólya's 1945 book, How to Solve It:George PólyaHow to Solve It If you are having difficulty understanding a problem, try drawing a picture. If you can't find a solution, try assuming that you have a solution and seeing what you can derive from that ("working backward"). If the problem is abstract, try examining a concrete example. Try solving a more general problem first (the "inventor's paradox": the more ambitious plan may have more chances of success).inventor's paradox 3

The origins: bounded rationality The concept was originally introduced by Nobel laureate Herbert A. Simon. Simon's original, primary object of research was problem solving which showed that we operate within what he calls bounded rationality. Herbert A. Simonbounded rationality He coined the term "satisficing", which denotes the situation where people seek solutions or accept choices or judgments that are "good enough" for their purposes, but could be optimized.satisficing 4

"Heuristic device" "Heuristic device" is used when an entity X exists to enable understanding of, or knowledge concerning, some other entity Y. A good example is a model that, as it is never identical with what it models, is a heuristic device to enable understanding of what it models.modelit is never identical with what it models Stories, metaphors, etc., can also be termed heuristic in that sense. "Heuristic" is also often used as a noun to describe a rule- of-thumb (carpenter), procedure, or method.noun 5

Shortest paths For shortest path problems, a heuristic is a function, defined on the nodes of a search tree, which serves as an estimate of the cost of the cheapest path from that node to the goal node.shortest path problemsfunctionsearch treegoal Heuristics are used by informed search algorithms such as greedy best-first search and A* to choose the best node to explore.informed search algorithmsreedy best-first searchA* 6

A* search algorithm In computer science, A* (pronounced "A star" ( listen)) is a computer algorithm that is widely used in pathfinding and graph traversal, the process of plotting an efficiently traversable path between points, called nodes.computer sciencelisten computer algorithmpathfinding graph traversal Noted for its performance and accuracy, it enjoys widespread use.performance In practical travel-routing systems, it is generally outperformed by algorithms which can pre-process the graph to attain better performance, although other work has found A* to be superior to other approaches. 7

Greedy best-first search Greedy best-first search will choose the node that has the lowest value for the heuristic function. A* search will expand nodes that have the lowest value for, where is the (exact) cost of the path from the initial state to the current node. If is admissible, i.e., if never overestimates the costs of reaching the goal, then A* will always find an optimal solution.admissible optimal The classical problem involving heuristics is the n-puzzle. Commonly used heuristics for this problem include counting the number of misplaced tiles and finding the sum of the Manhattan distances between each block and its position in the goal configuration.n-puzzleManhattan distances 8

Effect of heuristics on computational performance In any searching problem where there are choices at each node and a depth of at the goal node, a naive searching algorithm would have to potentially search around nodes before finding a solution. Heuristics improve the efficiency of search algorithms by reducing the branching factor from to a lower constant, using a cutoff mechanism. The branching factor can be used for defining a partial order on the heuristics, such that if has a lower branch factor than for a given node of the search tree. Heuristics giving lower branching factors at every node in the search tree are preferred for the resolution of a particular problem, as they are more computationally efficient.branching factorpartial order 9

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