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Local search is typically an approximation or incomplete algorithm because the search may stop even if the current best solution found is not optimal. This can happen even if termination happens because the current best solution could not be improved, as the optimal solution can lie far from the neighborhood of the solutions crossed by the ...
TSP is known to be NP-hard so an optimal solution for even a moderate size problem is difficult to solve. Instead, the greedy algorithm can be used to give a good but not optimal solution (it is an approximation to the optimal answer) in a reasonably short amount of time. The greedy algorithm heuristic says to pick whatever is currently the ...
There are also other definitions and measures. All characterizations of economic efficiency are encompassed by the more general engineering concept that a system is efficient or optimal when it maximizes desired outputs (such as utility ) given available inputs.
The beam width bounds the memory required to perform the search. Since a goal state could potentially be pruned, beam search sacrifices completeness (the guarantee that an algorithm will terminate with a solution, if one exists). Beam search is not optimal (that is, there is no guarantee that it will find the best solution).
In practice, a consumer may not always pick an optimal bundle. For example, it may require too much thought or too much time. Bounded rationality is a theory that explains this behaviour. Examples of alternatives to utility maximisation due to bounded rationality are; satisficing, elimination by aspects and the mental accounting heuristic.
This solution is optimal, although possibly not unique. The algorithm may also be stopped early, with the assurance that the best possible solution is within a tolerance from the best point found; such points are called ε-optimal. Terminating to ε-optimal points is typically necessary to ensure finite termination.
The distinction between "maximizing" and "satisficing" was first made by Herbert A. Simon in 1956. [1] [2] Simon noted that although fields like economics posited maximization or "optimizing" as the rational method of making decisions, humans often lack the cognitive resources or the environmental affordances to maximize.
Example: Consider pricing commodities. An analysis of 628 used car dealers showed that 97% relied on a form of satisficing. [11] Most set the initial price α in the middle of the price range of comparable cars and lowered the price if the car was not sold after 24 days (β) by about 3% (γ).