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Specific applications of search algorithms include: Problems in combinatorial optimization, such as: . The vehicle routing problem, a form of shortest path problem; The knapsack problem: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as ...
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There are many specialized problem-solving techniques and methods in fields such as science, engineering, business, medicine, mathematics, computer science, philosophy, and social organization. The mental techniques to identify, analyze, and solve problems are studied in psychology and cognitive sciences .
In mathematical optimization and computer science, heuristic (from Greek εὑρίσκω "I find, discover" [1]) is a technique designed for problem solving more quickly when classic methods are too slow for finding an exact or approximate solution, or when classic methods fail to find any exact solution in a search space.
Brute force search should not be confused with backtracking, where large sets of solutions can be discarded without being explicitly enumerated (as in the textbook computer solution to the eight queens problem above). The brute-force method for finding an item in a table – namely, check all entries of the latter, sequentially – is called ...
Classic combinatorial search problems include solving the eight queens puzzle or evaluating moves in games with a large game tree, such as reversi or chess. A study of computational complexity theory helps to motivate combinatorial search. Combinatorial search algorithms are typically concerned with problems that are NP-hard. Such problems are ...
In computer science, local search is a heuristic method for solving computationally hard optimization problems. Local search can be used on problems that can be formulated as finding a solution that maximizes a criterion among a number of candidate solutions .
Hill-climbing techniques are well-suited for optimizing over such surfaces, and will converge to the global maximum. In numerical analysis , hill climbing is a mathematical optimization technique which belongs to the family of local search .