| Combinatorial Optimization |
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Combinatorial optimization algorithms are often implemented in an efficient Imperative Programming language, in an expressive Declarative Programming language such as Prolog , or some compromise, perhaps a Functional Programming language such as Haskell , or a multi-paradigm language such as LISP . A study of Computational Complexity Theory helps to motivate combinatorial optimization. Combinatorial optimization algorithms are typically concerned with problems that are NP-hard . Such problems are not believed to be efficiently solvable in general. However, the various approximations of complexity theory suggest that some instances (e.g. "small" instances) of these problems could be efficiently solved. This is indeed the case, and such instances often have important practical ramifications. INFORMAL DEFINITION The domain of combinatorial optimization is optimization problems where the set of Feasible Solution s is Discrete or can be reduced to a discrete one, and the goal is to find the best possible solution. FORMAL DEFINITION An Instance of a combinatorial optimization problem can be described in a formal way as a Tuple where
EXAMPLE PROBLEMS METHODS Heuristic search methods ( Metaheuristic algorithms) as those listed below have been used to solve problems of this type.
SEE ALSO A question of great interest concerns the efficiency of such methods, i.e. the question of whether one search method is better than the other across all types of problems. An answer to this question was provided in the 90's by the No-free-lunch Theorem . REFERENCES
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