(definition)

**Definition:**
A computational problem in which the object is to find the best of all possible solutions. More formally, find a solution in the *feasible region* which has the minimum (or maximum) value of the *objective function*.

**See also**
*decision problem*, *optimal solution*, *optimal value*, *geometric optimization problem*, *witness*, *local optimum*, *global optimum*, Classical optimization problems: *bin packing problem*, *knapsack problem*, *cutting stock problem*, *Chinese postman problem*, *traveling salesman*, *vehicle routing problem*, *prisoner's dilemma*, Solution methods: *dynamic programming*, *metaheuristic*, *relaxation*, *simulated annealing*.

*Note:
An optimization problem asks, what is the best solution? A decision problem asks, is there a solution with a certain characteristic? For instance, the traveling salesman problem is an optimization problem, while the corresponding decision problem asks if there is a Hamiltonian cycle with a cost less than some fixed amount k. *

From Algorithms and Theory of Computation Handbook, pages 29-20 and 34-17, Copyright © 1999 by CRC Press LLC. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC.

Author: CRC-A

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 27 April 2009.

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Cite this as:

Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "optimization problem", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 27 April 2009. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/optimization.html