Editing Combinatorial optimization (section)

{{Short description|Subfield of mathematical optimization}}
[[File:Minimum spanning tree.svg|thumb|300px|right|A [[minimum spanning tree]] of a weighted [[planar graph]]. Finding a minimum spanning tree is a common problem involving combinatorial optimization.]]

'''Combinatorial optimization''' is a subfield of [[mathematical optimization]]  <!-- synonymous or subfield?: '''discrete optimization'''{{Citation needed|date=May 2012}}--> that consists of finding an optimal object from a [[finite set]] of objects,<ref>{{harvnb|Schrijver|2003|p=1}}.</ref> where the set of [[Candidate solution|feasible solutions]] is [[Discrete set|discrete]] or can be reduced to a discrete set. Typical combinatorial optimization problems are the [[travelling salesman problem]] ("TSP"), the [[minimum spanning tree|minimum spanning tree problem]] ("MST"), and the [[knapsack problem]]. In many such problems, such as the ones previously mentioned, [[exhaustive search]] is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or [[approximation algorithm]]s must be resorted to instead.

Combinatorial optimization is related to [[operations research]], [[algorithm|algorithm theory]], and [[computational complexity theory]]. It has important applications in several fields, including [[artificial intelligence]], [[machine learning]], [[auction theory]], [[software engineering]], [[VLSI]], [[applied mathematics]] and [[theoretical computer science]].