Combinatorial optimization
In applied mathematics and theoretical computer science, combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects.
Description
In many such problems, brute-force search is not feasible. It operates on the domain of those optimization problems, in which the set of feasible solutions is discrete or can be reduced to discrete, and in which the goal is to find the best solution.
Some common problems involving combinatorial optimization are the traveling salesman problem ("TSP") and the minimum spanning tree problem ("MST").
Combinatorial optimization is a subset of mathematical optimization that is related to operations research, algorithm theory, and computational complexity theory.
It has important applications in several fields, including artificial intelligence, machine learning, mathematics, auction theory, and software engineering.
Some research literature considers discrete optimization to consist of integer programming together with combinatorial optimization (which in turn is composed of optimization problems dealing with graph structures) although all of these topics have closely intertwined research literature. It often involves determining the way to efficiently allocate resources used to find solutions to mathematical problems.
See also
Specific problems
- Assignment problem
- Closure problem
- Constraint satisfaction problem
- Cutting stock problem
- Integer programming
- Knapsack problem
- Minimum spanning tree
- Nurse scheduling problem
- Stable marriage problem
- Traveling salesman problem
- Vehicle routing problem
- Vehicle rescheduling problem
- Weapon target assignment problem
External links
- Combinatorial optimization @ Wikipedia
