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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 that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment.
It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem, the vehicle routing problem and the ring star problem [1] are three generalizations of TSP.
In combinatorial optimization, a field within mathematics, the linear bottleneck assignment problem (LBAP) is similar to the linear assignment problem. [1] In plain words the problem is stated as follows: There are a number of agents and a number of tasks.
The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.
The multidimensional assignment problem (MAP) is a fundamental combinatorial optimization problem which was introduced by William Pierskalla. [1] This problem can be seen as a generalization of the linear assignment problem. [2] In words, the problem can be described as follows:
Branch and bound (BB, B&B, or BnB) is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical ...
The word tabu comes from the Tongan word to indicate things that cannot be touched because they are sacred. [4]Tabu search is a metaheuristic algorithm that can be used for solving combinatorial optimization problems (problems where an optimal ordering and selection of options is desired).