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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:
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.
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The journal Mathematical Programming Computation; Optima, the newsletter of the MOS, contains articles on optimization, conference information and book reviews. MPS/SIAM Series on Optimization is a series of books that is jointly published by the MOS (formerly MPS) and the Society for Industrial and Applied Mathematics (SIAM).
The solution time of a combinatorial problem can be reduced by adding new constraints, referred as symmetry breaking constraints, such that some of the symmetric solutions are eliminated from the search space while preserving the existence of at least one solution. [1] Symmetry is common in many real-life combinatorial problems.
In 2017, the journal's four editors-in-chief and editorial board resigned to protest the publisher's high prices and limited accessibility. [1] [2] They criticized Springer for "double-dipping", that is, charging large subscription fees to libraries in addition to high fees for authors who wished to make their publications open access. [3]
Classic combinatorial search problems include solving the eight queens puzzle or evaluating moves in games with a large game tree, such as reversi or chess. A study of computational complexity theory helps to motivate combinatorial search. Combinatorial search algorithms are typically concerned with problems that are NP-hard. Such problems are ...
The nurse scheduling problem (NSP), also called the nurse rostering problem (NRP), is the operations research problem of finding an optimal way to assign nurses to shifts, typically with a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative quality of valid solutions. [1]