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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 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:
Combinatorial optimization is the study of optimization on discrete and combinatorial objects. It started as a part of combinatorics and graph theory, but is now viewed as a branch of applied mathematics and computer science, related to operations research , algorithm theory and computational complexity theory .
The Fano matroid, derived from the Fano plane.Matroids are one of many kinds of objects studied in algebraic combinatorics. Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
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]
In most cases, the annual conference is followed by a peer reviewed special issue of an international journal, presenting a selection of the contributions presented at the meeting. Recent special issues appeared on Annals of Operations Research , [ 4 ] Optimization , [ 5 ] Journal of Scheduling , [ 6 ] Discrete Applied Mathematics , [ 7 ] [ 8 ...
Journal of Medical Biochemistry: Biochemistry: Walter de Gruyter: English: 1982–present Journal of Medical Biography: Medical Personnel: SAGE Publishing: English: 1993–present Journal of Medical Case Reports: Medicine: BioMed Central: English: 2007–present Journal of Medical Economics: Medicine: Taylor and Francis Group: English: 1998 ...
It can also be multi-objective optimization problem. Jobs may have constraints, for example a job i needs to finish before job j can be started (see workflow). Also, the objective function can be multi-criteria. [4] Set of jobs can relate to different set of machines. Deterministic (fixed) processing times or probabilistic processing times.