Ad
related to: discrete optimization model
Search results
Results From The WOW.Com Content Network
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization , some or all of the variables used in a discrete optimization problem are restricted to be discrete variables —that is, to assume only a discrete set of values, such as the integers .
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. [1] [2] It is generally divided into two subfields: discrete optimization and continuous optimization.
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.
An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set. A problem with continuous variables is known as a continuous optimization, in which an optimal value from a continuous function must be found.
In discrete optimization, a special ordered set (SOS) is an ordered set of variables used as an additional way to specify integrality conditions in an optimization model. . Special order sets are basically a device or tool used in branch and bound methods for branching on sets of variables, rather than individual variables, as in ordinary mixed integer programm
In combinatorial optimization, A is some subset of a discrete space, like binary strings, permutations, or sets of integers. The use of optimization software requires that the function f is defined in a suitable programming language and connected at compilation or run time to the optimization software.
In practice, this generally requires numerical techniques for some discrete approximation to the exact optimization relationship. Alternatively, the continuous process can be approximated by a discrete system, which leads to a following recurrence relation analog to the Hamilton–Jacobi–Bellman equation:
Specifically, the likelihood function is maximized subject to the constraints imposed by the model, and expressed in terms of the additional variables that describe the model's structure. This approach requires powerful optimization software such as Artelys Knitro because of the high dimensionality of the optimization problem. Once it is solved ...