Lecture

Discrete Optimization: Set Covering

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Description

This lecture introduces the set covering problem using the example of Camille completing her sticker collection after the FIFA World Cup. The goal is to select collections of stickers at a minimum cost to fill her album.

In MOOC

Optimization: principles and algorithms - Network and discrete optimization

Introduction to the mathematical concept of networks, and to two important optimization problems on networks: the transshipment problem and the shortest path problem. Short introduction to the modeling power of discrete optimization, with reference to classical problems. Introduction to the branch and bound algorithm, and the concept of cuts.

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Related concepts (16)

Discrete optimization

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 mathematical program are restricted to be discrete variables—that is, to assume only a discrete set of values, such as the integers. Three notable branches of discrete optimization are: combinatorial optimization, which refers to problems on graphs, matroids and other discrete structures integer programming constraint programming These branches are all closely intertwined however since many combinatorial optimization problems can be modeled as integer programs (e.

Combinatorial optimization

Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead.

Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

Optimization problem

In mathematics, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: 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.

Discrete mathematics

Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry.

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