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Combinatorial optimization is a branch of optimization in applied mathematics and computer science, related to operations research, algorithm theory and computational complexity theory. In mathematics, optimization is the discipline which is concerned with finding the maxima and minima of functions, possibly subject to constraints. ...
Applied mathematics is a branch of mathematics that concerns itself with the application of mathematical knowledge to other domains. ...
Wikibooks Wikiversity has more about this subject: School of Computer Science Open Directory Project: Computer Science Collection of Computer Science Bibliographies Belief that title science in computer science is inappropriate Categories: Computer science ...
Operations research, operational research, or simply OR, is the use of mathematical models, statistics and algorithms to aid in decision-making. ...
Flowcharts are often used to represent algorithms. ...
Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ...
Sometimes it is called "discrete optimization", however the latter term is considered to be somewhat different. Discrete optimization is a branch of optimization in applied mathematics and computer science. ...
Informal definition
The domain of combinatorial optimization is optimization problems where the set of feasible solutions is discrete or can be reduced to a discrete one, and the goal is to find the best possible solution. In mathematics, the term optimization refers to the study of problems that have the form Given: a function f : A R from some set A to the real numbers Sought: an element x0 in A such that f(x0) ≤ f(x) for all x in A (minimization) or such that...
The word discrete comes from the Latin word discretus which means separate. ...
Formal definition An instance of a combinatorial optimization problem can be described in a formal way as a tuple (X,P,Y,f,extr) where An object is fundamental concept in object-oriented programming. ...
In mathematics, a tuple is a finite sequence of objects, that is, a list of a limited number of objects (an infinite sequence is a family). ...
- X is the solution space (on which f and P are defined)
- P is the feasibility predicate.
- Y is the set of feasible solutions.
- f is the objective function.
- extr is the extreme (usually min or max.)
In mathematics, a predicate is a relation. ...
Optimization is a branch of mathematics which is concerned with finding maxima and minima of real-valued functions. ...
Min can be: 闽 Mǐn, an abbreviation for the Chinese province of Fujian Min, a category of spoken Chinese found in Fujian and elsewhere Min, a kingdom in modern-day Fujian during the Five Dynasties and Ten Kingdoms Period Min River (Fujian) 岷 Mín, a place name in the Chinese...
A Max/MSP patch written and used by Autechre Max is a graphical development environment for music and multimedia developed and maintained by San Francisco-based software company Cycling74. ...
Examples Examples of problems are the The traveling salesman problem or travelling salesman problem (TSP), also known as the traveling salesperson problem, is a problem in discrete or combinatorial optimization. ...
Given a connected, undirected graph, a spanning tree of that graph is a subgraph which is a tree and connects all the vertices together. ...
In mathematics, linear programming (LP) problems are optimization problems in which the objective function and the constraints are all linear. ...
Methods Heuristic search methods (metaheuristic algorithms), such as A metaheuristic is an algorithmic approach to approximate optimal solutions for problems in combinatorial optimization. ...
can be used to find optimal solutions of combinatorial optimization problems. A question of great interest concerns the efficiency of such methods, i.e. the question of whether one search method is better than the other across all types of problems. An answer to this question was provided in the 90's by the no-free-lunch theorem. Local search is a metaheuristic that is commonly used for solving computationally hard problem such as the traveling salesman problem (TSP). ...
Simulated annealing (SA) is a generic probabilistic meta-algorithm for the global optimization problem, namely locating a good approximation to the global optimum of a given function in a large search space. ...
Greedy randomized adaptive search procedure - Wikipedia /**/ @import /skins-1. ...
Swarm intelligence (SI) is an artificial intelligence technique based around the study of collective behaviour in decentralised, self-organised, systems. ...
Tabu search is a mathematical optimization method, belonging to the class of local search techniques. ...
A genetic algorithm (GA) is an algorithm used to find approximate solutions to difficult-to-solve problems through application of the principles of evolutionary biology to computer science. ...
Categories: Stub | Optimization | Theorems ...
References - William J. Cook, William H. Cunningham, William R. Pulleyblank, Alexander Schrijver; Combinatorial Optimization; John Wiley & Sons; 1 edition (November 12, 1997); ISBN 047155894X.
- Christos H. Papadimitriou, and Kenneth Steiglitz; Combinatorial Optimization : Algorithms and Complexity; Dover Pubns; (paperback, Unabridged edition, July 1998) ISBN 0486402584.
Journals - Journal of Combinatorial Optimization
- Discrete Optimization
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