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. 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.
Combinatorial optimization is related to operations research, algorithm theory, and computational complexity theory. It has important applications in several fields, including artificial intelligence, machine learning, auction theory, software engineering, VLSI, applied mathematics and theoretical computer science.
^Schrijver 2003, p. 1.
and 26 Related for: Combinatorial optimization information
Combinatorialoptimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the...
Quantum optimization algorithms are quantum algorithms that are used to solve optimization problems. Mathematical optimization deals with finding the best...
science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided...
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization, some or all of the...
analogies between counting and measure. Combinatorialoptimization is the study of optimization on discrete and combinatorial objects. It started as a part of...
unconstrained binary optimization (QUBO), also known as unconstrained binary quadratic programming (UBQP), is a combinatorialoptimization problem with a wide...
stochastic optimization, so that the solution found is dependent on the set of random variables generated. In combinatorialoptimization, by searching...
by using another overlaying optimizer, a concept known as meta-optimization, or even fine-tuned during the optimization, e.g., by means of fuzzy logic...
Convex hulls have wide applications in mathematics, statistics, combinatorialoptimization, economics, geometric modeling, and ethology. Related structures...
generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from...
the principle of indifference. They also have applications in combinatorialoptimization and in analyzing the pattern of frequencies in the hydrogen spectral...
and returns to the origin city?" It is an NP-hard problem in combinatorialoptimization, important in theoretical computer science and operations research...
numerous optimization tasks involving some sort of graph, e.g., vehicle routing and internet routing. As an example, ant colony optimization is a class...
Alexander (2003), CombinatorialOptimization, Springer, ISBN 3-540-44389-4 Lee, Jon (2004), A First Course in CombinatorialOptimization, Cambridge University...
algorithm design paradigm for discrete and combinatorialoptimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists...
The knapsack problem is the following problem in combinatorialoptimization: Given a set of items, each with a weight and a value, determine which items...
fields. Matroids have found applications in geometry, topology, combinatorialoptimization, network theory, and coding theory. There are many equivalent...
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently...
Jünger, Michael; Reinelt, Gerhard (1988). "An Application of CombinatorialOptimization to Statistical Physics and Circuit Layout Design". Operations...
completing a doctoral dissertation titled "The complexity of combinatorialoptimization problems." Papadimitriou has taught at Harvard, MIT, the National...
The assignment problem is a fundamental combinatorialoptimization problem. In its most general form, the problem is as follows: The problem instance has...
Submodular and supermodular set functions are also studied in combinatorialoptimization. Many of the results in (Shapley 1971) have analogues in (Edmonds...
The European Chapter on CombinatorialOptimization (also, EURO Working Group on CombinatorialOptimization, or EWG ECCO) is a working group whose objective...