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Subfield of mathematical optimization
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the
Combinatorial_optimization
Optimization algorithms using quantum computing
Quantum optimization algorithms are quantum algorithms that are used to solve optimization problems. Mathematical optimization deals with finding the best
Quantum optimization algorithms
Quantum_optimization_algorithms
Branch of discrete mathematics
analogies between counting and measure. Combinatorial optimization is the study of optimization on discrete and combinatorial objects. It started as a part of
Combinatorics
Problem of finding the best feasible solution
science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided
Optimization_problem
Branch of mathematical optimization
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization, some or all of the
Discrete_optimization
Combinatorial optimization problem
unconstrained binary optimization (QUBO), also known as unconstrained binary quadratic programming (UBQP), is a combinatorial optimization problem with a wide
Quadratic unconstrained binary optimization
Quadratic_unconstrained_binary_optimization
Class of artificial neural networks
citation networks, molecular biology, chemistry, physics and NP-hard combinatorial optimization problems. Open source libraries implementing GNNs include PyTorch
Graph_neural_network
Mathematical optimization problem restricted to integers
An integer programming, also known as integer optimization, problem is a mathematical optimization or feasibility program in which some or all of the variables
Integer_programming
Special-purpose computer for combinatorial optimization
An Ising machine is a special-purpose computer that solves combinatorial optimization problems by mapping them onto the search for the ground state of
Ising_machine
Study of mathematical algorithms for optimization problems
generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from
Mathematical_optimization
Cycle graph with all opposite nodes linked
relaxations for the linear ordering problem". Integer Programming and Combinatorial Optimization: 8th International IPCO Conference, Utrecht, The Netherlands,
Möbius_ladder
American computer scientist and educator
research is in the design and analysis of algorithms, with work in combinatorial optimization, graph partitioning, network flow, metric embeddings, and computational
Satish_B._Rao
Population-based search algorithm
exploration of the search space. It can be used for both combinatorial optimization and continuous optimization. The only condition for the application of the bees
Bees_algorithm
Problem in combinatorial optimization
The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items
Knapsack_problem
NP-hard problem in combinatorial optimization
and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research
Travelling_salesman_problem
Smallest convex set containing a given set
Convex hulls have wide applications in mathematics, statistics, combinatorial optimization, economics, geometric modeling, and ethology. Related structures
Convex_hull
The European Chapter on Combinatorial Optimization (also, EURO Working Group on Combinatorial Optimization, or EWG ECCO) is a working group whose objective
European Chapter on Combinatorial Optimization
European_Chapter_on_Combinatorial_Optimization
Branch of geometry that studies combinatorial properties and constructive methods
geometry, combinatorial optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry, and combinatorial topology
Discrete_geometry
Sequence of locally optimal choices
choices. Greedy algorithms are often used to solve combinatorial optimization problems. If an optimization problem only depends on the partial solution of
Greedy_algorithm
Greek-American computer scientist (b. 1949)
completing a doctoral dissertation titled "The complexity of combinatorial optimization problems." Papadimitriou has taught at Harvard, MIT, the National
Christos_Papadimitriou
Principle in mathematical optimization
In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives
Duality_(optimization)
Optimization technique
stochastic optimization, so that the solution found is dependent on the set of random variables generated. In combinatorial optimization, there are many
Metaheuristic
American mathematician
author of A First Course in Combinatorial Optimization (Cambridge University Press, 2004) and A First Course in Linear Optimization (Reex Press, 2013). He
Jon_Lee_(mathematician)
Abstraction of linear independence of vectors
fields. Matroids have found applications in geometry, topology, combinatorial optimization, network theory, and coding theory. There are many equivalent
Matroid
Combinatorial optimization method for pseudo-Boolean functions
Quadratic pseudo-Boolean optimisation (QPBO) is a combinatorial optimization method for minimizing quadratic pseudo-Boolean functions in the form f ( x
Quadratic pseudo-Boolean optimization
Quadratic_pseudo-Boolean_optimization
Method for problem solving in optimization
possible. Local search is a sub-field of: Metaheuristics Stochastic optimization Optimization Fields within local search include: Hill climbing Simulated annealing
Local_search_(optimization)
Mathematician and engineer
an Israeli-American mathematician working on graph theory and combinatorial optimization. She is a 2012 MacArthur Fellow. Chudnovsky is a professor in
Maria_Chudnovsky
Shared independent set of two matroids
In combinatorial optimization, the matroid intersection problem is to find a largest common independent set in two matroids over the same ground set. If
Matroid_intersection
Czech mathematician (1897–1970)
He also made pioneering, but long-neglected, contributions to combinatorial optimization. The Gauss circle problem asks for the number of points of the
Vojtěch_Jarník
Combinatorial optimization method
Branch and cut is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some
Branch_and_cut
Optimization problem
The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet
Vehicle_routing_problem
Combinatorial optimization problem
The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has
Assignment_problem
Quantum Computing company in Boston, Massachusetts
simulating systems of Rydberg atoms and finding solutions to combinatorial optimization problems. In 2022, it released its 256-qubit machine Aquila to
QuEra
Set-to-real map with diminishing returns
Alexander (2003), Combinatorial Optimization, Springer, ISBN 3-540-44389-4 Lee, Jon (2004), A First Course in Combinatorial Optimization, Cambridge University
Submodular_set_function
Algorithmic problem in computer science
the fractional knapsack problem) is an algorithmic problem in combinatorial optimization in which the goal is to fill a container (with a fixed capacity)
Continuous_knapsack_problem
One over a whole number
the principle of indifference. They also have applications in combinatorial optimization and in analyzing the pattern of frequencies in the hydrogen spectral
Unit_fraction
In statistics, combinatorial data analysis (CDA) is the study of data sets where the order in which objects are arranged is important. CDA can be used
Combinatorial_data_analysis
Combinatorial optimization problem
assignment problem (QAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics, from
Quadratic_assignment_problem
Iterative simulation method
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
Particle_swarm_optimization
value). Optimization of this objective is carried out using some form of discrete or combinatorial optimization. Most campaign creatives are optimized statically
Dynamic_creative_optimization
Optimization problem in computer science
Talent scheduling is a combinatorial optimization problem in computer science and operations research. Consider a scenario where multiple films are to
Talent_scheduling
Algorithmic optimization method
In the design and analysis of algorithms for combinatorial optimization, parametric search is a technique invented by Nimrod Megiddo in 1983 for transforming
Parametric_search
American/Canadian mathematician and computer scientist
life. He has made fundamental contributions to the fields of combinatorial optimization, polyhedral combinatorics, discrete mathematics and the theory
Jack_Edmonds
Polynomial-time algorithm for the assignment problem
The Hungarian algorithm or Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated
Hungarian_algorithm
American mathematician (born 1950)
academic work has focused on mathematical optimization, particularly integer programming and combinatorial optimization. He served as program chair of the International
Gérard_Cornuéjols
Algorithmic paradigm for constraint satisfaction or enumeration problems
convenient technique for parsing, for the knapsack problem and other combinatorial optimization problems. It is also the program execution strategy used in the
Backtracking
Optimization by removing non-optimal solutions to subproblems
algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists
Branch_and_bound
Optimization algorithm
numerous optimization tasks involving some sort of graph, e.g., vehicle routing and internet routing. As an example, ant colony optimization is a class
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Unproven computational hardness assumption
Gerhard (2003), "Exact algorithms for NP-hard problems: A survey", Combinatorial Optimization — Eureka, You Shrink! (PDF), Lecture Notes in Computer Science
Exponential_time_hypothesis
Partition of a graph's nodes into 2 disjoint subsets
23–28. Korte, B. H.; Vygen, Jens (2008), "8.6 Gomory–Hu Trees", Combinatorial Optimization: Theory and Algorithms, Algorithms and Combinatorics, vol. 21
Cut_(graph_theory)
Game where groups of players may enforce cooperative behaviour
Submodular and supermodular set functions are also studied in combinatorial optimization. Many of the results in (Shapley 1971) have analogues in (Edmonds
Cooperative_game_theory
System that regulates the formation of blocks on a blockchain
original on 2016-08-26. Retrieved 2007-11-25. Fitzi, Matthias. "Combinatorial Optimization via Proof-of-Useful-Work" (PDF). IACR conference Crypto 2022.
Proof_of_work
German mathematician (born 1948)
September 1948) is a German mathematician known for his research on combinatorial optimization, polyhedral combinatorics, and operations research. From 1991
Martin_Grötschel
In the field of mathematics called combinatorial optimization, the method of symmetry-breaking constraints can be used to take advantage of symmetries
Symmetry-breaking_constraints
Variant of the traveling salesman problem
salesman problem (bottleneck TSP) is a problem in discrete or combinatorial optimization. The problem is to find the Hamiltonian cycle (visiting each node
Bottleneck traveling salesman problem
Bottleneck_traveling_salesman_problem
searched or some type of average. Brute-force search Combinatorial explosion Combinatorial optimization Search algorithm State space search Russell and Norvig
Combinatorial_search
Concept in integral mathematics
performed on methods for finding these facets for different types of combinatorial optimization problems, under the framework of polyhedral combinatorics. The
Linear_programming_relaxation
Set of edges without common vertices
the article on matching polynomials. A fundamental problem in combinatorial optimization is finding a maximum matching. This problem has various algorithms
Matching_(graph_theory)
Subfield of mathematical optimization
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently
Convex_optimization
Finding shortest walks through all graph edges
In graph theory and combinatorial optimization, Guan's route problem, the Chinese postman problem, postman tour or route inspection problem is to find
Chinese_postman_problem
In combinatorial optimization, A is some subset of a discrete space, like binary strings, permutations, or sets of integers. The use of optimization software
List_of_optimization_software
Mathematical combinatorial optimization method
In applied mathematics, branch and price is a method of combinatorial optimization for solving integer linear programming (ILP) and mixed integer linear
Branch_and_price
Mathematical problem in operations research
pieces of specified sizes while minimizing material wasted. It is an optimization problem in mathematics that arises from applications in industry. In
Cutting_stock_problem
Computational problem in graph theory
In graph theory and combinatorial optimization, a closure of a directed graph is a set of vertices C, such that no edges leave C. The closure problem is
Closure_problem
American computer scientist
and Circuit Lower Bounds". Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International
Russell_Impagliazzo
Equivalence of optimization problems
Kenneth Steiglitz (1998). "6.1 The Max-Flow, Min-Cut Theorem". Combinatorial Optimization: Algorithms and Complexity. Dover. pp. 120–128. ISBN 0-486-40258-4
Max-flow_min-cut_theorem
Choosing the fewest coins to make a given amount of money
The change-making problem addresses the question of finding the minimum number of coins (of certain denominations) that add up to a given amount of money
Change-making_problem
Overview of and topical guide to combinatorics
Probabilistic combinatorics Topological combinatorics Coding theory Combinatorial optimization Combinatorics and dynamical systems Combinatorics and physics
Outline_of_combinatorics
Problem in graph theory
Alberto; Protasi, Marco (2003), Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties, Springer. Maximum
Maximum_cut
Belgian-American mathematician
Massachusetts Institute of Technology working in discrete mathematics and combinatorial optimization at CSAIL and MIT Operations Research Center. Goemans earned his
Michel_Goemans
Disproved conjecture in network flow theory
In combinatorial optimization, the Dinitz–Garg–Goemans conjecture, also called Goemans' conjecture or the cost conjecture, is a statement about single-source
Dinitz–Garg–Goemans conjecture
Dinitz–Garg–Goemans_conjecture
List of concepts in artificial intelligence
combined with global search, and can be used for both combinatorial optimization and continuous optimization. The only condition for the application of the bees
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
German mathematician and computer scientist (1938–2025)
scientist, a professor at the University of Bonn and an expert in combinatorial optimization. Korte earned his doctorate (Doctor rerum naturalium) from the
Bernhard_Korte
On short connecting nets with added points
Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization. While Steiner tree problems may be formulated in a number of
Steiner_tree_problem
Mathematical concept
multiattribute optimization) is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously
Multi-objective_optimization
German computer scientist (born 1971)
mathematical image, partial differential equations, convex and combinatorial optimization, machine learning and statistical inference. Cremers received
Daniel_Cremers
Dutch mathematician and computer scientist
and László Lovász on applications of the ellipsoid method to combinatorial optimization; he won the same prize in 2003 (shared with Satoru Iwata, Lisa
Alexander_Schrijver
Combinatorial optimization problem
metric k-center problem or vertex k-center problem is a classical combinatorial optimization problem studied in theoretical computer science that is NP-hard
Metric_k-center
Type of optimization heuristic
Extremal optimization (EO) is an optimization heuristic inspired by the Bak–Sneppen model of self-organized criticality from the field of statistical physics
Extremal_optimization
Integer matrices with +1 or −1 determinant; invertible over the integers. GL_n(Z)
matrices are extremely important in polyhedral combinatorics and combinatorial optimization since they give a quick way to verify that a linear program is
Unimodular_matrix
Family of numerical optimization methods
of optimization methods that sample from a hypersphere surrounding the current position. Random optimization is a related family of optimization methods
Pattern_search_(optimization)
Indian-American computer scientist
include approximation algorithms, hardness of approximation, combinatorial optimization, and sublinear algorithms. Khanna received his undergraduate degrees
Sanjeev_Khanna
Mexican-American mathematician
Mathematical Society "for contributions to discrete geometry and combinatorial optimization as well as for service to the profession, including mentoring
Jesús_A._De_Loera
Combinatorial algorithm
In combinatorial optimization, Lin–Kernighan is one of the best heuristics for solving the symmetric travelling salesman problem.[citation needed] It belongs
Lin–Kernighan_heuristic
German mathematician (1941–2014)
May 2014) was a German mathematician who worked with linear and combinatorial optimization. He and Ellis L. Johnson won the John von Neumann Theory Prize
Manfred_W._Padberg
Czech-Canadian mathematician
published extensively on topics in graph theory, combinatorics, and combinatorial optimization. Chvátal was born in 1946 in Prague and educated in mathematics
Václav_Chvátal
Subfield of convex optimization
field of optimization which is of growing interest for several reasons. Many practical problems in operations research and combinatorial optimization can be
Semidefinite_programming
Metaheuristic method for optimization problems
1997, is a metaheuristic method for solving a set of combinatorial optimization and global optimization problems. It explores distant neighborhoods of the
Variable_neighborhood_search
Computing company founded in 2014
uses for quantum computing is combinatorial optimization, as its applications extend to logistics, supply chain optimization, and route planning. In 2023
Quantinuum
Method of mathematical optimization
problem being optimized, which means DE does not require the optimization problem to be differentiable, as is required by classic optimization methods such
Differential_evolution
Mathematical optimization theory
Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought
Robust_optimization
In combinatorial optimization, a field within mathematics, the linear bottleneck assignment problem (LBAP) is similar to the linear assignment problem
Linear bottleneck assignment problem
Linear_bottleneck_assignment_problem
Compiler that optimizes generated code
equivalent code optimized for some aspect. Optimization is limited by a number of factors. Theoretical analysis indicates that some optimization problems are
Optimizing_compiler
Weighted tree representing s-t cuts of a graph
In combinatorial optimization, the Gomory–Hu tree of an undirected graph with capacities is a weighted tree that represents the minimum s-t cuts for all
Gomory–Hu_tree
Generalization of linear assignment problem from two to multiple dimensions
The multidimensional assignment problem (MAP) is a fundamental combinatorial optimization problem which was introduced by William Pierskalla. This problem
Multidimensional assignment problem
Multidimensional_assignment_problem
Heuristic algorithm for finding partitions of graphs
The Kernighan–Lin algorithm is a heuristic algorithm for finding partitions of graphs. The algorithm has important practical application in the layout
Kernighan–Lin_algorithm
implementations of common data structures and algorithms with focus on combinatorial optimization tasks connected mainly with graphs and networks. The library is
LEMON_(C++_library)
Topics referred to by the same term
Combinatorial principles, combinatorial methods used in combinatorics, a branch of mathematics Combinatorial optimization, combinatorial methods in applied mathematics
Combinatorial_method
International evolutionary computation event
Invited speakers were José Antonio Lozano (talk on The Essence of Combinatorial Optimization Problems, video available on) and Roberto Serra (Dynamically Critical
EvoStar
Overview of and topical guide to algorithms
Local search (optimization) Hill climbing Tabu search Genetic algorithm Ant colony optimization algorithms Particle swarm optimization Evolutionary algorithm
Outline_of_algorithms
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