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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
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
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
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
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
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
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
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
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
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
Quantum Computing company in Boston, Massachusetts
simulating systems of Rydberg atoms and finding solutions to combinatorial optimization problems. QuEra Computing was founded by Mikhail Lukin, Vladan
QuEra
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
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)
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
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
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
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
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
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
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
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
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
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
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
Mathematical concept
Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute
Multi-objective_optimization
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
combined with global search, and can be used for both combinatorial optimization and continuous optimization. The only condition for the application of the bees
Bees_algorithm
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
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)
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
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
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
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
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
Indian-American computer scientist
include approximation algorithms, hardness of approximation, combinatorial optimization, and sublinear algorithms. Khanna received his undergraduate degrees
Sanjeev_Khanna
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
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
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
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
issues in tree alignment. Combinatorial optimization is a good strategy to solve MSA problems. The idea of combinatorial optimization strategy is to transform
Tree_alignment
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
Upper bound on a graph's Shannon capacity
Alexander (1981), "The ellipsoid method and its consequences in combinatorial optimization" (PDF), Combinatorica, 1 (2): 169–197, doi:10.1007/BF02579273
Lovász_number
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
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
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
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
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
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
Branch of artificial intelligence
These include dynamic programming, reinforcement learning and combinatorial optimization. Languages used to describe planning and scheduling are often
Automated planning and scheduling
Automated_planning_and_scheduling
American professor of operations research
is an American operations researcher and academic who studies combinatorial optimization, and is known for his work on sports scheduling, transportation
Michael_Trick
searched or some type of average. Brute-force search Combinatorial explosion Combinatorial optimization Search algorithm State space search Russell and Norvig
Combinatorial_search
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
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
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
Problem in graph theory
Alberto; Protasi, Marco (2003), Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties, Springer. Maximum
Maximum_cut
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)
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
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
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
Node labeling problem in graph theory
and Combinatorial Optimization: Algorithms and Techniques, 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems
Graph_bandwidth
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)
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
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
Subfield of computer science and mathematics
Computer Science (ITCS) Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX) Workshop on Randomization and Computation (RANDOM)
Theoretical_computer_science
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
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
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
Optimal network design is a problem in combinatorial optimization. It is an abstract representation of the problem faced by states and municipalities when
Optimal_network_design
Class of computational problems
In combinatorial optimization, network flow problems are a class of computational problems in which the input is a flow network (a graph with numerical
Network_flow_problem
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
Problem of grouping into triples
problem SP1 in Appendix A.3.1. Korte, Bernhard; Vygen, Jens (2006), Combinatorial Optimization: Theory and Algorithms (3rd ed.), Springer, Section 15.5. Papadimitriou
3-dimensional_matching
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
Iterative method for minimizing convex functions
data, but not on the number of rows, so it remained important in combinatorial optimization theory for many years. Only in the 21st century have interior-point
Ellipsoid_method
Israeli computer scientist
scientist specializing in combinatorial optimization, including knapsack problems, interval scheduling, and the optimization of submodular set functions
Hadas_Shachnai
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
Israeli mathematician
known for his contributions to integer programming and nonlinear combinatorial optimization. Shmuel Onn did his high school education in Kadoorie Agricultural
Shmuel_Onn
Largest independent set of paired elements
In combinatorial optimization, the matroid parity problem is a problem of finding the largest independent set of paired elements in a matroid, a structure
Matroid_parity_problem
Algorithm for searching a problem space
theorems of optimization and search state that all optimization strategies are equally effective with respect to the set of all optimization problems. Conversely
Memetic_algorithm
Problem in combinatorial optimization
In the theory of combinatorial optimization, submodular flow is a general class of optimization problems that includes as special cases the minimum-cost
Submodular_flow
Combinatorial optimization graph problem
In mathematics, the minimum k-cut is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph
Minimum_k-cut
Optimization problem
applications beyond that type of instance. It is a well-known combinatorial optimization problem and was the first to undergo competitive analysis, introduced
Job-shop_scheduling
German applied mathematician and theoretical computer scientist
scientist known for her research on approximation algorithms for combinatorial optimization problems including the travelling salesperson problem and the
Vera_Traub
Sequential model-based optimization of expensive black-box functions
Bayesian optimization is a sequential model-based strategy for global optimization of black-box objective functions whose evaluations are costly. It is
Bayesian_optimization
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
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
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
American AI safety researcher
MIT, he researched data structures, quantum cryptography, and combinatorial optimization. He then went on to complete a PhD at the University of California
Paul_Christiano
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
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
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
Method for mathematical optimization
the theory of oriented matroids (OMs), which is a combinatorial abstraction of linear-optimization theory. Indeed, Bland's pivoting rule was based on
Criss-cross_algorithm
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
Measure of algorithmic complexity
László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag
Strongly-polynomial_time
The knapsack problem is one of the most studied problems in combinatorial optimization, with many real-life applications. For this reason, many special
List_of_knapsack_problems
Belgian computer scientist
published several books, including Online Stochastic Combinatorial Optimization, Hybrid Optimization, and Constraint-Based Local Search. Van Hentenryck
Pascal_Van_Hentenryck
Method to solve optimization problems
programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject
Linear_programming
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
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COMBINATORIAL OPTIMIZATION