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Combinatorial optimization problem
The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research
Quadratic_assignment_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
In mathematics, the quadratic bottleneck assignment problem (QBAP) is one of the fundamental combinatorial optimization problems in the branch of optimization
Quadratic bottleneck assignment problem
Quadratic_bottleneck_assignment_problem
algorithm Closure problem Generalized assignment problem Linear bottleneck assignment problem Quadratic assignment problem Stable marriage problem Andersen, A
Weapon-target assignment problem
Weapon-target_assignment_problem
scheduling Partition problem Quadratic assignment problem Quadratic programming (NP-hard in some cases, P if convex) Subset sum problem Variations on the
List_of_NP-complete_problems
Optimization algorithm
for Quadratic Assignment Problems". CiteSeerX 10.1.1.47.5167. • Stützle, Thomas (July 1997). MAX-MIN Ant System for Quadratic Assignment Problems (Technical
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Topics referred to by the same term
Colombian newscast that aired between 1992 and 1997 Quadratic assignment problem Quadratic assignment procedure, a method for evaluating the significance
QAP
Combinatorial optimization problem
Quadratic unconstrained binary optimization (QUBO), also known as unconstrained binary quadratic programming (UBQP), is a combinatorial optimization problem
Quadratic unconstrained binary optimization
Quadratic_unconstrained_binary_optimization
range of parameter settings, particularly in the case of the quadratic assignment problem. A general version of the GLS algorithm, using a min-conflicts
Guided_local_search
Discipline concerning the application of advanced analytical methods
allocation problems Facility location Assignment Problems: Assignment problem Generalized assignment problem Quadratic assignment problem Weapon target
Operations_research
Optimization by removing non-optimal solutions to subproblems
number of NP-hard problems: Integer programming Nonlinear programming Travelling salesman problem (TSP) Quadratic assignment problem (QAP) Maximum satisfiability
Branch_and_bound
Optimizing objective functions that have constrained variables
problem is a nonlinear programming problem. If all the hard constraints are linear and some are inequalities, but the objective function is quadratic
Constrained_optimization
Optimization problem
Weber problem), or one might elect to minimize the maximum of all such distances (à la the 1-center problem). Graph center Quadratic assignment problem Location-allocation
Optimal_facility_location
Algorithm for searching a problem space
classical NP problems. To cite some of them: graph partitioning, multidimensional knapsack, travelling salesman problem, quadratic assignment problem, set cover
Memetic_algorithm
multidimensional knapsack problem 0-1 knapsack problem maximum cut problem quadratic assignment problem facility layout problem wind farm layout Hyper-heuristics
Hyper-heuristic
British mathematician (1927–2021)
resulting in contributions to data envelopment analysis, the quadratic assignment problem, and combinatorial auctions. In addition to her methodological
Ailsa_Land
solvability of the quadratic assignment problem (QAP), heuristic solvability and sensitivity analysis for the Hub Location Problem (HLP), and optimization
Jadranka_Skorin-Kapov
Study of optimal transportation and allocation of resources
This motivating special case of the transportation problem is an instance of the assignment problem. More specifically, it is equivalent to finding a minimum
Transportation theory (mathematics)
Transportation_theory_(mathematics)
capacity, we can have multiple subset sum problem. Quadratic knapsack problem: Set-Union Knapsack Problem: SUKP is defined by Kellerer et al (on page
List_of_knapsack_problems
Mathematical relation assigning a probability event to a cost
based on the quadratic loss function. The quadratic loss function is also used in linear-quadratic optimal control problems. In these problems, even in the
Loss_function
disjoint sets Antichain Arrangement of hyperplanes Assignment problem Quadratic assignment problem Audioactive decay Barcode Matrix code QR Code Universal
Index of combinatorics articles
Index_of_combinatorics_articles
1016/j.dam.2003.08.005, MR 2049654. Çela, Eranda (1998), The Quadratic Assignment Problem: Theory and Algorithms, Combinatorial Optimization, vol. 1, Dordrecht:
Kalmanson combinatorial conditions
Kalmanson_combinatorial_conditions
Optimization solver
(LP), quadratic programming (QP), quadratically constrained programming (QCP), mixed integer linear programming (MILP), mixed-integer quadratic programming
Gurobi_Optimizer
Combinatorial optimization method for pseudo-Boolean functions
computer vision problems such as image segmentation and stereo matching. If the coefficients w p q {\displaystyle w_{pq}} of the quadratic terms satisfy
Quadratic pseudo-Boolean optimization
Quadratic_pseudo-Boolean_optimization
Method to solve optimization problems
Abstraction of ordered linear algebra Quadratic programming – Solving an optimization problem with a quadratic objective function Semidefinite programming –
Linear_programming
Subfield of mathematical optimization
the class of NPO problems that are polynomially-bounded. Assignment problem Bin packing problem Chinese postman problem Closure problem Constraint satisfaction
Combinatorial_optimization
Problem in formal logic
The problem is also in P by the same transformation: any satisfying assignment to this Horn formula is the negation of a satisfying assignment to the
Horn-satisfiability
Engineer
problems." Management Science 40.11 (1994): 1542-1561. Malakooti, B., and G. I. D'souza. "Multiple objective programming for the quadratic assignment
Behnam_Malakooti
Monte Carlo method for importance sampling and optimization
salesman, quadratic assignment, DNA sequence alignment, max-cut and buffer allocation problems.[citation needed] Consider the general problem of estimating
Cross-entropy_method
On solvability of Diophantine equations
Shnidman, Ari (30 January 2025). "Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field". arXiv:2501
Hilbert's_tenth_problem
Chronological table of metaheuristic algorithms
Optimization: A new metaheuristic approach and its performance on quadratic assignment problem". Information Sciences. 217: 65–77. doi:10.1016/j.ins.2012.06
Table_of_metaheuristics
Combinatorial optimization method for a family of functions of discrete variables
capture the nature of the problem and it can provide higher quality results that could be difficult to achieve with quadratic models. For instance in computer
Graph_cut_optimization
Task of computing complete subgraphs
In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete
Clique_problem
Problem optimization method
simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart
Dynamic_programming
Pakistani computer scientist
linear systems as band matrices with low bandwidth, and to the quadratic assignment problem. This is the work for which Bokhari was cited in his IEEE Fellow
Shahid_Hussain_Bokhari
American mathematician (1914–2005)
both problems, still believing that they were an assignment that was overdue. Six weeks later, an excited Neyman eagerly told him that the problems he had
George_Dantzig
Logic problem, AND of pairwise ORs
2-satisfiability problem is to find a truth assignment to the variables of a formula in this form that makes the whole formula true. Such an assignment chooses
2-satisfiability
Approach in control theory to achieve fault-tolerant control for dynamic systems
control schemes include: linear-quadratic regulator design (LQR), model predictive control (MPC) and eigenstructure assignment methods. Some probabilistic
Control_reconfiguration
Fractal named after mathematician Benoit Mandelbrot
Mandelbrot first visualized the set. Mandelbrot studied the parameter space of quadratic polynomials in an article that appeared in 1980. The mathematical study
Mandelbrot_set
German computer scientist
of a Deterministic Annealing Method for Graph Matching and Quadratic Assignment Problems in Computer Vision". He then studied computer science at Brown
Stefan_Roth
Optimization algorithm
(1984). "A modified Frank-Wolfe algorithm for solving the traffic assignment problem". Transportation Research Part B: Methodological. 18 (2): 169–177
Frank–Wolfe_algorithm
Stage of electronic circuit design
placement density as a linear term into the quadratic cost function and solves the placement problem by pure quadratic programming. A common enhancement is weighting
Placement (electronic design automation)
Placement_(electronic_design_automation)
Linear programming algorithm
Approach to a Tensor Optimisation Problem with Application to Upper Bounds in Integer Quadratic Optimization Problems, Proceedings of Second Conference
Karmarkar's_algorithm
Method for problem solving in optimization
satisfiability problem, in which a candidate solution is a truth assignment, and the target is to maximize the number of clauses satisfied by the assignment; in
Local_search_(optimization)
Procedure for finding a stable matching
to run in time quadratic in the number of participants, and linear in the size of the input to the algorithm. The stable matching problem, and the Gale–Shapley
Gale–Shapley_algorithm
Measure of variation in statistics
_{i=1}^{N}\left(x_{i}-{\bar {x}}\right)^{2}}},} The error in this approximation decays quadratically (as 1/N2), and it is suited for all but the smallest samples or highest
Standard_deviation
Finding values for variables that make an equation true
case when considering polynomial equations, such as quadratic equations. However, for some problems, all variables may assume either role. Depending on
Equation_solving
Generalization of binary functions
than 2, one can always employ reductions to obtain an equivalent quadratic problem with additional variables. One possible reduction is − x 1 x 2 x 3
Pseudo-Boolean_function
Node labeling problem in graph theory
weighted versions are special cases of the quadratic bottleneck assignment problem. The bandwidth problem is NP-hard, even for some special cases. Regarding
Graph_bandwidth
Primal-Dual algorithm optimization for convex problems
Chambolle–Pock algorithm is an algorithm used to solve convex optimization problems. It was introduced by Antonin Chambolle and Thomas Pock in 2011 and has
Chambolle–Pock_algorithm
Type of numerical analysis
algorithm for solving the quadratic program is the pool adjacent violators algorithm. Conversely, Best and Chakravarti studied the problem as an active set identification
Isotonic_regression
Typesetting system
specifically for mathematical formulas. For example, the quadratic formula (which is the solution of the quadratic equation) appears as: The formula is printed in
TeX
Categorization of data using statistics
and clustering are examples of the more general problem of pattern recognition, which is the assignment of some sort of output value to a given input value
Statistical_classification
Density-based data clustering algorithm
Commons Math contains a Java implementation of the algorithm running in quadratic time. ELKI offers an implementation of DBSCAN as well as GDBSCAN and other
DBSCAN
When every path in a control-flow graph must go through one node to reach another
they applied it to the problem of efficiently computing the placement of φ functions, which are used in static single assignment form. Dominators, and
Dominator_(graph_theory)
Computer compiler optimization technique
use of the interference graph, which can have a worst-case size that is quadratic in the number of live ranges. The traditional formulation of graph-coloring
Register_allocation
Type of experimental design
and seed matrices, respectively, with Plackett–Burmans. For example, a quadratic design for 30 variables requires a 30 column PB plan matrix of zeroes
Plackett–Burman_design
Graph drawing with vertices in horizontal layers
position with respect to its neighbors. Sugiyama's original work proposed a quadratic programming formulation of this step; a later method of Brandes and Köpf
Layered_graph_drawing
constant or balanced Grover's algorithm: provides a quadratic speedup for unstructured search problems Hadamard test: circuit technique for estimating real
List_of_algorithms
Evolutionary algorithm
stochastic variable-metric method. In the very particular case of a convex-quadratic objective function f ( x ) = 1 2 ( x − x ∗ ) T H ( x − x ∗ ) {\displaystyle
CMA-ES
DisCOP) is the distributed analogue to constraint optimization. A DCOP is a problem in which a group of agents must distributedly choose values for a set of
Distributed constraint optimization
Distributed_constraint_optimization
Mathematical combinatorial optimization method
multi-coloring problem can be used to model a variety of applications including job scheduling and telecommunication channel assignment. Vehicle routing problems. Generalized
Branch_and_price
Method of making choices that maximises utility
auctions, calculating the optimal assignment is NP-hard. Sometimes there are approximation algorithms to the optimization problem, but, using such an approximation
Vickrey–Clarke–Groves mechanism
Vickrey–Clarke–Groves_mechanism
(elaborated below). Bipartite matching is achieved by solving the assignment problem, namely minimizing a sum of costs over all matched pairs. In the typical
Detection_Transformer
Optimization using parameterization
function in (multi)parametric (mixed-integer) linear, quadratic and nonlinear programming problems is performed. Note that this generally assumes the constraints
Parametric_programming
Least squares approximation of linear functions to data
then for f {\displaystyle f} , this minimization problem becomes the quadratic minimization problem above with X i j = φ j ( x i ) , {\displaystyle X_{ij}=\varphi
Linear_least_squares
Computational complexity
in 1994 (Papadimitriou 1994 Problem 16.4.10, "Symmetric space"). Since larger space classes are not affected by quadratic increases, the nondeterministic
NL_(complexity)
Method used in statistics, pattern recognition, and other fields
Without any further assumptions, the resulting classifier is referred to as quadratic discriminant analysis (QDA). LDA instead makes the additional simplifying
Linear_discriminant_analysis
Approximation method in statistics
distribution on the parameter vector. The optimization problem may be solved using quadratic programming or more general convex optimization methods
Least_squares
Distance function defined between probability distributions
X\subset \mathbb {R} ^{n}} with smooth boundary. Consider the quadratic cost transport problem from the uniform distribution on X {\displaystyle X} to the
Wasserstein_metric
Natural number
his axioms to begin the sequence with 0. In the Von Neumann cardinal assignment of natural numbers, where each number is defined as a set that contains
1
Machine learning algorithm
simplifies the algorithm by not requiring the solution of a quadratic programming problem (see below). When used in a one-vs-all configuration, binary
Margin-infused relaxed algorithm
Margin-infused_relaxed_algorithm
Mathematical formula expressing equality
letters at the beginning, a, b, c, d, ... . For example, the general quadratic equation is usually written ax2 + bx + c = 0. The process of finding the
Equation
Process in artificial intelligence and operations research
conditions that the variables must satisfy. A solution is therefore an assignment of values to the variables that satisfies all constraints—that is, a point
Constraint_satisfaction
Real Two-dimensional Woodboard Cutting Problem" Area: Applications - Clémence Bisot. "Dynamic Linear Assignment for Pairing Two Parts in Production - A
ICORES
Method for division with remainder
result. It is also possible to use a mixture of quadratic and cubic iterations. Using at least one quadratic iteration ensures that the error is positive
Division_algorithm
Automated recognition of patterns and regularities in data
generative or discriminative. Parametric: Linear discriminant analysis Quadratic discriminant analysis Maximum entropy classifier (aka logistic regression
Pattern_recognition
of any graph is at most quadratic in its maximum degree; they provide an example showing that for some graphs this quadratic dependence is necessary.
Thue_number
Statistical value representing the center or average of a distribution
is not invariant to different rescaling of the different dimensions. Quadratic mean (often known as the root mean square) useful in engineering, but
Central_tendency
Association of one output to each input
Functions can be classified by the nature of formulas that define them: A quadratic function is a function that may be written f ( x ) = a x 2 + b x + c
Function_(mathematics)
(disambiguation) Quadrat Quadrant count ratio Quadratic classifier Quadratic form (statistics) Quadratic variation Qualitative comparative analysis Qualitative
List_of_statistics_articles
Belarusian mathematician (1931–2024)
programming problems, and she created numerical methods for the solution of linear, quadratic, nonlinear programming, and optimal control problems. She developed
Faina_Kirillova
Mathematical constant used in combinatorics
vertex has exactly four neighbors. An orientation of this graph is an assignment of a direction to each edge. It is an Eulerian orientation if it gives
Lieb's_square_ice_constant
Measure of the shape of a function
expectation of a square, so it is non-negative for all a; however it is also a quadratic polynomial in a. Its discriminant must be non-positive, which gives the
Moment_(mathematics)
Optimization algorithms using quantum computing
exists: this gives the minimal solution to the SDP problem. The quantum algorithm provides a quadratic improvement over the best classical algorithm in
Quantum optimization algorithms
Quantum_optimization_algorithms
American mathematician
and, as a Diophantine equation, the problem is to determine all rational solutions, i.e., assignments of rational numbers to the variables x {\displaystyle
Jennifer_Balakrishnan
Greek-American electrical engineer (1942–2026)
algorithmic convergence issues around augmented Lagrangian and sequential quadratic programming methods. "Parallel and Distributed Computation: Numerical
Dimitri_Bertsekas
Collection of statistical models
Box, G. E. P. (1954). "Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, II. Effects of Inequality of Variance and
Analysis_of_variance
Method of result aggregation from multiple clustering algorithms
simplest heuristic, but its computational and storage complexity are both quadratic in n. SC3 is an example of a CSPA type algorithm. The following two methods
Consensus_clustering
Type of grammar for describing formal languages
asymptotically equivalent to boolean matrix multiplication (thus likely between quadratic and cubic time). One classical example of a formal language which is provably
Parsing_expression_grammar
Indian mathematician (1887–1920)
summing divergent infinite series Ramanujan's constant Ramanujan's ternary quadratic form – Unique algebraic expression given by Srinivasa Ramanujan Rank of
Srinivasa_Ramanujan
Statistical approach
not been able to afford to fit a cubic three-level design to estimate a quadratic model, and their biased linear-models estimated the gradient to be zero
Response_surface_methodology
Form of artificial neural network
conversion, job-shop scheduling problem, quadratic assignment and other related NP-complete problems, channel allocation problem in wireless networks, mobile
Hopfield_network
Georgian Professor in the Ocean and Mechanical Engineering
With J. N. Reddy, Elishakoff has written on solving quadratic equations without resorting to quadratic formula. He also writes educational papers Elishakoff
Isaac_Elishakoff
Mathematical description of spacetime used in relativity
Minkowski spacetime is a pseudo-Euclidean space equipped with an isotropic quadratic form called the spacetime interval or the Minkowski norm squared. In Euclidean
Minkowski_spacetime
Teaching, learning, and scholarly research in mathematics
exercises of a similar type, such as adding simple fractions or solving quadratic equations. Rote learning: the teaching of mathematical results, definitions
Mathematics_education
Solid-state electrically operated switch also used as an amplifier
increases exponentially for VGS below threshold, and then at a roughly quadratic rate: (IDS ∝ (VGS − VT)2, where VT is the threshold voltage at which drain
Transistor
Principle in Bayesian statistics
the maximum entropy principle may require the solution to a quadratic programming problem, and thus provide a sparse mixture model as the optimal density
Principle_of_maximum_entropy
Software environment
Symbolic Regression Lawn Mower Multiplexer NK[P,Q] Landscapes OneMax Quadratic Assignment Job Shop Scheduling Orienteering Regression Robocode Single-Objective
HeuristicLab
Fewest cliques covering a graph's edges
representation requires a near-quadratic number of cliques. Another class of applications comes from scheduling problems in which multiple users of a shared
Intersection number (graph theory)
Intersection_number_(graph_theory)
QUADRATIC ASSIGNMENT-PROBLEM
QUADRATIC ASSIGNMENT-PROBLEM
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Boy/Male
Muslim
Problem solver
Girl/Female
Muslim/Islamic
Away from all Problems
Girl/Female
Indian, Telugu
Destroyer of Problems
Boy/Male
Indian, Tamil
People with this Name are Preferably Intelligent and Very Generous; Highly Knowledgeable in Problem Solving Skills
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Boy/Male
Hindu, Indian
Problem
QUADRATIC ASSIGNMENT-PROBLEM
QUADRATIC ASSIGNMENT-PROBLEM
Boy/Male
Australian, Chinese, Danish, Dutch, French, German, Netherlands, Swedish, Teutonic
Estate Ruler
Boy/Male
Hindu
Last of Moksha
Surname or Lastname
Dutch
Dutch : variant of Clemens.English : patronymic from the personal name Clement.Americanized spelling of German Klemens.
Boy/Male
Scottish Gaelic
Friend of Saint Michael.
Girl/Female
Tamil
Deepshika | தீபஷிகா
Flame, Lamp
Boy/Male
American, Australian, British, Chinese, Christian, English, German
Baker
Male
English
Anglicized form of Greek Mattathias, MATTATHIAH means "gift of God." In the bible, this is the name of one of Christ's ancestors.
Boy/Male
Indian, Sanskrit
Lotus Eyed
Surname or Lastname
English
English : variant of Bellows.
Boy/Male
Hindu, Indian
Sound
QUADRATIC ASSIGNMENT-PROBLEM
QUADRATIC ASSIGNMENT-PROBLEM
QUADRATIC ASSIGNMENT-PROBLEM
QUADRATIC ASSIGNMENT-PROBLEM
QUADRATIC ASSIGNMENT-PROBLEM
n.
The writing by which an interest is transferred.
a.
Quadrate; square.
imp. & p. p.
of Quadrate
n.
An allotting or an appointment to a particular person or use; or for a particular time, as of a cause or causes in court.
n.
A transfer of title or interest by writing, as of lease, bond, note, or bill of exchange; a transfer of the whole of some particular estate or interest in lands.
n.
A making over by transfer of title; assignment.
a.
Of or pertaining to a square, or to squares; resembling a quadrate, or square; square.
pl.
of Quadratrix
n.
Assignment of quarters for soldiers; quarters.
a.
The quadrate bone.
n.
The transfer of the property of a bankrupt to certain persons called assignees, in whom it is vested for the benefit of creditors.
a.
Pertaining to terms of the second degree; as, a quadratic equation, in which the highest power of the unknown quantity is a square.
pl.
of Quadratrix
n.
A curve made use of in the quadrature of other curves; as the quadratrix, of Dinostratus, or of Tschirnhausen.
n.
The act of allotting; assignment.
n.
See Alignment.
n.
That branch of algebra which treats of quadratic equations.
n.
A biquadratic equation.
p. pr. & vb. n.
of Quadrate
n.
The assignment of a cause.