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46 relations: Algorithm, Applied mathematics, Approximation algorithm, Artificial intelligence, Assignment problem, Auction theory, Brute-force search, Closure problem, Computational complexity theory, Concept testing, Constraint Composite Graph, Constraint satisfaction problem, Cutting stock problem, Discrete optimization, Feasible region, Finite set, Flow network, Graph (discrete mathematics), Integer programming, Isolated point, Knapsack problem, Linear programming, Machine learning, Matching (graph theory), Mathematical optimization, Matroid, Metaheuristic, Minimum spanning tree, NP-completeness, Nurse scheduling problem, Operations research, Optimization problem, P versus NP problem, Parameterized complexity, Search algorithm, Shortest path problem, Shortest-path tree, Software engineering, Spanning tree, Theoretical computer science, Time complexity, Travelling salesman problem, University of Waterloo, Vehicle rescheduling problem, Vehicle routing problem, Weapon target assignment problem.
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry.
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Approximation algorithm
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to NP-hard optimization problems with provable guarantees on the distance of the returned solution to the optimal one.
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Artificial intelligence
Artificial intelligence (AI, also machine intelligence, MI) is intelligence demonstrated by machines, in contrast to the natural intelligence (NI) displayed by humans and other animals.
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Assignment problem
The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics.
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Auction theory
Auction theory is an applied branch of economics which deals with how people act in auction markets and researches the properties of auction markets.
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Brute-force search
In computer science, brute-force search or exhaustive search, also known as generate and test, is a very general problem-solving technique that consists of systematically enumerating all possible candidates for the solution and checking whether each candidate satisfies the problem's statement.
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Closure problem
In graph theory and combinatorial optimization, a closure of a directed graph is a set of vertices with no outgoing edges.
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Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
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Concept testing
Concept testing (to be distinguished from pre-test markets and test markets which may be used at a later stage of product development research) is the process of using surveys (and sometimes qualitative methods) to evaluate consumer acceptance of a new product idea prior to the introduction of a product to the market.
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Constraint Composite Graph
The constraint composite graph is a node-weighted undirected graph associated with a given combinatorial optimization problem posed as a weighted constraint satisfaction problem.
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Constraint satisfaction problem
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations.
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Cutting stock problem
In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted.
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Discrete optimization
Discrete optimization is a branch of optimization in applied mathematics and computer science.
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Feasible region
In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints.
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Finite set
In mathematics, a finite set is a set that has a finite number of elements.
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Flow network
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Integer programming
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.
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Isolated point
In mathematics, a point x is called an isolated point of a subset S (in a topological space X) if x is an element of S but there exists a neighborhood of x which does not contain any other points of S. This is equivalent to saying that the singleton is an open set in the topological space S (considered as a subspace of X).
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Knapsack problem
The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.
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Linear programming
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
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Machine learning
Machine learning is a subset of artificial intelligence in the field of computer science that often uses statistical techniques to give computers the ability to "learn" (i.e., progressively improve performance on a specific task) with data, without being explicitly programmed.
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Matching (graph theory)
In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
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Matroid
In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces.
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Metaheuristic
In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity.
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Minimum spanning tree
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted (un)directed graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight.
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NP-completeness
In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.
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Nurse scheduling problem
The nurse scheduling problem (NSP), also called the nurse rostering problem (NRP), is the operations research problem of finding an optimal way to assign nurses to shifts, typically with a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative quality of valid solutions.
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Operations research
Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.
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Optimization problem
In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions.
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P versus NP problem
The P versus NP problem is a major unsolved problem in computer science.
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Parameterized complexity
In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output.
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Search algorithm
In computer science, a search algorithm is any algorithm which solves the search problem, namely, to retrieve information stored within some data structure, or calculated in the search space of a problem domain.
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Shortest path problem
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
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Shortest-path tree
Given a connected, undirected graph G, a shortest-path tree rooted at vertex v is a spanning tree T of G, such that the path distance from root v to any other vertex u in T is the shortest path distance from v to u in G. In connected graphs where shortest paths are well-defined (i.e. where there are no negative-length cycles), we may construct a shortest-path tree using the following algorithm.
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Software engineering
Software engineering is the application of engineering to the development of software in a systematic method.
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Spanning tree
In the mathematical field of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G, with minimum possible number of edges.
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Theoretical computer science
Theoretical computer science, or TCS, is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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Travelling salesman problem
The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.
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University of Waterloo
The University of Waterloo (commonly referred to as Waterloo, UW, or UWaterloo) is a public research university with a main campus in Waterloo, Ontario.
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Vehicle rescheduling problem
The vehicle rescheduling problem (VRSP) is a combinatorial optimization and integer programming problem seeking to service customers on a trip after change of schedule such as vehicle break down or major delay.
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Vehicle routing 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 of vehicles to traverse in order to deliver to a given set of customers?".
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Weapon target assignment problem
The weapon target assignment problem (WTA) is a class of combinatorial optimization problems present in the fields of optimization and operations research.
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Algorithms for combinatorial optimization, Applications of combinatorial optimization, Combinatorial Optimization, Combinatorial optimisation, Combinatorial optimization (mathematics), Combinatorial optimization algorithms.
References
[1] https://en.wikipedia.org/wiki/Combinatorial_optimization
