Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Multi-objective optimizationMulti-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective is a type of vector optimization that has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives.
Feasible regionIn 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. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.
Combinatorial optimizationCombinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, 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.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Program optimizationIn computer science, program optimization, code optimization, or software optimization, is the process of modifying a software system to make some aspect of it work more efficiently or use fewer resources. In general, a computer program may be optimized so that it executes more rapidly, or to make it capable of operating with less memory storage or other resources, or draw less power. Although the word "optimization" shares the same root as "optimal", it is rare for the process of optimization to produce a truly optimal system.
Optimization problemIn mathematics, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.
Heuristic (computer science)In mathematical optimization and computer science, heuristic (from Greek εὑρίσκω "I find, discover") is a technique designed for problem solving more quickly when classic methods are too slow for finding an exact or approximate solution, or when classic methods fail to find any exact solution. This is achieved by trading optimality, completeness, accuracy, or precision for speed. In a way, it can be considered a shortcut.
Optimal controlOptimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.
Peephole optimizationPeephole optimization is an optimization technique performed on a small set of compiler-generated instructions; the small set is known as the peephole or window. Peephole optimization involves changing the small set of instructions to an equivalent set that has better performance.
Optimizing compilerIn computing, an optimizing compiler is a compiler that tries to minimize or maximize some attributes of an executable computer program. Common requirements are to minimize a program's execution time, memory footprint, storage size, and power consumption (the last three being popular for portable computers). Compiler optimization is generally implemented using a sequence of optimizing transformations, algorithms which take a program and transform it to produce a semantically equivalent output program that uses fewer resources or executes faster.
HeuristicA heuristic (hjʊˈrɪstɪk; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, short-term goal or approximation. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision.
DesignA design is a concept of either an object, a process, or a system that is specific and, in most cases, detailed. Design refers to something that is or has been intentionally created by a thinking agent, though it is sometimes used to refer to the nature of something. The verb to design expresses the process of developing a design. In some cases, the direct construction of an object without an explicit prior plan may also be considered to be a design (such as in some artwork and craftwork).
Pareto efficiencyPareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related: Given an initial situation, a Pareto improvement is a new situation where some agents will gain, and no agents will lose.
Environmental justiceEnvironmental justice or eco-justice, is a social movement to address environmental injustice, which occurs when poor and marginalized communities are harmed by hazardous waste, resource extraction, and other land uses from which they do not benefit. The movement has generated hundreds of studies showing that exposure to environmental harm is inequitably distributed. The movement began in the United States in the 1980s. It was heavily influenced by the American civil rights movement and focused on environmental racism within rich countries.
Environmental scienceEnvironmental science is an interdisciplinary academic field that integrates physics, biology, and geography (including ecology, chemistry, plant science, zoology, mineralogy, oceanography, limnology, soil science, geology and physical geography, and atmospheric science) to the study of the environment, and the solution of environmental problems. Environmental science emerged from the fields of natural history and medicine during the Enlightenment. Today it provides an integrated, quantitative, and interdisciplinary approach to the study of environmental systems.
Environmental movementThe environmental movement (sometimes referred to as the ecology movement), is a social movement that aims to protect the natural world from harmful environmental practices in order to create sustainable living. Environmentalists advocate the just and sustainable management of resources and stewardship of the environment through changes in public policy and individual behavior. In its recognition of humanity as a participant in (not an enemy of) ecosystems, the movement is centered on ecology, health, and human rights.
Environmental racismEnvironmental racism, ecological racism or ecological apartheid is a form of institutional racism leading to landfills, incinerators, and hazardous waste disposal being disproportionately placed in communities of color. Internationally, it is also associated with extractivism, which places the environmental burdens of mining, oil extraction, and industrial agriculture upon indigenous peoples and poorer nations largely inhabited by people of color.
7-Zip7-Zip is a free and open-source , a utility used to place groups of files within compressed containers known as "archives". It is developed by Igor Pavlov and was first released in 1999. 7-Zip has its own archive format called 7z, but can read and write several others. The program can be used from a Windows graphical user interface that also features shell integration, from a Windows command-line interface as the command 7za or 7za.exe, and from POSIX systems as p7zip. Most of the 7-Zip source code is under the LGPL-2.
EconomyAn economy is an area of the production, distribution and trade, as well as consumption of goods and services. In general, it is defined as a social domain that emphasize the practices, discourses, and material expressions associated with the production, use, and management of scarce resources. A given economy is a set of processes that involves its culture, values, education, technological evolution, history, social organization, political structure, legal systems, and natural resources as main factors.
