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Stochastic Programming
In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty. A stochastic program is an optimization problem in which some or all problem parameters are uncertain, but follow known probability distributions. This framework contrasts with deterministic optimization, in which all problem parameters are assumed to be known exactly. The goal of stochastic programming is to find a decision which both optimizes some criteria chosen by the decision maker, and appropriately accounts for the uncertainty of the problem parameters. Because many real-world decisions involve uncertainty, stochastic programming has found applications in a broad range of areas ranging from finance to transportation to energy optimization. Two-stage problems The basic idea of two-stage stochastic programming is that (optimal) decisions should be based on data available at the time the decisions are made and cannot depend on futur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical 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 of sorts 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. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ethology
Ethology is the scientific study of animal behaviour, usually with a focus on behaviour under natural conditions, and viewing behaviour as an evolutionarily adaptive trait. Behaviourism as a term also describes the scientific and objective study of animal behaviour, usually referring to measured responses to stimuli or to trained behavioural responses in a laboratory context, without a particular emphasis on evolutionary adaptivity. Throughout history, different naturalists have studied aspects of animal behaviour. Ethology has its scientific roots in the work of Charles Darwin and of American and German ornithologists of the late 19th and early 20th century, including Charles O. Whitman, Oskar Heinroth, and Wallace Craig. The modern discipline of ethology is generally considered to have begun during the 1930s with the work of Dutch biologist Nikolaas Tinbergen and Austrian biologists Konrad Lorenz and Karl von Frisch, the three recipients of the 1973 Nobel Prize in Phys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Shortfall
Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is the expected return on the portfolio in the worst q\% of cases. ES is an alternative to value at risk that is more sensitive to the shape of the tail of the loss distribution. Expected shortfall is also called conditional value at risk (CVaR), average value at risk (AVaR), expected tail loss (ETL), and superquantile. ES estimates the risk of an investment in a conservative way, focusing on the less profitable outcomes. For high values of q it ignores the most profitable but unlikely possibilities, while for small values of q it focuses on the worst losses. On the other hand, unlike the discounted maximum loss, even for lower values of q the expected shortfall does not consider only the single most catastrophic outcome. A value of q often used in practice is 5%. Expected shortfall is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Value At Risk
Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses. For a given portfolio, time horizon, and probability ''p'', the ''p'' VaR can be defined informally as the maximum possible loss during that time after excluding all worse outcomes whose combined probability is at most ''p''. This assumes mark-to-market pricing, and no trading in the portfolio. For example, if a portfolio of stocks has a one-day 95% VaR of $1 million, that means that there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one-day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% proba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extended Mathematical Programming (EMP)
Algebraic modeling languages like AIMMS, AMPL, GAMS, MPL and others have been developed to facilitate the description of a problem in mathematical terms and to link the abstract formulation with data-management systems on the one hand and appropriate algorithms for solution on the other. Robust algorithms and modeling language interfaces have been developed for a large variety of mathematical programming problems such as linear programs (LPs), nonlinear programs (NPs), Mixed Integer Programs (MIPs), mixed complementarity programs (MCPs) and others. Researchers are constantly updating the types of problems and algorithms that they wish to use to model in specific domain applications. Extended Mathematical Programming (EMP) is an extension to algebraic modeling languages that facilitates the automatic reformulation of new model types by converting the EMP model into established mathematical programming classes to solve by mature solver algorithms. A number of important problem clas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AIMMS
AIMMS (acronym for Advanced Interactive Multidimensional Modeling System) is a prescriptive analytics software company with offices in the Netherlands, United States, China and Singapore. It has two main product offerings that provide modeling and optimization capabilities across a variety of industries. The AIMMS Prescriptive Analytics Platform allows advanced users to develop optimization-based applications and deploy them to business users. AIMMS SC Navigator, launched in 2017, is built on the AIMMS Prescriptive Analytics Platform and provides configurable Apps for supply chain teams. SC Navigator provides supply chain analytics to non-advanced users. History AIMMS B.V. was founded in 1989 by mathematician Johannes Bisschop under the name of Paragon Decision Technology. His vision was to make optimization more approachable by building models rather than programming. In Bisschop’s view, modeling was able to build the bridge between the people who had problems and the people ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Modeling Language
Algebraic modeling languages (AML) are high-level computer programming languages for describing and solving high complexity problems for large scale mathematical computation (i.e. large scale optimization type problems). One particular advantage of some algebraic modeling languages like AIMMS, AMPL, GAMS, Gekko, MathProg, Mosel, and OPL is the similarity of their syntax to the mathematical notation of optimization problems. This allows for a very concise and readable definition of problems in the domain of optimization, which is supported by certain language elements like sets, indices, algebraic expressions, powerful sparse index and data handling variables, constraints with arbitrary names. The algebraic formulation of a model does not contain any hints how to process it. An AML does not solve those problems directly; instead, it calls appropriate external algorithms to obtain a solution. These algorithms are called solvers and can handle certain kind of mathematical probl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Programming
Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively. Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have ''optimal substructure''. If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems.Cormen, T. H.; Leiserson, C. E.; Rives ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicholas Georgescu-Roegen
Nicholas Georgescu-Roegen (born Nicolae Georgescu, 4 February 1906 – 30 October 1994) was a Romanian mathematician, statistician and economist. He is best known today for his 1971 ''The Entropy Law and the Economic Process'', in which he argued that all natural resources are irreversibly degraded when put to use in economic activity. A progenitor and a paradigm founder in economics, Georgescu-Roegen's work was decisive for the establishing of ecological economics as an independent academic sub-discipline in economics. Several economists have hailed Georgescu-Roegen as a man who lived well ahead of his time, and some historians of economic thought have proclaimed the ingenuity of his work. In spite of such appreciation, Georgescu-Roegen was never awarded the Nobel Prize in Economics, although benefactors from his native Romania were lobbying for it on his behalf. After Georgescu-Roegen's death, his work was praised by a surviving friend of the highest rank: Prominent Keynesi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parasitoid
In evolutionary ecology, a parasitoid is an organism that lives in close association with its host (biology), host at the host's expense, eventually resulting in the death of the host. Parasitoidism is one of six major evolutionarily stable strategy, evolutionary strategies within parasitism, distinguished by the fatal prognosis for the host, which makes the strategy close to predation. Among parasitoids, strategies range from living inside the host (''endoparasitism''), allowing it to continue growing before emerging as an adult, to Paralysis, paralysing the host and living outside it (''ectoparasitism''). Hosts can include other parasitoids, resulting in hyperparasitism; in the case of oak galls, up to five levels of parasitism are possible. Some parasitoids Behavior-altering parasite, influence their host's behaviour in ways that favour the propagation of the parasitoid. Parasitoids are found in a variety of Taxon, taxa across the insect superorder Endopterygota, whose compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fledge
Fledging is the stage in a flying animal's life between hatching or birth and becoming capable of flight. This term is most frequently applied to birds, but is also used for bats. For altricial birds, those that spend more time in vulnerable condition in the nest, the nestling and fledging stage can be the same. For precocial birds, those that develop and leave the nest quickly, a short nestling stage precedes a longer fledging stage. All birds are considered to have fledged when the feathers and wing muscles are sufficiently developed for flight. A young bird that has recently fledged but is still dependent upon parental care and feeding is called a fledgling. People often want to help fledglings, as they appear vulnerable, but it is best to leave them alone. The USA National Phenology Network defines the phenophase (or life cycle stage) of fledged young for birds as "One or more young are seen recently departed from the nest. This includes young incapable of sustained fli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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