Stochastic programming
Encyclopedia
Stochastic programming is a framework for modeling optimization
problems that involve uncertainty
. Whereas deterministic optimization problems are formulated with known parameters, real world problems almost invariably include some unknown parameters. When the parameters are known only within certain bounds, one approach to tackling such problems is called robust optimization
. Here the goal is to find a solution which is feasible for all such data and optimal
in some sense. Stochastic programming models
are similar in style but take advantage of the fact that probability distributions governing the data are known or can be estimated. The goal here is to find some policy that is feasible for all (or almost all) the possible data instances and maximizes the expectation of some function of the decisions and the random variables. More generally, such models are formulated, solved analytically or numerically, and analyzed in order to provide useful information to a decision-maker.
As an example, consider two-stage linear programs. Here the decision maker takes some action in the first stage, after which a random event occurs affecting the outcome of the first-stage decision. A recourse decision can then be made in the second stage that compensates for any bad effects that might have been experienced as a result of the first-stage decision. The optimal policy from such a model is a single first-stage policy and a collection of recourse decisions (a decision rule) defining which second-stage action should be taken in response to each random outcome.
Stochastic programming has applications in a broad range of areas ranging from finance to transportation to energy optimization.
in such fields as behavioural ecology. Empirical tests of models of optimal foraging
, life-history
transitions such as fledging in birds
and egg laying in parasitoid
wasps have shown the value of this modelling technique in explaining the evolution of behavioural decision making. These models are typically many staged, rather than two-staged.
Optimization (mathematics)
In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
problems that involve uncertainty
Uncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...
. Whereas deterministic optimization problems are formulated with known parameters, real world problems almost invariably include some unknown parameters. When the parameters are known only within certain bounds, one approach to tackling such problems is called robust optimization
Robust optimization
Robust optimization is a field of optimization theory that deals with optimization problems where robustness is sought against uncertainty and/or variability in the value of a parameter of the problem.- History :...
. Here the goal is to find a solution which is feasible for all such data and optimal
Optimization (mathematics)
In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
in some sense. Stochastic programming models
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
are similar in style but take advantage of the fact that probability distributions governing the data are known or can be estimated. The goal here is to find some policy that is feasible for all (or almost all) the possible data instances and maximizes the expectation of some function of the decisions and the random variables. More generally, such models are formulated, solved analytically or numerically, and analyzed in order to provide useful information to a decision-maker.
As an example, consider two-stage linear programs. Here the decision maker takes some action in the first stage, after which a random event occurs affecting the outcome of the first-stage decision. A recourse decision can then be made in the second stage that compensates for any bad effects that might have been experienced as a result of the first-stage decision. The optimal policy from such a model is a single first-stage policy and a collection of recourse decisions (a decision rule) defining which second-stage action should be taken in response to each random outcome.
Stochastic programming has applications in a broad range of areas ranging from finance to transportation to energy optimization.
Biological Applications
Stochastic dynamic programming is frequently used to model animal behaviourAnimal behaviour
Animal behaviour is the subject of:* The field of Ethology* Animal Behaviour, a scientific journal...
in such fields as behavioural ecology. Empirical tests of models of optimal foraging
Optimal foraging theory
Optimal foraging theory is an idea in ecology based on the study of foraging behaviour and states that organisms forage in such a way as to maximize their net energy intake per unit time. In other words, they behave in such a way as to find, capture and consume food containing the most calories...
, life-history
Biological life cycle
A life cycle is a period involving all different generations of a species succeeding each other through means of reproduction, whether through asexual reproduction or sexual reproduction...
transitions such as fledging in birds
Fledge
Fledge is the stage in a young bird's life when the feathers and wing muscles are sufficiently developed for flight. It also describes the act of a chick's parents raising it to a fully grown state...
and egg laying in parasitoid
Parasitoid
A parasitoid is an organism that spends a significant portion of its life history attached to or within a single host organism in a relationship that is in essence parasitic; unlike a true parasite, however, it ultimately sterilises or kills, and sometimes consumes, the host...
wasps have shown the value of this modelling technique in explaining the evolution of behavioural decision making. These models are typically many staged, rather than two-staged.