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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.
Deterministic vs. probabilistic (stochastic). A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables; therefore, a deterministic model always performs the same way for a given set of initial conditions.
In contrast, some authors have argued that randomization can only improve a deterministic algorithm if the deterministic algorithm was poorly designed in the first place. [21] Fred W. Glover [22] argues that reliance on random elements may prevent the development of more intelligent and better deterministic components. The way in which results ...
Stochastic (/ s t ə ˈ k æ s t ɪ k /; from Ancient Greek στόχος (stókhos) ' aim, guess ') [1] is the property of being well-described by a random probability distribution. [1] Stochasticity and randomness are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; in everyday ...
The model is a simple regenerative optimal stopping stochastic dynamic problem faced by the decision maker, Harold Zurcher, superintendent of maintenance at the Madison Metropolitan Bus Company in Madison, Wisconsin.
Stochastic dynamic programs can be solved to optimality by using backward recursion or forward recursion algorithms. Memoization is typically employed to enhance performance. However, like deterministic dynamic programming also its stochastic variant suffers from the curse of dimensionality.
This type of modeling is distinct from stochastic modeling [2] or forward modeling. [3] Stochastic modeling uses random data in the model while forward modeling uses a given model to predict future behavior in a system. Deterministic models are used across the natural sciences, including geology, oceanography, [4] physics, and other disciplines.
In the case where the maximization is an integral of a concave function of utility over an horizon (0,T), dynamic programming is used. There is no certainty equivalence as in the older literature, because the coefficients of the control variables—that is, the returns received by the chosen shares of assets—are stochastic.