Simulation-based optimization: Difference between revisions

Revision as of 02:34, 21 October 2017

Revision as of 02:36, 21 October 2017

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==== Dynamic programming ====

[[Dynamic programming]] deals with situations where decisions are made in stagestages. The key to this kind of problems is to trade off the present and future costs.<ref>Cooper, Leon; Cooper, Mary W. Introduction to dynamic programming. New York: Pergamon Press, 1981</ref>

One dynamic basic model has two features:

1) HasIt has a discrete time dynamic system.

2) The cost function is additive over time.

For discrete featurefeatures, dynamic programming has the form:

:<math>x_{k+1} = f_k(x_{k},u_{k},w_{k}) , k=0,1,...,N-1</math>

:<math>k</math> represents the index of discrete time.

:<math>x_k</math> is the state of the time k, it contains the past information and prepare it for the future optimization.

:<math>u_k</math> is the control variable.

:<math>w_k</math> is the random parameter.

For the cost function, it has the form:

:<math>g_N(X_N) + \sum_{k=0}^{N-1} gk(x_k,u_k,W_k)</math>

<math>g_N(X_N)</math> is the cost at the end of the process.

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As the cost cannot be optimized meaningfully, it can be used the expect value:

:<math>E\{g_N(X_N) + \sum_{k=0}^{N-1} g_k(x_k,u_k,W_k) \}</math>

==== Neuro-dynamic programming ====