Simulation-based optimization: Difference between revisions

Revision as of 00:48, 12 May 2016

Revision as of 01:03, 12 May 2016

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Specific simulation based optimization methods can be chosen according to figure 1 based on the decision variable types.^{[[User:Lpetroia/sandbox|[2]]]}

[[File:Classification of simulation based optimization according to variable types.jpg|thumb|Fig 1. Classification of simulation based optimization according to variable types]]

[[Optimization (computer science)|Optimization]] exists in two main branches of operational research:

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Stochastic approximation is used when the function cannot be computed directly, only estimated via noisy observations. In this scenarios, this method (or family of methods) looks for the extrema of these function. The objective function would be:

<math>\underset{\text{x}\in\theta}{\min}f\bigl(\text{x}\bigr) = \underset{\text{x}\in\theta}{\min}\Epsilon[F\bigl(\text{x,y})]</math>

is a random variable that represents the noise.

<math>y</math> is a random variable that represents the noise.

is the parameter that minimizes .

<math>x</math> is the parameter that minimizes <math>f\bigl(\text{x}\bigr)</math>.

is the ___domain of the parameter .

<math>\theta</math> is the ___domain of the parameter <math>x</math>.

==== [[Derivative-free optimization|Derivative-free optimization methods]] ====

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For discrete feature, dynamic programming has the form:

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

represents the index of discrete time.

<math>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 cost function, it has the form:

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

is the cost at the end of the process.

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

As the cost cannot be optimized meaningfully, we can use 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: =====

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=== Examples ===

[[File:Simulation-based optimization for building performance studies.pdfpng|thumb|Fig 2. Simulation-based optimization for building performance studies]]

The literature presents many uses of Simulation Based Optimization. Nguyen et al.^{[[User:Lpetroia/sandbox|[10]]]}, for example, discuss in their paper the use of simulation-based optimization for supporting the project of high performance buildings, such as green buildings. The figure 2 presents their method simplified.

Saif et al.^{[[User:Lpetroia/sandbox|[11]]]} present another possible use of Simulation Based Optimization: allocate energy resources in an imperfect power distribution system, in an optimal way, considering ___location and capacity.

=== References ===

# '''[[User:Lpetroia/sandbox|Jump up^]]''' Carson, Yolanda, and Anu Maria. "Simulation optimization: methods and applications." ''Proceedings of the 29th conference on Winter simulation''. IEEE Computer Society, 1997.

# '''[[User:Lpetroia/sandbox|Jump up^]]''' Jalali, Hamed, and Inneke Van Nieuwenhuyse. "Simulation optimization in inventory replenishment: a classification." IIE Transactions 47.11 (2015): 1217-1235.

# '''[[User:Lpetroia/sandbox|Jump up^]]''' Abhijit Gosavi, Simulation‐Based Optimization: Parametric Optimization Techniques and Reinforcement Learning, Springer, 2nd Edition (2015)

# '''[[User:Lpetroia/sandbox|Jump up^]]''' Rahimi Mazrae Shahi, M., Fallah Mehdipour, E. and Amiri, M. (2016), Optimization using simulation and response surface methodology with an application on subway train scheduling. Intl. Trans. in Op. Res., 23: 797–811. doi:10.1111/itor.12150

# '''[[User:Lpetroia/sandbox|Jump up^]]''' Conn, A. R.; Scheinberg, K.; Vicente, L. N. (2009). [http://www.mat.uc.pt/~lnv/idfo/ ''Introduction to Derivative-Free Optimization'']. MPS-SIAM Book Series on Optimization. Philadelphia: SIAM. Retrieved 2014-01-18.

# '''[[User:Lpetroia/sandbox|Jump up^]]''' Van Roy, B., Bertsekas, D., Lee, Y., & Tsitsiklis, J. (1997). Neuro-dynamic programming approach to retailer inventory management. ''Proceedings of the IEEE Conference on Decision and Control,'' ''4'', 4052-4057.

# '''[[User:Lpetroia/sandbox|Jump up^]]''' Cooper, Leon; Cooper, Mary W. Introduction to dynamic programming. New York: Pergamon Press, 1981

# '''[[User:Lpetroia/sandbox|Jump up^]]''' Prasetio, Y. (2005). ''Simulation-based optimization for complex stochastic systems''. University of Washington.

# '''[[User:Lpetroia/sandbox|Jump up^]]''' Deng, G., & Ferris, Michael. (2007). ''Simulation-based Optimization,'' ProQuest Dissertations and Theses

# '''[[User:Lpetroia/sandbox|Jump up^]]''' Nguyen, S., Reiter, P., Rigo, A., & Anh-Tuan Nguyen, S. (2014). A review on simulation-based optimization methods applied to building performance analysis.''Applied Energy,'' ''113'', 1043-1058.

# '''[[User:Lpetroia/sandbox|Jump up^]]''' Saif, A., Ravikumar Pandi, V., Zeineldin, H., & Kennedy, S. (2013). Optimal allocation of distributed energy resources through simulation-based optimization. ''Electric Power Systems Research,'' ''104'', 1-8.

==References==