Simulation-based optimization: Difference between revisions

Revision as of 08:01, 15 January 2021

Revision as of 03:59, 16 February 2021

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'''Simulation-based optimization''' (also known as simply '''simulation optimization''') integrates [[optimization (mathematics)|optimization]] techniques into [[computer simulation|simulation]] modeling and analysis. Because of the complexity of the simulation, the [[objective function]] may become difficult and expensive to evaluate. Usually, the underlying simulation model is stochastic, so that that the objective function must be estimated using statistical estimation techniques (called output analysis in simulation methodology).

Once a system is mathematically modeled, computer-based simulations provide information about its behavior. Parametric simulation methods can be used to improve the performance of a system. In this method, the input of each variable is varied with other parameters remaining constant and the effect on the design objective is observed. This is a time-consuming method and improves the performance partially. To obtain the optimal solution with minimum computation and time, the problem is solved iteratively where in each iteration the solution moves closer to the optimum solution. Such methods are known as ‘numerical optimization’ or ‘simulation-based optimization’.<ref>Nguyen, Anh-Tuan, Sigrid Reiter, and Philippe Rigo. "[https://orbi.uliege.be/bitstream/2268/155988/1/Nguyen%20AT.pdf A review on simulation-based optimization methods applied to building performance analysis]."''Applied Energy'' 113 (2014): 1043–1058.</ref>

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=== Stochastic approximation ===

[[Stochastic approximation]] is used when the function cannot be computed directly, only estimated via noisy observations. In thisthese scenarios, this method (or family of methods) looks for the extrema of these function. The objective function would be:<ref>Powell, W. (2011). ''Approximate Dynamic Programming Solving the Curses of Dimensionality'' (2nd ed., Wiley Series in Probability and Statistics). Hoboken: Wiley.</ref>

:<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>

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:<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 prepareprepares it for the future optimization.

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

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== Limitations ==

Simulation -based optimization has some limitations, such as the difficulty of creating a model that imitates the dynamic behavior of a system in a way that is considered good enough for its representation. Another problem is complexity in the determining uncontrollable parameters of both real-world system and simulation. Moreover, only a statistical estimation of real values can be obtained. It is not easy to determine the objective function, since it is a result of measurements, which can be harmful forto the solutions.<ref>Prasetio, Y. (2005). ''[https://elibrary.ru/item.asp?id=9387151 Simulation-based optimization for complex stochastic systems]''. University of Washington.</ref><ref>Deng, G., & Ferris, Michael. (2007). ''Simulation-based Optimization,'' ProQuest Dissertations and Theses</ref>

==References==