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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 the objective function must be estimated using statistical estimation techniques (called output analysis in simulation methodology).
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In the simulation optimization setting, applicable methods include indifference zone approaches, optimal computing budget allocation, and knowledge gradient algorithms.
=== Response surface
In [[response surface methodology]], the objective is to find the relationship between the input variables and the response variables. The process starts from trying to fit a linear regression model. If the P-value turns out to be low, then a higher degree polynomial regression, which is usually quadratic, will be implemented. The process of finding a good relationship between input and response variables will be done for each simulation test. In simulation optimization, response surface method can be used to find the best input variables that produce desired outcomes in terms of response variables.<ref>Rahimi Mazrae Shahi, M., Fallah Mehdipour, E. and Amiri, M. (2016), [https://onlinelibrary.wiley.com/doi/abs/10.1111/itor.12150 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}}</ref>
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=== Derivative-free optimization methods ===
[[Derivative-free optimization]] is a subject of mathematical optimization. This method is applied to a certain optimization problem when its derivatives are unavailable or unreliable. Derivative-free methods establish a model based on sample function values or directly draw a sample set of function values without exploiting a detailed model. Since it needs no derivatives, it cannot be compared to derivative-based methods.<ref>Conn, A. R.; [[Katya Scheinberg|Scheinberg, K.]]; [[Luis Nunes Vicente|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.</ref>
For unconstrained optimization problems, it has the form:
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