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Simulation Optimization Using a Hybrid Scheme … 123

been used to obtain policies that modify system behavior. Burns and Malone (1974)
expressed the required policy as an open-loop solution (i.e., the solution function has not
the variables from the system). The drawback of this method is that if the system
fluctuates by some little impact, the open loop solution without information feedback
cannot adjust itself to the new state. Keloharju (1982) proposed a method of iterative
simulation where each iteration consists of a parameter optimization. He suggests
predefining the policy structure by allowing certain parameters of the model to be
variables and by adding new parameters. However, the policies obtained with
Keloharju’s method are not robust when subject to variations of external inputs because
the policy structure was predefined and thereafter optimized (Macedo, 1989). Coyle
(1985) included structural changes to the model, and applies the method to a production
system.
Kleijnen (1995) presented a method that includes design of experiments and response
surface methodology for optimizing the parameters of a model. The approach treats
system dynamics (SD) as a black box, creating a set of regression equations to
approximate the simulation model. The statistical design of experiments is applied to
determine which parameters are significant. After dropping the insignificant parameters,
the objective function is optimized by using the Lagrange multiplier method. The
parameter values obtained through the procedure are the final solution. Bailey et al.
(2000) extended Kleijnen’s method by using response surfaces not to replace the
simulation models with analytic equations, but instead to direct attention to regions
within the design space with the most desirable performance. Their approach identifies
the exploration points surrounding the solution of Kleijnen’s method and the finds a set
of real best combination of parameters from them (Chen and Jeng, 2004).
Grossmann (2002) used genetic algorithms (GA) to find optimal policies. He
demonstrates his approach in the Information Society Integrated System Model where he
evaluates different objective functions. Another method that uses genetic algorithms to
search the solution space is the one proposed by Chen and Jeng (2004). First, they
transform the SD model into a recurrent neural network. Next, they use a genetic
algorithm to generate policies by fitting the desired system behavior to patterns
established in the neural network. Chen and Jeng claim their approach is flexible in the
sense that it can find policies for a variety of behavior patterns including stable
trajectories. However, the transformation stage might become difficult when SD models
reach real-world sizes.
In optimal control applied to system dynamics, Macedo (1989) introduced a mixed
approach in which optimal control and traditional optimization are sequentially applied in
the improvement of the SD model. Macedo’s approach consists principally of two
models: a reference model and a control model. The reference model is an optimization
model whose main objective is to obtain the desired trajectories of the variables of
interest. The control model is an optimal linear-quadratic control model whose