2.3 Combination of Simulation and Optimization Methods
33
the basis for an assessment of the dynamic behavior of the mapped production
system.
The simulation starts with an initial parameter setting. On the basis of these
initial input data, the simulation model is executed for several iterations and
depending on existing stochastics in the model also with a defined number of
replications. The results are passed back to the optimization tool to generate
additional, ideally better parameter configurations based on the optimization algorithm. As shown in Figure 2.10, this process is repeated until the termination
criterion is reached [La2007, p. 658].
Yes
Optimization Package
Simulation Model
Simulate
specified
system
configuration
is
stopping rule
satisfied?
Specify
(additional)
system
configuration
Report
solution
Stop
No
Start
Report Simulation Results (Objective-Function Values)
Figure 2.10 Interactions between optimization and simulation model [La2007, p. 659]
For the simulation-based optimization, the objective function as well as the
constraints can either be linear or nonlinear, while the decision variables can be
continuous or discrete by nature. In most cases, the objective function f and/or
the constraint functions g include randomness, which leads to the fact, that they
cannot be evaluated exactly [JH2015, p. 1781; An1998, p. 308; Fu2015, p. 2].
The objective function f and the constraints may be written as
f (x) = E f (x, ξ), and
= {x : E g(x, ξ) ≥ 0}
(2.5)