34
2 Simulation-Based Optimization
with ξ
randomness of the system
x
decision variables
f (x, ξ) output of the simulation for the objective for one replication
g(x, ξ) constraint function for one replication
While the optimization of systems with many variables is complex anyway,
simulation-based optimization adds the complexity of dealing with estimates for
f (x) for any given x [JH2015, p. 1783; Fu2013, p. 1418]. It is hardly possible
to evaluate the performance of a particular experiment design exactly. “Because
we have estimates, it is not possible to conclude with assurance that one design
is better than another, and this uncertainty frustrates optimization algorithms that
try to move in improving directions. In principle, one can eliminate this complication by making so many replications, or such long runs, at each design point
that the performance estimate has essentially no variance” [Ba+2005, p. 412].
This is highly time and capacity consuming, as the execution time of a simulation is highly dependent on the number of system configurations that have to be
tested [La2007, p. 659]. When trying to come up with algorithms that reliably
identify high-quality solutions, simulation-based optimization is forced to make
compromises such as guaranteeing a prespecified probability of correct selections,
ensuring asymptotic convergence to the optimal solution, avoiding algorithms that
can be misled by sampling variability or the use of robust heuristics that include
randomness as a part of their search strategy as they are less sensitive to sampling
variability [Ba+2005, p. 412].
Despite the mentioned problems, the simulation-based optimization also brings
advantages. Since the simulation-based optimization is not subject to specific
restrictions regarding the form of the objective function, any number of targets
can be specified. Additionally, due to the so-called “any-time characteristic”, the
simulation-based optimization algorithms, which are generally iterative in nature,
determine a result, even in the case of insufficient computation time and premature termination of the calculation run as the best result detected up to this time is
used [Vö+2003, p. 37]. Further, the consideration of important constraints in the
underlying simulation model of the simulation-based optimization is a common
tool to depict special process conditions, which is—in most cases—easier than
the mathematical formulation of systems of inequations [Vö+2003, p. 38].
Based on the availability of fast computers and improved optimization heuristics, most simulation software vendors have nowadays integrated optimization
packages in their simulation software [La2007, p. 658]. According to Bayraskan
in Fu et al. [Fu+2014, p. 3698] “recent developments in the software side are
2 Simulation-Based Optimization
with ξ
randomness of the system
x
decision variables
f (x, ξ) output of the simulation for the objective for one replication
g(x, ξ) constraint function for one replication
While the optimization of systems with many variables is complex anyway,
simulation-based optimization adds the complexity of dealing with estimates for
f (x) for any given x [JH2015, p. 1783; Fu2013, p. 1418]. It is hardly possible
to evaluate the performance of a particular experiment design exactly. “Because
we have estimates, it is not possible to conclude with assurance that one design
is better than another, and this uncertainty frustrates optimization algorithms that
try to move in improving directions. In principle, one can eliminate this complication by making so many replications, or such long runs, at each design point
that the performance estimate has essentially no variance” [Ba+2005, p. 412].
This is highly time and capacity consuming, as the execution time of a simulation is highly dependent on the number of system configurations that have to be
tested [La2007, p. 659]. When trying to come up with algorithms that reliably
identify high-quality solutions, simulation-based optimization is forced to make
compromises such as guaranteeing a prespecified probability of correct selections,
ensuring asymptotic convergence to the optimal solution, avoiding algorithms that
can be misled by sampling variability or the use of robust heuristics that include
randomness as a part of their search strategy as they are less sensitive to sampling
variability [Ba+2005, p. 412].
Despite the mentioned problems, the simulation-based optimization also brings
advantages. Since the simulation-based optimization is not subject to specific
restrictions regarding the form of the objective function, any number of targets
can be specified. Additionally, due to the so-called “any-time characteristic”, the
simulation-based optimization algorithms, which are generally iterative in nature,
determine a result, even in the case of insufficient computation time and premature termination of the calculation run as the best result detected up to this time is
used [Vö+2003, p. 37]. Further, the consideration of important constraints in the
underlying simulation model of the simulation-based optimization is a common
tool to depict special process conditions, which is—in most cases—easier than
the mathematical formulation of systems of inequations [Vö+2003, p. 38].
Based on the availability of fast computers and improved optimization heuristics, most simulation software vendors have nowadays integrated optimization
packages in their simulation software [La2007, p. 658]. According to Bayraskan
in Fu et al. [Fu+2014, p. 3698] “recent developments in the software side are