2.3 Combination of Simulation and Optimization Methods
37
WITNESS Optimizer uses Adaptive Thermo-Statistical Simulated Annealing
(ATSA) as a primary search procedure. ATSA is a combination of simulated annealing and tabu search, which is able to modify its search strategy accordingly by
learning from its experience of the problem domain [Es+2011, p. 2365]. The
WITNESS Optimizer has three stopping rules. Firstly, it stops after a defined
maximum number of configurations has been reached. Secondly, the algorithm is
stopped when a number of consecutive configurations for which we see no improvement in the values of the objective function is reached and thirdly, the optimizer
stops when all feasible configurations have been run through. WITNESS Optimizer calculates feasible configurations, considering constraints formulated for
an optimization problem. Additionally, it includes a mechanism to evaluate “the
replication-to-replication variability of the objective function for a particular
configuration” [La2007, p. 661].
In addition to the embedded optimization solutions previously described,
there are also software solutions with a so-called open architecture, whose core
cannot be changed, but which can be extended significantly by the use of toolboxes. Matlab is one example of such a software solution [Be2010, p. 3].
The Matlab toolboxes are understood to be a collection of predefined subprograms to expand the Matlab functionalities 19 . They are on the one hand
offered by MathWorks itself to supplement the software but are also freely available online in the form of non-commercial toolboxes. MathWorks provides the
option of including an Optimization Toolbox™ for finding parameters for minimizing or maximizing objective functions and to solve linear programming (LP),
mixed-integer linear programming (MILP), quadratic programming (QP), nonlinear programming (NLP), constrained linear least squares, nonlinear least squares,
and nonlinear equations [Th2019a]. Additionally, a global optimization toolbox is
available, which allows for the use of any optimization algorithm including pattern search, genetic algorithms, particle swarm optimization, simulated annealing,
multi-start optimization, and global search algorithms. The Global Optimization
Toolbox can solve optimization problems “where the objective or constraint function is continuous, discontinuous, stochastic, does not possess derivatives, or
includes simulations or black-box functions” [Th2019b].
19 The interested reader is referred to the further literature on the Optimization Toolbox™ at
this point, since only a very briefly overview of the functionalities can be given in this work.
The MathsWorks, Inc. offers a very detailed manual on the optimization functionalities of
the toolbox [Th2019a], in addition there are further explanations in Angermann et al.
[An+2017, pp. 241–286] and Benker [Be2010, pp. 213–226]. Ait El Cadi, Gharbi and
Artiba provide a comprehensive comparison of the functionalities and the performance of
OptQuest and the Optimization Toolbox™ [AGA2016].
37
WITNESS Optimizer uses Adaptive Thermo-Statistical Simulated Annealing
(ATSA) as a primary search procedure. ATSA is a combination of simulated annealing and tabu search, which is able to modify its search strategy accordingly by
learning from its experience of the problem domain [Es+2011, p. 2365]. The
WITNESS Optimizer has three stopping rules. Firstly, it stops after a defined
maximum number of configurations has been reached. Secondly, the algorithm is
stopped when a number of consecutive configurations for which we see no improvement in the values of the objective function is reached and thirdly, the optimizer
stops when all feasible configurations have been run through. WITNESS Optimizer calculates feasible configurations, considering constraints formulated for
an optimization problem. Additionally, it includes a mechanism to evaluate “the
replication-to-replication variability of the objective function for a particular
configuration” [La2007, p. 661].
In addition to the embedded optimization solutions previously described,
there are also software solutions with a so-called open architecture, whose core
cannot be changed, but which can be extended significantly by the use of toolboxes. Matlab is one example of such a software solution [Be2010, p. 3].
The Matlab toolboxes are understood to be a collection of predefined subprograms to expand the Matlab functionalities 19 . They are on the one hand
offered by MathWorks itself to supplement the software but are also freely available online in the form of non-commercial toolboxes. MathWorks provides the
option of including an Optimization Toolbox™ for finding parameters for minimizing or maximizing objective functions and to solve linear programming (LP),
mixed-integer linear programming (MILP), quadratic programming (QP), nonlinear programming (NLP), constrained linear least squares, nonlinear least squares,
and nonlinear equations [Th2019a]. Additionally, a global optimization toolbox is
available, which allows for the use of any optimization algorithm including pattern search, genetic algorithms, particle swarm optimization, simulated annealing,
multi-start optimization, and global search algorithms. The Global Optimization
Toolbox can solve optimization problems “where the objective or constraint function is continuous, discontinuous, stochastic, does not possess derivatives, or
includes simulations or black-box functions” [Th2019b].
19 The interested reader is referred to the further literature on the Optimization Toolbox™ at
this point, since only a very briefly overview of the functionalities can be given in this work.
The MathsWorks, Inc. offers a very detailed manual on the optimization functionalities of
the toolbox [Th2019a], in addition there are further explanations in Angermann et al.
[An+2017, pp. 241–286] and Benker [Be2010, pp. 213–226]. Ait El Cadi, Gharbi and
Artiba provide a comprehensive comparison of the functionalities and the performance of
OptQuest and the Optimization Toolbox™ [AGA2016].