10 Sequential Parameter Optimization for Mixed-Discrete Problems
339
optimization techniques can lead to regions with seemingly good function caused by
a misinterpretation of the noisy data. This issue appears if surrogate models confuse
noise with the actual behaviour of the objective function.
Thus, finding efficient methods to deal with uncertainty appears to be a nontrivial problem. A popular approach is searching for robust optima. This is done
by replacing the deterministic objective function f in favour of a modified ˜
f that
feeds an estimation of f back to the optimizer. This is evaluated observing the
response of f a number of times with the same design solution. Popular examples
of ˜
f are the expected value, expected value + k standard deviation (the importance
of the standard deviations in respect of the mean is weighted by the coefficient
k) or the 95% quantile. The obvious drawback of this method is the considerable
number of repetitions of f that are needed to make an accurate prediction of the
robust objective function. However, researchers are proposing methods to mitigate
the computational effort in estimating ˜
f replacing classic uncertainty quantification
methods, such as quasi-Monte Carlo quadrature, in favour of polynomial chaos with
coefficients determined by sparse quadrature and by point collocation, radial basis
function or Kriging models [32].
10.4 Sequential Parameter Optimization
The sequential parameter optimization toolbox (SPOT) [6] is an optimization
framework which is based on surrogate model-based optimization. The aim of
SMBO is to train a cheap numerical model that approximates the objective function
and utilize it to reduce the computational effort.
Initially proposed for algorithm tuning of metaheuristics, SPOT is a sophisticated
tool capable of handling both continuous and mixed-discrete problems [8]. SPOT
spends the available budget in a sequential manner to maximize information gain
and is particularly efficient for expensive problems. SPOT finds improved solutions
in the following way (see Algorithm 1): First, the search space is sampled with an
experimental design plan (see Sect. 10.4.1). With these samples, a first surrogate
model is constructed. Then, an infill criterion is optimized on the surrogate to find
new promising candidate solutions. The suggested candidates are evaluated with the
real objective function, and the surrogate is updated with the observed information.
In the following we will describe the fundamental steps of the SPOT methodology.
A more detailed description of SPOT can be found in [9].
339
optimization techniques can lead to regions with seemingly good function caused by
a misinterpretation of the noisy data. This issue appears if surrogate models confuse
noise with the actual behaviour of the objective function.
Thus, finding efficient methods to deal with uncertainty appears to be a nontrivial problem. A popular approach is searching for robust optima. This is done
by replacing the deterministic objective function f in favour of a modified ˜
f that
feeds an estimation of f back to the optimizer. This is evaluated observing the
response of f a number of times with the same design solution. Popular examples
of ˜
f are the expected value, expected value + k standard deviation (the importance
of the standard deviations in respect of the mean is weighted by the coefficient
k) or the 95% quantile. The obvious drawback of this method is the considerable
number of repetitions of f that are needed to make an accurate prediction of the
robust objective function. However, researchers are proposing methods to mitigate
the computational effort in estimating ˜
f replacing classic uncertainty quantification
methods, such as quasi-Monte Carlo quadrature, in favour of polynomial chaos with
coefficients determined by sparse quadrature and by point collocation, radial basis
function or Kriging models [32].
10.4 Sequential Parameter Optimization
The sequential parameter optimization toolbox (SPOT) [6] is an optimization
framework which is based on surrogate model-based optimization. The aim of
SMBO is to train a cheap numerical model that approximates the objective function
and utilize it to reduce the computational effort.
Initially proposed for algorithm tuning of metaheuristics, SPOT is a sophisticated
tool capable of handling both continuous and mixed-discrete problems [8]. SPOT
spends the available budget in a sequential manner to maximize information gain
and is particularly efficient for expensive problems. SPOT finds improved solutions
in the following way (see Algorithm 1): First, the search space is sampled with an
experimental design plan (see Sect. 10.4.1). With these samples, a first surrogate
model is constructed. Then, an infill criterion is optimized on the surrogate to find
new promising candidate solutions. The suggested candidates are evaluated with the
real objective function, and the surrogate is updated with the observed information.
In the following we will describe the fundamental steps of the SPOT methodology.
A more detailed description of SPOT can be found in [9].