  The Efficient Global Optimization (EGO) algorithm uses a conditional
Gaus-sian Process (GP) to approximate an objective function known at a finite
number of observation points and sequentially adds new points which maximize
the Expected Improvement criterion according to the GP. The important factor
that controls the efficiency of EGO is the GP covariance function (or kernel)
which should be chosen according to the objective function. Traditionally, a
pa-rameterized family of covariance functions is considered whose parameters
are learned through statistical procedures such as maximum likelihood or
cross-validation. However, it may be questioned whether statistical procedures
for learning covariance functions are the most efficient for optimization as
they target a global agreement between the GP and the observations which is not
the ultimate goal of optimization. Furthermore, statistical learning procedures
are computationally expensive. The main alternative to the statistical learning
of the GP is self-adaptation, where the algorithm tunes the kernel parameters
based on their contribution to objective function improvement. After
questioning the possibility of self-adaptation for kriging based optimizers,
this paper proposes a novel approach for tuning the length-scale of the GP in
EGO: At each iteration, a small ensemble of kriging models structured by their
length-scales is created. All of the models contribute to an iterate in an
EGO-like fashion. Then, the set of models is densified around the model whose
length-scale yielded the best iterate and further points are produced.
Numerical experiments are provided which motivate the use of many
length-scales. The tested implementation does not perform better than the
classical EGO algorithm in a sequential context but show the potential of the
approach for parallel implementations.
