3 research outputs found
The True Destination of EGO is Multi-local Optimization
Efficient global optimization is a popular algorithm for the optimization of
expensive multimodal black-box functions. One important reason for its
popularity is its theoretical foundation of global convergence. However, as the
budgets in expensive optimization are very small, the asymptotic properties
only play a minor role and the algorithm sometimes comes off badly in
experimental comparisons. Many alternative variants have therefore been
proposed over the years. In this work, we show experimentally that the
algorithm instead has its strength in a setting where multiple optima are to be
identified
Tuning optimization algorithms for real-world problems by means of surrogate modeling
The case-specific tuning of parameters of optimization metaheuristics like evolutionary algorithms almost always leads to significant improvements in performance. But if the evaluation of the objective function is computationally expensive, which is typically the case for real-worlds problems, an extensive parameter tuning phase on the original problem is prohibitive. Therefore we have developed another approach: Provided that a (computationally cheap) surrogate model is available that reflects the structural characteristics of the original problem then the parameter tuning can be run on the surrogate problem before using the best parameters thereby identified for the metaheuristic when optimizing the original problem. In this experimental study we aim to assess how many function evaluations on the original problem are necessary to build a surrogate model endowed with the characteristics of the original problem and to develop a methodology that measures to which extent such a matching has been achieved
Hypervolume based metaheuristics for multiobjective optimization
The purpose of multiobjective optimization is to find solutions that are optimal
regarding several goals. In the branch of vector or Pareto optimization all these
goals are considered to be of equal importance, so that compromise solutions that
cannot be improved regarding one goal without deteriorating in another are Paretooptimal.
A variety of quality measures exist to evaluate approximations of the Paretooptimal
set generated by optimizers, wherein the hypervolume is the most significant
one, making the hypervolume calculation a core problem of multiobjective
optimization. This thesis tackles that challenge by providing a new hypervolume algorithm
from computational geometry and analyzing the problem’s computational
complexity.
Evolutionary multiobjective optimization algorithms (EMOA) are state-of-the-art
methods for Pareto optimization, wherein the hypervolume-based algorithms belong
to the most powerful ones, among them the popular SMS-EMOA. After its
promising capabilities have already been demonstrated in first studies, this thesis
is dedicated to deeper understand the underlying optimization process of the
SMS-EMOA and similar algorithms, in order to specify their performance characteristics.
Theoretical analyses are accomplished as far as possible with established
and newly developed tools. Beyond the limitations of rigorous scrutiny, insights
are gained via thorough experimental investigation. All considered problems are
continuous, whereas the algorithms are as well applicable to discrete problems.
More precisely, the following topics are concerned. The process of approaching
the Pareto-optimal set of points is characterized by the convergence speed, which
is analyzed for a general framework of EA with hypervolume selection on several
classes of bi-objective problems. The results are achieved by a newly developed
concept of linking single and multiobjective optimization. The optimization on the
Pareto front, that is turning the population into a set with maximal hypervolume,
is considered separately, focusing on the question under which circumstances the
steady-state selection of exchanging only one population member suffices to reach a
global optimum. We answer this question for different bi-objective problem classes.
In a benchmarking on so-called many-objective problems of more than three objectives,
the qualification of the SMS-EMOA is demonstrated in comparison to other
EMOA, while also studying their cause of failure. Within the mentioned examinations,
the choice of the hypervolume’s reference point receives special consideration
by exposing its influence. Beyond the study of the SMS-EMOA with default setup,
it is analyzed to what extent the performance can be improved by parameter tuning
of the EMOA anent to certain problems, focusing on the influence of variation operators.
Lastly, an optimization algorithm based on the gradient of the hypervolume
is developed and hybridized with the SMS-EMOA