51 research outputs found
Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Holder constants
In this paper, the global optimization problem with
being a hyperinterval in and satisfying the Lipschitz condition
with an unknown Lipschitz constant is considered. It is supposed that the
function can be multiextremal, non-differentiable, and given as a
`black-box'. To attack the problem, a new global optimization algorithm based
on the following two ideas is proposed and studied both theoretically and
numerically. First, the new algorithm uses numerical approximations to
space-filling curves to reduce the original Lipschitz multi-dimensional problem
to a univariate one satisfying the H\"{o}lder condition. Second, the algorithm
at each iteration applies a new geometric technique working with a number of
possible H\"{o}lder constants chosen from a set of values varying from zero to
infinity showing so that ideas introduced in a popular DIRECT method can be
used in the H\"{o}lder global optimization. Convergence conditions of the
resulting deterministic global optimization method are established. Numerical
experiments carried out on several hundreds of test functions show quite a
promising performance of the new algorithm in comparison with its direct
competitors.Comment: 26 pages, 10 figures, 4 table
Numerical methods using two different approximations of space-filling curves for black-box global optimization
In this paper, multi-dimensional global optimization problems are
considered, where the objective function is supposed to be Lipschitz
continuous, multiextremal, and without a known analytic expression.
Two different approximations of Peano-Hilbert curve to reduce the
problem to a univariate one satisfying the Hölder condition are dis-
cussed. The first of them, piecewise-linear approximation, is broadly
used in global optimization and not only whereas the second one, non-
univalent approximation, is less known. Multi-dimensional geomet-
ric algorithms employing these Peano curve approximations are intro-
duced and their convergence conditions are established. Numerical
experiments executed on 800 randomly generated test functions taken
from the literature show a promising performance of algorithms em-
ploying Peano curve approximations w.r.t. their direct competitors
Metaheuristic optimization of power and energy systems: underlying principles and main issues of the 'rush to heuristics'
In the power and energy systems area, a progressive increase of literature
contributions containing applications of metaheuristic algorithms is occurring.
In many cases, these applications are merely aimed at proposing the testing of
an existing metaheuristic algorithm on a specific problem, claiming that the
proposed method is better than other methods based on weak comparisons. This
'rush to heuristics' does not happen in the evolutionary computation domain,
where the rules for setting up rigorous comparisons are stricter, but are
typical of the domains of application of the metaheuristics. This paper
considers the applications to power and energy systems, and aims at providing a
comprehensive view of the main issues concerning the use of metaheuristics for
global optimization problems. A set of underlying principles that characterize
the metaheuristic algorithms is presented. The customization of metaheuristic
algorithms to fit the constraints of specific problems is discussed. Some
weaknesses and pitfalls found in literature contributions are identified, and
specific guidelines are provided on how to prepare sound contributions on the
application of metaheuristic algorithms to specific problems
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