The covariancematrix adaptation evolution strategy (CMA-ES) is one
of themost powerful
evolutionary algorithms for real-valued single-objective optimization.
In this paper,
we develop a variant of the CMA-ES for multi-objective optimization
(MOO).We
first introduce a single-objective, elitist CMA-ES using plus-selection
and step size control
based on a success rule. This algorithm is compared to the standard
CMA-ES.
The elitist CMA-ES turns out to be slightly faster on unimodal functions,
but is more
prone to getting stuck in sub-optimal local minima. In the new multi-objective
CMAES
(MO-CMA-ES) a population of individuals that adapt their search strategy
as in
the elitist CMA-ES is maintained. These are subject to multi-objective
selection. The
selection is based on non-dominated sorting using either the crowding-distance
or the
contributing hypervolume as second sorting criterion. Both the elitist
single-objective
CMA-ES and the MO-CMA-ES inherit important invariance properties,
in particular
invariance against rotation of the search space, from the original
CMA-ES. The benefits
of the new MO-CMA-ES in comparison to the well-known NSGA-II and to
NSDE,
a multi-objective differential evolution algorithm, are experimentally
shown.
%0 Journal Article
%1 Igel:2007
%A Igel, Christian
%A Hansen, Nikolaus
%A Roth, Stefan
%D 2007
%J Evolutionary Computation
%K Multi-objective adaptation covariance evolution matrix optimization, strategy,
%P 1-28
%T Covariance Matrix Adaptation for Multi-objective Optimization
%V 15
%X The covariancematrix adaptation evolution strategy (CMA-ES) is one
of themost powerful
evolutionary algorithms for real-valued single-objective optimization.
In this paper,
we develop a variant of the CMA-ES for multi-objective optimization
(MOO).We
first introduce a single-objective, elitist CMA-ES using plus-selection
and step size control
based on a success rule. This algorithm is compared to the standard
CMA-ES.
The elitist CMA-ES turns out to be slightly faster on unimodal functions,
but is more
prone to getting stuck in sub-optimal local minima. In the new multi-objective
CMAES
(MO-CMA-ES) a population of individuals that adapt their search strategy
as in
the elitist CMA-ES is maintained. These are subject to multi-objective
selection. The
selection is based on non-dominated sorting using either the crowding-distance
or the
contributing hypervolume as second sorting criterion. Both the elitist
single-objective
CMA-ES and the MO-CMA-ES inherit important invariance properties,
in particular
invariance against rotation of the search space, from the original
CMA-ES. The benefits
of the new MO-CMA-ES in comparison to the well-known NSGA-II and to
NSDE,
a multi-objective differential evolution algorithm, are experimentally
shown.
@article{Igel:2007,
abstract = {The covariancematrix adaptation evolution strategy (CMA-ES) is one
of themost powerful
evolutionary algorithms for real-valued single-objective optimization.
In this paper,
we develop a variant of the CMA-ES for multi-objective optimization
(MOO).We
first introduce a single-objective, elitist CMA-ES using plus-selection
and step size control
based on a success rule. This algorithm is compared to the standard
CMA-ES.
The elitist CMA-ES turns out to be slightly faster on unimodal functions,
but is more
prone to getting stuck in sub-optimal local minima. In the new multi-objective
CMAES
(MO-CMA-ES) a population of individuals that adapt their search strategy
as in
the elitist CMA-ES is maintained. These are subject to multi-objective
selection. The
selection is based on non-dominated sorting using either the crowding-distance
or the
contributing hypervolume as second sorting criterion. Both the elitist
single-objective
CMA-ES and the MO-CMA-ES inherit important invariance properties,
in particular
invariance against rotation of the search space, from the original
CMA-ES. The benefits
of the new MO-CMA-ES in comparison to the well-known NSGA-II and to
NSDE,
a multi-objective differential evolution algorithm, are experimentally
shown.},
added-at = {2009-06-26T15:25:19.000+0200},
author = {Igel, Christian and Hansen, Nikolaus and Roth, Stefan},
biburl = {https://www.bibsonomy.org/bibtex/2da3bff96337997b9266cca4660b87b07/butz},
description = {diverse cognitive systems bib},
interhash = {2dca97e41e0ff1847218b04b0db73fee},
intrahash = {da3bff96337997b9266cca4660b87b07},
journal = {Evolutionary Computation},
keywords = {Multi-objective adaptation covariance evolution matrix optimization, strategy,},
owner = {butz},
pages = {1-28},
timestamp = {2009-06-26T15:25:38.000+0200},
title = {Covariance Matrix Adaptation for Multi-objective Optimization},
volume = 15,
year = 2007
}