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Many-Objective Evolutionary Optimisation
Francesco di Pierro
University of Exeter, UK
Soon-Thiam Khu
University of Exeter, UK
Dragan A. Savić
University of Exeter, UK
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INTRODUCTION
Many-objective evolutionary optimisation is a recent
research area that is concerned with the optimisation of
problems consisting of a large number of performance
criteria using evolutionary algorithms. Despite the
tremendous development that multi-objective evolu-
tionary algorithms (MOEAs) have undergone over the
last decade, studies addressing problems consisting of a
large number of objectives are still rare. The main reason
is that these problems cause additional challenges with
respect to low-dimensional ones. This chapter gives a
detailed analysis of these challenges, provides a critical
review of the traditional remedies and methods for the
evolutionary optimisation of many-objective problems
and presents the latest advances in this feld.
BACKGROUND
There has been considerable recent interest in the op-
timisation of problems consisting of more than three
performance criteria, realm that was coined many-
objective optimisation by Farina and Amato (Farina,
& Amato, 2002). To date, the vast majority of the
literature has focused on two and three-dimensional
problems (Deb, 2001). However, in recent years, the
incorporation of multiple indicators into the problem
formulation has clearly emerged as a prerequisite for
a sound approach in many engineering applications
(Coello Coello, Van Veldhuizen, & Lamont, 2002).
Despite the tremendous development that MOEAs
have undergone over the last decade, and their ample
success in disparate applications, studies addressing
high-dimensional real-life problems are still rare (Coello
Coello, & Aguirre, 2002). The main reason is that
many-objective problems cause additional challenges
with respect to low-dimensional ones:
If the dimensionality of the objective space increases,
then in general, the dimensionality of the Pareto-optimal
front also increases.
The number of points required to characterise the
Pareto-optimal front increases exponentially with the
number of objectives considered.
It is clear that these two features represent a hin-
drance for most of the population-based methods,
including MOEAs. In fact, in order to provide a good
approximation of a high-dimensional optimal Pareto
front, this class of algorithms must evolve populations
of solutions of considerable size. This has a profound
impact on their performance, since evaluating each in-
dividual solution may be a time-consuming task. Using
smaller populations would not be a viable option, at least
for Pareto-based algorithms, given the progressive loss
of selective pressure they experience as the number of
objectives increases, with a consequent deterioration of
performances, as it is theoretically shown in (Farina,
& Amato, 2004) and empirically evidenced in (Deb,
2001, pages 404-405). In contrast to Pareto-based
methods, traditional multi-objective optimisation ap-
proaches, which work by reducing the multi-objective
problem into a series of parameterised single-objective
ones that are solved in succession, are not affected by
the curse of dimensionality. However, such strategies
cause each optimisation to be executed independent to
each other, thereby losing the implicit parallelism of
population-based multi-objective algorithms.
The remainder of this chapter provides a detailed
review of the methods proposed to address the frst two