Abstract

Many-objective optimisation poses great challenges to evolutionary algorithms. To
start with, the ineffectiveness of the Pareto dominance relation, which is the most
important criterion in multi-objective optimisation, results in the underperformance
of traditional Pareto-based algorithms. Also, the aggravation of the conflict between
proximity and diversity, along with increasing time or space requirement as well as
parameter sensitivity, has become key barriers to the design of effective many-objective
optimisation algorithms. Furthermore, the infeasibility of solutions' direct observation
can lead to serious difficulties in algorithms' performance investigation and comparison.
In this thesis, we address these challenges, aiming to make evolutionary algorithms
as effective in many-objective optimisation as in two- or three-objective optimisation.
First, we signifficantly enhance Pareto-based algorithms to make them suitable for
many-objective optimisation by placing individuals with poor proximity into crowded
regions so that these individuals can have a better chance to be eliminated. Second,
we propose a grid-based evolutionary algorithm which explores the potential of the
grid to deal with many-objective optimisation problems. Third, we present a bi-goal
evolution framework that converts many objectives of a given problem into two objectives
regarding proximity and diversity, thus creating an optimisation problem in
which the objectives are the goals of the search process itself. Fourth, we propose a
comprehensive performance indicator to compare evolutionary algorithms in optimisation
problems with various Pareto front shapes and any objective dimensionality.
Finally, we construct a test problem to aid the visual investigation of evolutionary
search, with its Pareto optimal solutions in a two-dimensional decision space having
similar distribution to their images in a higher-dimensional objective space.
The work reported in this thesis is the outcome of innovative attempts at addressing
some of the most challenging problems in evolutionary many-objective optimisation.
This research has not only made some of the existing approaches, such as Pareto-based
or grid-based algorithms that were traditionally regarded as unsuitable, now
effective for many-objective optimisation, but also pushed other important boundaries
with novel ideas including bi-goal evolution, a comprehensive performance indicator
and a test problem for visual investigation. All the proposed algorithms have been
systematically evaluated against existing state of the arts, and some of these algorithms
have already been taken up by researchers and practitioners in the field.