Evolutionary many-objective optimisation: pushing the boundaries

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonMany-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 significantly 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.Department of Computer Science, Brunel University Londo

User-preference based evolutionary algorithms for many-objective optimisation

Evolutionary Algorithms (EA) have enjoyed great success in finding solutions for multi-objective problems that have two or three-objectives in the past decade. The majority of these Evolutionary Multi-objective Optimisation (EMO) algorithms explored the decision-space using the selection pressure governed methods that are based on dominance relation. Although these algorithms are effective locating solutions for multi-objective problems, they have not been very successful for problem instances having more than three objectives, usually named as many-objective problems. The main reason behind this shortcoming is the fact that the dominance comparison becomes ineffective as the number of objectives increases. In this thesis, we incorporate some user-preference methods into EMO algorithms to enhance their ability to handle many-objective problems. To this end, we introduce a distance metric derived from user-preference schemes such as the reference point method and light beam search found in multi-criteria decision making. This distance metric is used to guide the EMO algorithm to locate solutions within certain areas of the objective-space known as preferred regions. In our distance metric approach, the decision maker is allowed to specify the amount of spread of solutions along the solution front as well. We name this distance metric based EMO algorithm as d-EMO, which is a generalised framework that can be constructed using any EA. This distance metric approach is computationally less expensive as it does not rely on dominance ranking methods, but very effective in solving many-objective problems. One key issue that remains to be resolved is that there are no suitable metrics for comparing the performance of these user-preference EMO algorithms. Therefore, we introduce a variation of the normalised Hyper-Volume (HV) metric suitable for comparing user-preference EMO algorithms. The key feature in our HV calculation process is to consider only the solutions within each preferred region. This methodology favours user-preference EMO algorithms that have converged closely to the Pareto front within a preferred region. We have identified two real-world engineering design problems in optimising aerofoil and lens designs, and formulated them as many-objective problems. The optimisation process of these many-objective problems is computationally expensive. Hence, we use a reference point PSO algorithm named MDEPSO to locate solutions effectively in fewer function evaluations. This PSO algorithm is less prone to getting stuck in local optimal fronts and still retains its fast convergence ability. In MDEPSO, this feature is achieved by generating leader particles using a differential evolution rule rather than picking particles directly from the population or an external archive. The main feature of the optimisation process of these aerofoil and lens design problems is the derivation of reference points based on existing designs. We illustrate how these existing designs can be used to either obtain better or new design solutions that correspond to various requirements. This process of deriving reference points based on existing design models, and integrating them into a user-preference EMO framework is a novel approach in the optimisation process of such computationally expensive engineering design problems

Free Search – comparative analysis 100

Abstract: Search methods’ abilities for adaptation to various multidimensional tasks where optimisation parameters are hundreds, thousands and more, without retuning of algorithms’ parameters seems to be a great challenge for modern computational intelligence. Many evolutionary, swarm and adaptive methods, which perform well on numerical tests with up to ten dimensions are suffering insuperable stagnation when applied to 100 and more dimensional tests. This article presents a comparison between particle swarm optimisation, differential evolution both with enhanced adaptivity and Free Search applied to 100 multidimensional heterogeneous real-value numerical tests. The aim is to extend the knowledge on how high dimensionality reflects on search space complexity, in particular to identify minimal time and minimal number of objective function evaluations required by used methods for reaching acceptable solution with non-zero probability on tasks with high dimensions’ number. The achieved experimental results are summarised and analysed. Brief discussion on concepts, which support search methods effectiveness, concludes the article

SIP: Optimal Product Selection from Feature Models using Many-Objective Evolutionary Optimisation

© ACM, 2016. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Software Engineering and Methodology, Vol. 25, No. 2, Article 17, Publication date: April 2016. https://doi.acm.org/10.1145/2897760The European Commission (FEDER) and Spanish Government under CICYT project TAPAS (TIN2012-32273) and the Andalusian Government projects THEOS (TIC-5906) and COPAS (P12-TIC-1867

A multi-objective window optimisation problem

We present an optimisation problem which seeks to locate the Pareto-optimal front of building window and shading designs minimising two objectives: projected energy use of the operational building and its construction cost. This problem is of particular interest because it has many variable interactions and each function evaluation is relatively timeconsuming. It also makes use of a freely-available building simulation program EnergyPlus which may be used in many other building design optimisation problems. We describe the problem and report the results of experiments comparing the performance of a number of existing multi-objective evolutionary algorithms applied to it. We conclude that this represents a promising real-world application area

On the evolutionary optimisation of many conflicting objectives

This inquiry explores the effectiveness of a class of modern evolutionary algorithms, represented by Non-dominated Sorting Genetic Algorithm (NSGA) components, for solving optimisation tasks with many conflicting objectives. Optimiser behaviour is assessed for a grid of mutation and recombination operator configurations. Performance maps are obtained for the dual aims of proximity to, and distribution across, the optimal trade-off surface. Performance sweet-spots for both variation operators are observed to contract as the number of objectives is increased. Classical settings for recombination are shown to be suitable for small numbers of objectives but correspond to very poor performance for higher numbers of objectives, even when large population sizes are used. Explanations for this behaviour are offered via the concepts of dominance resistance and active diversity promotion

A convergence acceleration operator for multiobjective optimisation

A novel multiobjective optimisation accelerator is introduced that uses direct manipulation in objective space together with neural network mappings from objective space to decision space. This operator is a portable component that can be hybridized with any multiobjective optimisation algorithm. The purpose of this Convergence Acceleration Operator (CAO) is to enhance the search capability and the speed of convergence of the host algorithm. The operator acts directly in objective space to suggest improvements to solutions obtained by a multiobjective evolutionary algorithm (MOEA). These suggested improved objective vectors are then mapped into decision variable space and tested. The CAO is incorporated with two leading MOEAs, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2) and tested. Results show that the hybridized algorithms consistently improve the speed of convergence of the original algorithm whilst maintaining the desired distribution of solutions

Multi-objective evolutionary algorithms and hyper-heuristics for wind farm layout optimisation

Wind farm layout optimisation is a challenging real-world problem which requires the discovery of trade-off solutions considering a variety of conflicting criteria, such as minimisation of the land area usage and maximisation of energy production. However, due to the complexity of handling multiple objectives simultaneously, many approaches proposed in the literature often focus on the optimisation of a single objective when deciding the locations for a set of wind turbines spread across a given region. In this study, we tackle a multi-objective wind farm layout optimisation problem. Different from the previously proposed approaches, we are applying a high-level search method, known as selection hyper-heuristic to solve this problem. Selection hyper-heuristics mix and control a predefined set of low-level (meta)heuristics which operate on solutions. We test nine different selection hyper-heuristics including an online learning hyper-heuristic on a multi-objective wind farm layout optimisation problem. Our hyper-heuristic approaches manage three well-known multi-objective evolutionary algorithms as low-level metaheuristics. The empirical results indicate the success and potential of selection hyper-heuristics for solving this computationally difficult problem. We additionally explore other objectives in wind farm layout optimisation problems to gain a better understanding of the conflicting nature of those objectives

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners