Multi-Objective Optimisation Methods Applied to Complex Engineering Systems
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CRANFIELD UNIVERSITY John M. Oliver Multi-Objective Optimisation Methods Applied to Complex Engineering Systems SCHOOL OF ENGINEERING PhD Academic Year: 2013 - 2014 Supervisor: Professor A. Mark Savill Co-supervisor: Dr Timoleon Kipouros September 2014 CRANFIELD UNIVERSITY SCHOOL OF ENGINEERING PhD Academic Year: 2013 - 2014 John M. Oliver Multi-Objective Optimisation Methods Applied to Complex Engineering Systems Supervisor: Professor A. Mark Savill Co-supervisor: Dr Timoleon Kipouros September 2014 This thesis is submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy © Cranfield University, 2014-2016. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright owner. Declaration of Authorship I, John M. Oliver, declare that this thesis titled, `Multi-Objective Optimisation Methods Applied to Complex Engineering Systems' and the work presented in it are my own. I confirm that: This work was done wholly or mainly while in candidature for a research degree at this University. Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated. Where I have consulted the published work of others, this is always clearly attributed. Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work. I have acknowledged all main sources of help. Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself. Signed: Date: 3 \Nothing at all takes place in the universe in which some rule of maximum or minimum does not appear." Leonhard Euler \It always takes longer than you expect, even when you take into account Hofs- tadter's Law." Douglas Hofstadter, G¨odel,Escher, Bach: An Eternal Golden Braid, 1979 \What limit can be put to this power, acting during long ages and rigidly scru- tinising the whole constitution, structure, and habits of each creature, favouring the good and rejecting the bad? I can see no limit to this power, in slowly and beautifully adapting each form to the most complex relations of life." Charles Darwin, On the Origin of Species by Means of Natural Selection, 1859 Abstract This research proposes, implements and analyses a novel framework for multi- objective optimisation through evolutionary computing aimed at, but not re- stricted to, real-world problems in the engineering design domain. Evolutionary algorithms have been used to tackle a variety of non-linear multi- objective optimisation problems successfully, but their success is governed by key parameters which have been shown to be sensitive to the nature of the particular problem, incorporating concerns such as the number of objectives and variables, and the size and topology of the search space, making it hard to determine the best settings in advance. This work describes a real-encoded multi-objective optimising evolutionary algorithm framework, incorporating a genetic algorithm, that uses self-adaptive mutation and crossover in an attempt to avoid such problems, and which has been benchmarked against both standard optimisation test problems in the literature and a real-world airfoil optimisation case. For this last case, the minimisation of drag and maximisation of lift coefficients of a well documented standard airfoil, the framework is integrated with a free- form deformation tool to manage the changes to the section geometry, and XFoil, a tool which evaluates the airfoil in terms of its aerodynamic efficiency. The performance of the framework on this problem is compared with those of two other heuristic MOO algorithms known to perform well, the Multi-Objective Tabu Search (MOTS) and NSGA-II, showing that this framework achieves better or at least no worse convergence. 5 The framework of this research is then considered as a candidate for smart (electricity) grid optimisation. Power networks can be improved in both techni- cal and economical terms by the inclusion of distributed generation which may include renewable energy sources. The essential problem in national power net- works is that of power flow and in particular, optimal power flow calculations of alternating (or possibly, direct) current. The aims of this work are to propose and investigate a method to assist in the determination of the composition of optimal or high-performing power networks in terms of the type, number and location of the distributed generators, and to analyse the multi-dimensional results of the evolutionary computation component in order to reveal relationships between the network design vector elements and to identify possible further methods of im- proving models in future work. The results indicate that the method used is a feasible one for the achievement of these goals, and also for determining optimal flow capacities of transmission lines connecting the bus bars in the network. Keywords Evolutionary, Algorithm, Self-Adaptive, Framework, Electrical Power, Plexos, Power Flow, Network, Grid, MOOEA, Multi-Objective, Optimization, MOO, MOOP, Airfoil Acknowledgements This research was carried out at the School of Engineering of Cranfield University and was enabled and supported by funding from the Engineering and Physical Sciences Research Council (EPSRC), for which I am glad to have this opportunity to express my gratitude. I acknowledge gratefully and give my wholehearted thanks to: My PhD supervisor, Professor Mark Savill, for the opportunity to undertake this work, his support, and his invaluable guidance. My co-supervisor, Dr Timoleon Kipouros, for his insights, suggestions and liaising with colleagues in other institutions. My fellow PhD students past and present with whom I was lucky to share an office, for discussions, their support and friendship, and other colleagues in Professor Savill's group, for the same reasons. My wife, for support, love and tea. 7 Contents Declaration of Authorship3 Abstract5 Acknowledgements7 List of Figures 13 List of Tables 17 Glossary 19 Physical Constants 21 Symbols 23 1 Introduction 27 1.1 Thesis organisation........................... 27 1.2 Background and motivation...................... 28 1.3 Thesis aims and objectives....................... 30 1.4 Publications............................... 31 1.5 Software Produced........................... 32 2 Heuristic multi-objective optimisation algorithms 33 2.1 Introduction............................... 33 2.2 Features of real-world optimisation.................. 33 2.3 Optimisation.............................. 36 2.3.1 Optimisation overview..................... 36 2.3.2 Multi-objective optimisation.................. 41 2.4 Performance of optimisation algorithms................ 47 2.5 Heuristics and meta-heuristics..................... 51 2.5.1 Heuristics............................ 51 2.5.2 Meta-heuristics......................... 52 2.6 Evolutionary algorithms........................ 56 2.6.1 Algorithm adjuncts and concerns............... 62 9 Contents 10 2.6.2 Self-adaptation......................... 67 2.7 Optimisation frameworks........................ 70 2.7.1 Synopsis............................. 70 2.7.2 Non-commercial frameworks.................. 71 2.7.3 Commercial frameworks.................... 72 3 The self-adaptive MOOEA 77 3.1 Introduction............................... 77 3.2 Ganesh: Framework and algorithm.................. 79 3.2.1 The GA Algorithm....................... 79 3.2.1.1 Simplified non-dominated sorting.......... 82 3.2.2 Self-adaptation......................... 89 3.2.3 Framework and architecture.................. 92 3.2.4 Algorithm characteristics, benefits and novelty........ 95 3.2.4.1 Synopsis........................ 96 3.2.4.2 Self-adaptivity.................... 97 3.2.4.3 Crossover mechanisms................ 97 3.2.4.4 Chromosome types.................. 97 3.2.4.5 Plug-in experiment code............... 98 3.2.4.6 Using external software as (supplier of) objective functions....................... 98 3.2.4.7 Callable from external software........... 99 3.2.4.8 Duplicate solutions control.............. 99 3.2.4.9 Constraints...................... 99 3.2.4.10 Chromosome Initialisers............... 100 3.2.4.11 Population Initialisers................ 101 3.2.4.12 Operator Configuration............... 101 3.2.4.13 Problem-specific parameters............. 102 3.2.4.14 Resume from previous run.............. 103 3.2.4.15 Command line run-time parameters......... 105 3.2.4.16 Conclusion...................... 105 3.3 Benchmark test problems and results................. 107 3.3.1 Problem definitions....................... 107 3.3.2 Benchmark test results..................... 109 3.4 Comparison with random search.................... 114 3.4.1 Random search algorithm................... 115 3.4.2 Further optimisation test problems.............. 117 3.4.2.1 DTLZ1........................ 117 3.4.2.2 DTLZ2........................ 118 3.4.2.3 DTLZ3........................ 118 3.4.2.4 DTLZ4........................ 119 3.4.2.5 DTLZ5........................ 119 3.4.2.6 DTLZ6........................ 120 3.4.2.7 DTLZ7........................ 120 Contents 11 3.4.2.8 DTLZ8........................ 121 3.4.2.9 DTLZ9........................ 122 3.4.2.10 MOKP 0/5...................... 122 3.4.3 Results.............................. 123 3.4.4 Summary............................ 130 3.5 Experiments in self-adaptation....................