View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Online Research @ Cardiff Enhancements for the Bees Algorithm A thesis submitted to Cardiff University in the candidature for the degree of Doctor of Philosophy By Azar Imanguliyev Manufacturing Engineering Centre School of Engineering Cardiff University United Kingdom September 2013 ABSTRACT This work introduces new enhancements to the Bees Algorithm in order to improve its overall performance. These enhancements are early neighbourhood search process, efficiency based recruitment for neighbourhood search process, hybrid strategy involving tabu search, new escape mechanism to escape locals with similar fitness values and autonomy to minimise interaction between search process and the user. The proposed enhancements were applied alone or in pair to develop improved versions of the Bees Algorithm. Three Enhanced Bees Algorithms were introduced: the Early Neighbourhood Search and Efficiency Based recruitment Bees Algorithm (ENSEBRBA), the Hybrid Tabu Bees Algorithm (TBA) and the Autonomous Bees Algorithm (ABA). The ENSEBRBA with an empowered initialisation stage and extra recruitment for neighbourhood search is introduced to improve performance of the Bees Algorithms on high dimensional problems. The TBA is proposed as a new version of the Bees Algorithm which utilises the memory lists to memorise less productive patches. Moreover, the local escape strategy was also implemented to this algorithm. Proposed modifications increased the productivity of the Bees Algorithm by decreasing number of evaluations needed to converge to the global optimum. ii The ABA is developed to provide independency to the Bees Algorithm, thus it is able to self tune its control parameters in a sub-optimal manner. All enhanced Algorithms were tested on continuous type benchmark functions and additionally, statistical analysis was carried out. Observed experimental results proved that proposed enhancements improved the Bees Algorithm’s performance. iii ACKNOWLEDGEMENTS I would like to thank my first supervisor Professor Duc Truong Pham for his excellent supervision, help and continuous encouragement. My thanks go to him for accepting me to be one of his students in the Manufacturing Engineering Centre (MEC) at Cardiff University. In addition, without the assistance of my main supervisors Dr. Michael Packianather and Professor Rossi Setchi this thesis might not have been possible to produce. I also thank to the Ministry of Education of The Azerbaijan Republic for sponsoring me during my study. Also, special thanks to Dr. Fuad Omar, Dr. Baris Yuce, Dr. Mario Javier Gonzalez Romo, Dr Janyarat Phrueksanant and Dr. Siti Azfanizam Ahmad. Last but not least, I thank my lovely family for always supporting me; mentally, emotionally and physically during this four years journey. iv DECLARATION AND STATEMENTS DECLARATION This work has not previously been accepted in substance for any degree and is not concurrently submitted in candidature for any degree. Signed ……………………. … (Azar Imanguliyev) Date…………………………. STATEMENT 1 This thesis is being submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy (PhD). Signed ……………………. … (Azar Imanguliyev) Date…………………………. STATEMENT 2 This thesis is the result of my own independent work/investigation, except where otherwise stated. Other sources are acknowledged by explicit references. Signed ……………………. … (Azar Imanguliyev) Date…………………………. STATEMENT 3 I hereby give consent for my thesis, if accepted, to be available for photocopying and for inter-library loan, and for the title and summary to be made available to outside organisations. Signed ……………………. … (Azar Imanguliyev) Date…………………………. v CONTENTS ABSTRACT..............................................................................................ii ACKNOWLEDGEMENTS....................................................................iv DECLARATION AND STATEMENTS................................................v CONTENTS ............................................................................................vi LIST OF FIGURES.................................................................................ix LIST OF TABLES.................................................................................xiv ABBREVIATIONS.................................................................................xv LIST OF SYMBOLS.............................................................................xvi Chapter 1: Introduction …………………………………......................1 1.1. Introduction …………………………………………………………….........…..2 1.2. Motivation……………………………………………………………….............3 1.3. Aims and objectives …………………………………………………….............4 1.3. Research methods ……………………………………………………........….....5 1.4. Outline of the thesis ……………………………………………………........…..6 Chapter 2: Optimisation Techniques …………………….....................8 2.1. Preliminaries …………………………………………………………….............9 2.2. Optimisation Techniques ………………………………………………........…..9 2.2.1. Classification of the optimisation techniques………………………...........12 2.2.2. Deterministic optimisation techniques ……………………………............14 2.2.2.1. State space search ……………………………………………….....14 vi 2.2.2.2. Algebraic geometry …………………………………………......…15 2.2.2.3. Branch bound ……………………………………………………...15 2.2.3. Stochastic optimisation techniques …………………………………..…...15 2.2.3.1. Stochastic hill climbing …………………………………………....16 2.2.3.2. Random optimisation ……………………………………………...16 2.2.3.3. Simulated annealing …………………………………………..…..17 2.2.3.4. Tabu search ……………………………………………….…....….17 2.2.3.5. Genetic algorithms …………………………………………….......20 2.2.3.6. Genetic programming ………………………………………...……21 2.2.3.7. Evolutionary programming ………………………………………..21 2.2.3.8. Ant colony optimisation …………………………………………...22 2.2.3.9. Particle swarm optimisation …………………………………….....25 2.2.3.10. Artificial Bees Colony ……………………………………….…...28 2.2.4. The Basic Bees Algorithm ……………………………………………..…30 2.2.4.1. Foraging behaviour of honey bees …………………………….…..30 2.2.4.2. The Algorithm …………………………………………….......…..34 2.2.5. Applications of the Bees Algorithm …………………………………..…..36 2.6. Summary ……………………………………………………………………..…39 CHAPTER 3: The Bees Algorithm with Early Neighbourhood Search and Efficiency-Based Recruitment Strategies ……........…40 3.1. Preliminaries …………………………………………………………………...41 3.2. The Early Neighbourhood Search Strategy …………………………………....44 3.3. Efficiency-based Recruitment Strategy ……………………………………......45 3.4. Experiments …………………………………………………………………....48 vii 3.5. Results and Discussion ………………………………………………………...56 3.6. Summary …………………………………………………………………….…71 Chapter 4: The Tabu Bees Algorithm …………………………........72 4.1. Preliminaries ……………………………………………………………………73 4.2. Defining Tabu List ……………………………………………………………..76 4.3. Adaptive Neighbourhood Search ………………………………………………77 4.4. Updating the Tabu list ………………………………………………………….80 4.5. Experiments ………………………………………………………………....….81 4.6 Results and Discussion ………………………………………………………….84 4.7. Summary ………………………………………………………………………..98 Chapter 5: The Autonomous Bees Algorithm …………………........99 5.1. Preliminaries ………………………………………………………………......100 5.2. Autonomous Behaviour ………………………………………………........….102 5.3. Experiments ………………………………………………………………...…118 5.4. Results and Discussion ………………………………………………………..118 5.5. Summary ……………………………………………………………………....134 Chapter 6: Conclusion and Future Work ……………….............…135 6.1 Contributions ………………………………………………………............…...136 6.2 Conclusions ………………………………………………………................….137 6.3 Future work ………………………………………………………................….149 References ………………………………………………...............…..141 Appendix A ………………………………………………….........…..151 viii LIST OF FIGURES Figure 2.1: Graph of the optimisation process............................................................11 Figure 2.2: Classification of optimisation techniques based on types of the parameters....................................................................................................................13 Figure 2.3: Pseudo code of Tabu Search with short term memory.............................19 Figure 2.4: Pseudo code for simple version of ACO..................................................23 Figure 2.5: Pseudo code for simple PSO....................................................................26 Figure 2.6: Pseudo code of the ABC...........................................................................29 Figure 2.7: Waggle dance of the scout bee.................................................................31 Figure 2.8: Relation between duration of dance and distance to the food..................32 Figure 2.9: Relation between dance and the Direction of the food source.................33 Figure 2.10: Pseudo code for the basic Bees Algorithm.............................................35 Figure 3.1: Pseudo code of the ENSEBRBA..............................................................42 Figure 3.2: The flow chart of the ENSEBRBA...........................................................43 Figure 3.3: The results of a hundred runs for the BBA and the ENSEBRBA on Goldstein & Price (2D)................................................................................................61 Figure 3.4: The results of a hundred runs for the BBA and the ENSEBRBA on Schewel 2D.................................................................................................................61 Figure 3.5: The results of a hundred runs for the BBA and the ENSEBRBA