Ant Colony Optimisation for Dynamic and Dynamic Multi-objective Railway Rescheduling Problems by Jayne Eaton A thesis submitted in partial fulfillment for the degree of Doctor of Philosophy in the School of Computer Science and Informatics De Montfort University 2017 Declaration of Authorship The content of this submission was undertaken in the School of Computer Science and Informatics, De Montfort University, and supervised by Prof. Shengxiang Yang and Dr. Mario Gongora during the period of registration. I hereby declare that the materials of this submission have not previously been published for a degree or diploma at any other university or institute. All the materials submitted for assessment are from my own research, except the reference work in any format by other authors, which are properly acknowledged in the content. Part of the research work presented in this submission has been published or has been submitted for publication in the following papers: J. Eaton and S. Yang. Dynamic railway junction rescheduling using population based ant colony optimisation. In Computational Intelligence (UKCI), 2014 14th UK Workshop on, pages 1-8, Sept 2014. J. Eaton, S. Yang, and M. Mavrovouniotis. Ant colony optimization with immigrants schemes for the dynamic railway junction rescheduling problem with multiple delays. Soft Computing, 20(8):2951-2966, August 2016. J. Eaton and S. Yang. Railway platform reallocation after dynamic perturbations using ant colony optimisation. In IEEE Symposium Series on Computational Intelligence, 2016 Proceedings of the IEEE, 2016. J. Eaton, S. Yang and M. Gongora. Ant Colony Optimisation for Simulated Dynamic Multi-objective Railway Junction Rescheduling. IEEE Transactions on Intelligent Transportation Systems, 2017 (in press) i Abstract Recovering the timetable after a delay is essential to the smooth and efficient op- eration of the railways for both passengers and railway operators. Most current railway rescheduling research concentrates on static problems where all delays are known about in advance. However, due to the unpredictable nature of the railway system, it is possible that further unforeseen incidents could occur while the trains are running to the new rescheduled timetable. This will change the problem, making it a dynamic problem that changes over time. The aim of this work is to investigate the application of ant colony optimisation (ACO) to dynamic and dynamic multi- objective railway rescheduling problems. ACO is a promising approach for dynamic combinatorial optimisation problems as its inbuilt mechanisms allow it to adapt to the new environment while retaining potentially useful information from the previ- ous environment. In addition, ACO is able to handle multi-objective problems by the addition of multiple colonies and/or multiple pheromone and heuristic matrices. The contributions of this work are the development of a junction simulator to model unique dynamic and multi-objective railway rescheduling problems and an investigation into the application of ACO algorithms to solve those problems. A further contribution is the development of a unique two-colony ACO framework to solve the separate problems of platform reallocation and train resequencing at a UK railway station in dynamic delay scenarios. Results showed that ACO can be effectively applied to the rescheduling of trains in both dynamic and dynamic multi-objective rescheduling problems. In the dy- namic junction rescheduling problem ACO outperformed First Come First Served (FCFS), while in the dynamic multi-objective rescheduling problem ACO outper- formed FCFS and Non-dominated Sorting Genetic Algorithm II (NSGA-II), a state- of-the-art multi-objective algorithm. When considering platform reallocation and rescheduling in dynamic environments, ACO outperformed Variable Neighbourhood Search (VNS), Tabu Search (TS) and running with no rescheduling algorithm. These results suggest that ACO shows promise for the rescheduling of trains in both dy- namic and dynamic multi-objective environments. ii Acknowledgments I would like to thank my supervisors Prof. Shengxiang Yang and Dr. Mario Gongora for their help and advice with this project and Dr. Simon Coupland and Dr. Steve Ackland for their help and advice on the physics of train simulation. I would also like to thank Dr Dave Kirkwood at the University of Birmingham for sharing his expertise on train simulations and for supplying the power and resistance tables and the energy equation used in the Stenson Junction simulation. Thank you to the other PhD students in my office without whom this journey would have been a much more desolate undertaking. In particular thank you to Shouyong Jiang for his limitless knowledge of so many things, to Conor Fahy for making me laugh, all the time, to Muhannod Younis for his limitless good humour and optimism and to Manal Alghieth for her gentle and kind camaraderie. Also thank you to Dr. Michalis Mavrounitis for his advice on ACO algorithms, he's moved on to pastures new but he is not forgotten. Thank you also to Dr. Ben Passow for taking time to talk to me when I was lost in the PhD wilderness. Thank you to my kind and patient husband, Nick, for his calm belief that I could do this, for his stoical proof-reading of my journal papers and for his endless baking of comfort food. Thank you to my two supportive and enthusiastic sons who were proud that their mum was doing a PhD and were always there to offer encouragement and advice. Thank you also to my mum and my sister for their unwavering belief in me. Finally thank you to my renal nurse Emma, my consultant Mr. Ferraro and my surgeon Mr. Dutta at Nottingham City Hospital, without whom I may have failed to survive to the end of this thesis. And thank you again to my husband who plans to give me one of the greatest gift of all, a new kidney and a chance of a normal life without dialysis. iii Contents 1 Introduction 1 1.1 Dynamic Railway Rescheduling . .2 1.2 What are Dynamic Optimisation Problems (DOPs)? . .2 1.3 Dynamic Multi-objective Railway Rescheduling . .4 1.4 Motivation . .5 1.5 Why Ant Colony Optimization (ACO)? . .5 1.6 Aims . .6 1.7 Unique Contribution . .7 1.8 Thesis Structure . .8 2 Of Ants and Trains 10 2.1 Railway Terms . 10 2.1.1 Block Sections . 10 2.1.2 Blocking Time . 11 2.1.3 Running Time . 11 2.1.4 Dwell Time . 11 2.1.5 Headway . 11 2.1.6 Fixed Block Systems . 11 2.1.7 Moving Block System . 12 2.1.8 Automatic Block . 12 2.1.9 Interlocking . 12 2.1.10 Timing Points . 13 2.1.11 TIPLOC . 13 2.1.12 Route . 13 2.1.13 Primary Delay . 13 2.1.14 Secondary Delay . 13 2.1.15 Microscopic Models . 13 2.1.16 Macroscopic Models . 13 2.2 Ant Colony Optimisation (ACO) . 14 iv Contents 2.2.1 The Basic ACO Algorithm . 14 2.2.2 Population-Based ACO (P-ACO) . 16 2.2.3 Max-Min Ant System (MMAS) . 17 2.2.4 Ant Colony System (ACS) . 18 2.2.5 ACO for DOPs . 19 2.3 Summary . 19 3 Literature Review 20 3.1 Railway Rescheduling Definitions . 20 3.2 The difference between Scheduling and Rescheduling . 21 3.3 Railway Rescheduling Literature . 21 3.4 Single Objective Railway Rescheduling Problems . 22 3.4.1 EC techniques for solving Railway Rescheduling Problems . 22 3.4.2 Non-EC techniques for solving Railway Rescheduling Problems 27 3.4.3 Dynamic Railway Rescheduling Problems . 46 3.4.4 An Alternative Definition of Dynamic Rescheduling . 49 3.5 Multi-objective Train Rescheduling Problems . 50 3.5.1 EC Techniques for Solving Multi-Objective Railway Reschedul- ing Problems . 52 3.5.2 Non-EC Techniques for Solving Multi-Objective Railway Reschedul- ing Problems . 55 3.5.3 Multi-Objective Railway Rescheduling that Produces a Set of Pareto Optimal Solutions (POS) . 63 3.5.4 Dynamic Multi-objective Train Rescheduling . 64 3.6 ACO for Dynamic Rescheduling . 66 3.7 ACO for Multi-objective Problems . 67 3.8 ACO for Dynamic Multi-objective Optimisation Problems (DMOPs) . 68 3.9 Summary . 69 4 Railway Junction Rescheduling in Dynamic Environments 71 4.1 Description of the Problems and Simulators . 72 4.1.1 The Dynamic Railway Junction Rescheduling Problem . 72 4.1.2 The Extended DRJRP . 74 4.1.3 The Stenson Junction Train Simulator . 75 4.1.4 The Extended Stenson Junction Train Simulator . 77 4.2 ACO for the DRJRP . 79 4.2.1 Proposed P-ACO Algorithm for the DRJRP . 80 4.2.2 P-ACO for the Extended DRJRP . 83 v Contents 4.2.3 Proposed MMAS Algorithm for the Extended DRJRP . 88 4.3 Experimental Design . 89 4.3.1 Dynamics Implementation . 89 4.3.2 Handling Constraints . 90 4.3.3 Limitations of the Model . 90 4.3.4 Performance Measure . 90 4.4 Experimental Investigation 1 . 91 4.4.1 Experimental Settings . 91 4.4.2 Experimental Results . 91 4.5 Experimental Investigation 2 . 93 4.5.1 Experimental Settings . 94 4.5.2 Experiment Results . 94 4.5.3 Algorithm Computation Time . 99 4.6 Summary . 100 5 Multi-objective Railway Junction Rescheduling in Dynamic Envi- ronments 102 5.1 The Dynamic Multi-objective Railway Junction Rescheduling Prob- lem (DM-RJRP) . 103 5.1.1 The Problem Objectives . 104 5.1.2 The Stenson Junction Train Simulator . 106 5.1.3 Model Realism . 108 5.1.4 Model Limitations . 108 5.2 Proposed MOACO Algorithms for the DM-RJRP . 108 5.2.1 MOACOs for the DM-RJRP . 108 5.2.2 Dynamic Multi-objective P-ACO . 109 5.2.3 Dynamic Multi-objective MMAS . 110 5.2.4 Dynamics Implementation . 113 5.2.5 Comparison Algorithms .