An-Najah National University Faculty of Graduate Studies Optimization of Traffic Signals Timing Using Parameter-less Metaheuristic Optimization Algorithms By Thaer Thaher Supervisor Dr. Baker Abdulhaq This Thesis is Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Advanced Computing, Faculty of Graduate Studies, An-Najah National University, Nablus- Palestine. 2018 II Optimization of Traffic Signals Timing using Parameter-less Metaheuristic Optimization Algorithms By Thaer Thaher This thesis was defended successfully on 22 /7/2018, and approved by: Defense Committee Members Signature - Dr. Baker Abdulhaq/ Supervisor …………………………... - Dr. Majdi Mafarja/ External Examiner …………………………... - Dr. Ahmed Awad/ Internal Examiner …………………………... III Acknowledgement First and foremost, I would like to thank our Almighty God for giving me the strength and knowledge to undertake and complete this research study. I'm also very grateful for the following people for their support and encouragement. Firstly, no thanking words will be enough to express my appreciation to Dr. Baker Abdulhaq for his invaluable guidance and advice, suggestions, patience, encouragement and continuous support as my research supervisor. In addition, the door to Dr. Abdulhaq office was always open whenever I had a question about my research and writing. I'm very thankful to him for giving me an opportunity to work in the field of traffic and optimization algorithms. Special thanks to my instructors of the advanced computing program at An-Najah National University, Dr. Adnan Salman, Dr. Fadi Draidi, Dr. Sameer Matar, Dr. Mohammad Najeeb, Dr. Ali Barakat, Dr. Anwar Saleh, and Dr. Abdel-Razzak Natsheh for enhancing my knowledge and ability to complete my research. Furthermore, I would like to express my sincere thanks to the members of the discussion committee for their time and effort in reviewing this study. IV I also thank my cousin Marah Hamdi for her help with proofreading this work. Finally, I must express my greatest gratitude to my parents, my wife and children, my brothers and sisters for their endless love and continuous encouragement throughout my years of study. My deep appreciation is also extended to all individuals, even those who played a little role, for their efforts in making this work a success. Without your tireless efforts, this work would not have been possible. V اإلقزار انا الموقع أدناه مقدم الرسالة التي تحمل العنوان: "Optimization of Traffic Signals Timing Using Parameter-less Metaheuristic Optimization Algorithms" أقر بأن ما اشتممت عميو ىذه الرسالة إنما ىي نتاج جيدي الخاص، باستثناء ما تمت ن ىذه الرسالة ككل، أو أي جزء منيا لم يقدم من قبل لنيل أية اإلشارة إليو حيثما ورد، وا أية مؤسسة تعميمية أو بحثية أخرىدرجة عممية أو لقب عممي أو بحثي لدى Declaration The work provided in this thesis, unless otherwise referenced, is the researcher's own work and has not been submitted elsewhere for any other degree or qualification. Student's name: اسن الطالب: ثائر أحمد درويش ظاهر Signature: :الحوقيع Date: :الحاريخ VI Table of Contents Acknowledgement ....................................................................................................................... III Declaration .................................................................................................................................... V List of Tables ................................................................................................................................ X List of Figures ............................................................................................................................ XIII List of Abbreviations ................................................................................................................. XVI Abstract ..................................................................................................................................... XVII 1. Introduction ............................................................................................................................... 1 1.1 Research Background and Motivation ................................................................................ 1 1.2 Research Objectives ............................................................................................................ 7 1.3 Research Hypotheses .......................................................................................................... 8 1.4 Significance of the Research ............................................................................................... 8 1.5 Thesis Structure................................................................................................................... 9 2. Theoretical Background .......................................................................................................... 11 2.1 Introduction to Optimization ............................................................................................ 11 2.2 Metaheuristic Optimization Techniques ........................................................................... 13 2.2.1 Parameter-less Algorithms ......................................................................................... 16 2.2.1.1 Teaching-Learning-Based Optimization (TLBO) Algorithm ..................................... 16 2.2.1.2 Jaya Algorithm ..................................................................................................... 22 2.2.2 Algorithms that Require Parameters ......................................................................... 24 2.2.2.1 Genetic Algorithm ............................................................................................... 25 2.2.2.2 Particle Swarm Optimization (PSO) ..................................................................... 30 2.2.2.3 Weighted Teaching-Learning Based Optimization .............................................. 32 2.3 Conclusion ......................................................................................................................... 33 2.4 Modeling and Simulation of Traffic Systems .................................................................... 33 2.4.1 Introduction ............................................................................................................... 33 2.4.2 Traffic Modeling Approaches Based on the Level of Details ..................................... 35 2.4.2.1 Microscopic Models ............................................................................................ 35 2.4.2.2 Macroscopic Models ........................................................................................... 36 2.4.2.3 Mesoscopic Models ............................................................................................. 36 2.4.2.4 Sub-microscopic Models ..................................................................................... 37 2.4.3 SUMO Simulator: ........................................................................................................ 38 3. Literature Review .................................................................................................................... 41 3.1 Traffic Lights Timing Optimization .................................................................................... 41 VII 3.1.1 Mathematical Optimization Models .......................................................................... 42 3.1.2 Simulation-based Approaches ................................................................................... 42 3.1.2.1 Off-line Optimization Tools ................................................................................. 43 3.1.2.2 On-line Optimization Tools ................................................................................. 44 3.2 Review of TLBO and Jaya algorithms ................................................................................ 45 3.3 Heuristic Optimization Techniques for TSOP .................................................................... 47 3.3.1 Genetic Algorithm ...................................................................................................... 47 3.3.2 Simulated Annealing .................................................................................................. 50 3.3.3 Particle Swarm Optimization ..................................................................................... 50 3.3.4 Ant Colony Optimization Algorithm ........................................................................... 52 3.3.5 Harmony Search Algorithm ........................................................................................ 53 3.3.6 Multiple algorithms .................................................................................................... 54 3.4 Other Approaches ............................................................................................................. 55 3.5 Summary of Literature Review ......................................................................................... 57 3.6 Weaknesses of the Previous Research .............................................................................. 60 4. The Methodology of the Study ............................................................................................... 61 4.1 Introduction ...................................................................................................................... 61 4.3.1 Genetic Algorithm ...................................................................................................... 65 4.3.2 Particle Swarm Optimization Algorithm .................................................................... 66 4.4 Cases of the Study ............................................................................................................. 67 4.4.1 Case Study 1 ............................................................................................................... 67 4.4.2 Case Study 2 ............................................................................................................... 68 4.4.3 Case Study 3 ............................................................................................................... 69 4.5 Solution Design ................................................................................................................. 71 4.5.1 Cycle Program of Traffic Light .................................................................................... 71 4.5.2 Traffic Signal Optimization Model .............................................................................. 73 4.5.2.1 Solution Representation ..................................................................................... 74 4.5.2.2 The Objective ...................................................................................................... 74 4.5.2.3 The Evaluation Function ...................................................................................... 74 4.6 Experimental Setup ........................................................................................................... 76 4.6.1 Experiment Design ..................................................................................................... 76 4.6.1.1 SUMO Operation: ................................................................................................ 76 4.6.1.2 Optimization Strategy ......................................................................................... 78 4.6.2 Parameters Settings ................................................................................................... 80 4.6.3 Statistical Analysis Methods ....................................................................................... 81 VIII 4.7 Experiments and Procedures ............................................................................................ 84 4.7.1 Comparing Optimization Techniques in Case study 1 ................................................ 84 4.7.1.1 Phase 1 Experiments: .......................................................................................... 84 4.7.1.2 Phase 2 Experiments ........................................................................................... 84 4.7.2 Comparing Optimization Techniques on Case Study 2 .............................................. 85 4.7.3 Comparing Optimization Techniques on Case Study 3 .............................................. 85 4.8 Summary ........................................................................................................................... 86 5. Results and Data Analysis ........................................................................................................ 87 5.1 Introduction ...................................................................................................................... 87 5.2 Comparing Optimization Techniques on Case Study 1 ..................................................... 88 5.2.1 Phase 1 Experiments .................................................................................................. 88 5.2.1.1 Performance and convergence speed of basic TLBO .......................................... 88 5.2.1.2 Performance and convergence speed of WTLBO ............................................... 91 5.2.1.3 Performance and convergence speed of Jaya .................................................... 93 5.2.1.4 Performance and convergence speed of GA ...................................................... 96 5.2.1.5 Performance and convergence speed of PSO ..................................................... 99 5.2.1.6 Comparison of TLBO, WTLBO, Jaya, GA, and PSO ............................................. 102 5.2.2 Phase 2 Experiments ................................................................................................ 105 5.2.2.1 Performance and Convergence Speed of Basic TLBO ....................................... 105 5.2.2.2 Performance and Convergence Speed of WTLBO ............................................. 107 5.2.2.3 Performance and Convergence Speed of Jaya .................................................. 110 5.2.2.4 Performance and convergence speed of GA .................................................... 113 5.2.2.5 Performance and Convergence Speed of PSO .................................................. 116 5.2.2.6 Comparison of TLBO, WTLBO, Jaya, GA, and PSO ............................................. 120 5.3 Comparing Optimization Techniques on Case Study 2 ................................................... 123 5.3.1 Performance and Convergence Speed of Basic TLBO .............................................. 124 5.3.2 Performance and Convergence Speed of WTLBO .................................................... 126 5.3.3 Performance and Convergence Speed of Jaya ......................................................... 128 5.3.4 Performance and Convergence Speed of GA ........................................................... 131 5.3.5 Performance and Convergence Speed of PSO ......................................................... 133 5.3.6 Comparison of TLBO, WTLBO, Jaya, GA, and PSO .................................................... 136 5.4 Comparing Optimization Techniques on Case Study 3 ................................................... 141 5.4.1 Performance and convergence speed of basic TLBO ............................................... 141 5.4.2 Performance and Convergence Speed of WTLBO .................................................... 142 5.4.3 Performance and Convergence Speed of Jaya ......................................................... 143 IX 5.4.4 Performance and Convergence Speed of GA ........................................................... 145 5.4.5 Performance and Convergence Speed of PSO ......................................................... 147 5.4.6 Comparison of TLBO, WTLBO, Jaya, GA, and PSO .................................................... 150 5.5 Summary ......................................................................................................................... 154 6. Conclusions and Discussion................................................................................................... 160 6.1 Overview ......................................................................................................................... 160 6.2 Summary ......................................................................................................................... 160 6.3 Conclusions ..................................................................................................................... 161 6.4 Limitations of the Study .................................................................................................. 165 6.5 Future research ............................................................................................................... 166 References................................................................................................................................. 167 Appendices ................................................................................................................................ 180 Appendix A: post hoc comparisons tables ............................................................................ 180 Appendix B: Algorithms ......................................................................................................... 193 X List of Tables Table 2.1: SUMO features (Abdalhaq & Abu Baker, 2014) ----------------------------------------------- 39 Table 2.2: Main applications included in SUMO (Pattberg,n.d.) ---------------------------------------- 40 Table 3.1: Recently published papers related to TLBO and Jaya---------------------------------------- 46 Table 3.2: Summary of heuristic algorithms for traffic signal optimization -------------------------- 58 Table 4.1: Parameters of the case studies ------------------------------------------------------------------- 71 Table 4.2: Summary of experiments settings ---------------------------------------------------------------- 86 Table 5.1: Phase 1 experiments settings --------------------------------------------------------------------- 88 Table 5.2: Descriptive statistics of Basic TLBO on case study 1 with phase duration 10-60 ----- 88 Table 5.4: Homogeneous subsets of Psize (TLBO on case 1 phase duration 10-60) --------------- 90 Table 5.5: Descriptive statistics of WTLBO on case study 1 with phase duration 10-60 ---------- 91 Table 5.7: Homogeneous subsets of Psize (WTLBO on case 1 phase duration 10-60) ------------ 93 Table 5.8: Descriptive statistics of Basic Jaya on case study 1 with phase duration 10-60------- 93 Table 5.10: Homogeneous subsets of Psize (Jaya on case 1 phase duration 10-60) --------------- 95 Table 5.11: Descriptive statistics of GA on case study 1 with phase duration 10-60 -------------- 96 Table 5.13: Homogeneous subsets of Psize (GA on case 1 phase duration 10-60) ---------------- 99 Table 5.14: Descriptive statistics of PSO on case study 1 with phase duration 10-60------------- 99 Table 5.16: Homogeneous subsets of Psize (PSO on case 1 phase duration 10-60) ------------- 101 Table 5.17: Summary results of statistical tests for algorithms, each with different population sizes (case 1 phase durations 10-60) ------------------------------------------------------------------------ 102 Table 5.18: Comparative results of TLBO, WTLBO, Jaya, GA, and PSO case study 1 with phase duration 10-60 ---------------------------------------------------------------------------------------------------- 102 Table 5.19:Statistical results for algorithms by Games-Howell post hoc test (case 1 phase duration 10-60) --------------------------------------------------------------------------------------------------- 104 Table 5.20: Phase 2 experiments settings ------------------------------------------------------------------ 105 Table5.21: Descriptive statistics of Basic TLBO on case study 1 with phase duration 10-100 - 105 Table 5.23: Homogeneous subsets of Psize (TLBO on case1 phase duration10-100) ----------- 107 Table 5.24: Descriptive statistics of WTLBO on case study 1 with phase duration 10-100 ---- 107 Table 5.26: Homogeneous subsets of Psize (WTLBO on case 1 phase duration 10-100) ------- 110 Table 5.27: Descriptive statistics of Jaya on case study 1 with phase duration 10-100 --------- 110 Table 5.29: Homogeneous subsets of Psize (Jaya on case 1 phase duration 10-100) ----------- 113 Table 5.30: Descriptive statistics of GA on case study 1 with phase duration 10-100 ---------- 113 Table 5.32: Homogeneous subsets of Psize (GA on case 1 phase duration 10-100) ------------- 116 XI Table 5.33: Descriptive statistics of PSO on case study 1 with phase duration 10-100 --------- 116 Table 5.35: Homogeneous subsets of Psize (PSO on case 1 phase duration 10-100) ----------- 118 Table 5.36: Summary results of statistical tests for algorithms, each with different population sizes (case 1 phase durations 10-100) ----------------------------------------------------------------------- 119 Table 5.37: Comparative results of TLBO, WTLBO, Jaya, GA, and PSO case study 1 with phase duration 10-100 -------------------------------------------------------------------------------------------------- 120 Table 5.38: Statistical results for algorithms by Games-Howell post hoc test (case 1 phase duration 10-100)-------------------------------------------------------------------------------------------------- 123 Table 5.39: Case 2 experiments settings ------------------------------------------------------------------- 123 Table 5.40: Descriptive statistics of Basic TLBO on case study 2-------------------------------------- 124 Table 5.42: Homogeneous subsets of Psize (TLBO on case 2) ----------------------------------------- 126 Table 5.43: Descriptive statistics of WTLBO on case study 2 ------------------------------------------ 126 Table 5.45: Homogeneous subsets of Psize (WTLBO on case 2) -------------------------------------- 128 Table 5.46:Descriptive statistics of Jaya on case study 2 ----------------------------------------------- 128 Table 5.48: Homogeneous subsets of Psize (Jaya on case 2) ------------------------------------------ 130 Table 5.49:Descriptive statistics of GA on case study 2 ------------------------------------------------- 131 Table 5.51: Homogeneous subsets of Psize (GA on case 2) ------------------------------------------- 133 Table 5.52: Descriptive statistics of PSO on case study 2 ---------------------------------------------- 133 Table 5.54:Homogeneous subsets of Psize (PSO on case 2) ------------------------------------------- 135 Table 5.55: Summary results of statistical tests for algorithms, each with different population sizes (case 2) ------------------------------------------------------------------------------------------------------- 136 Table 5.56: Comparative results of TLBO, WTLBO, Jaya, GA, and PSO case study 2 ------------- 137 Table 5.57: Statistical results for algorithms by Games-Howell post hoc test (case 2) --------- 138 Table 5.58: Case 3 experiments settings ------------------------------------------------------------------- 141 Table 5.59: Descriptive statistics of Basic TLBO on case study 3-------------------------------------- 141 Table 5.61: Descriptive statistics of WTLBO on case study 3 ------------------------------------------ 142 Table 5.62: Descriptive statistics of Jaya on case study 3 ---------------------------------------------- 143 Table 5.64: Descriptive statistics of GA on case study 3 ------------------------------------------------ 145 Table 5.66 Descriptive statistics of PSO on case study 3 ----------------------------------------------- 147 Table 5.67: Summary results of statistical tests for algorithms, each with different population sizes (case 3) ------------------------------------------------------------------------------------------------------- 149 Table 5.68: Comparative results of TLBO, WTLBO, Jaya, GA, and PSO case study3 ------------- 150 Table 5.69: Statistical results for algorithms by Games-Howell post hoc test (case 3) --------- 152 Table 5.70: Ccomparative results of all study cases in the form of descriptive and inferential statistics ------------------------------------------------------------------------------------------------------------ 155 XII Table 5.71: The ability of each algorithm to find a better mean solution -------------------------- 157 Table 4.3 Statistical results for TLBO by Games-Howell post hoc test (case 1 phase duration 10- 60) -------------------------------------------------------------------------------------------------------------------- 180 Table 4.6 Statistical results for WTLBO by Games-Howell post hoc test (case 1 phase duration 10-60) --------------------------------------------------------------------------------------------------------------- 181 Table 4.9 Statistical results for Jaya by Games-Howell post hoc test (case 1 phase duration 10- 60) -------------------------------------------------------------------------------------------------------------------- 182 Table 4.12 Statistical results for GA by Games-Howell post hoc test (case 1 phase duration 10- 60) -------------------------------------------------------------------------------------------------------------------- 183 Table 4.15 Statistical results for PS by Games-Howell post hoc test (case 1 phase duration 10- 60) -------------------------------------------------------------------------------------------------------------------- 184 Table 4.22 Statistical results for TLBO by Games-Howell post hoc test (case 1 phase duration 10-100) -------------------------------------------------------------------------------------------------------------- 185 Table 4.25 Statistical results for WTLBO by Games-Howell post hoc test (case 1 phase duration 10-100) -------------------------------------------------------------------------------------------------------------- 186 Table 4.28 Statistical results for Jaya by Games-Howell post hoc test (case 1 phase duration 10- 100) ------------------------------------------------------------------------------------------------------------------ 187 Table 4.31 Statistical results for GA by Games-Howell post hoc test (case 1 phase duration 10- 100) ------------------------------------------------------------------------------------------------------------------ 188 Table 4.34 Statistical results for PS by Games-Howell post hoc test (case 1 phase duration 10- 100) ------------------------------------------------------------------------------------------------------------------ 188 Table 4.41 Statistical results for TLBO by Games-Howell post hoc test (case 2) ------------------ 189 Table 4.44 Statistical results for WTLBO by Games-Howell post hoc test (case 2) --------------- 190 Table 4.47 Statistical results for Jaya by Games-Howell post hoc test (case 2) ------------------- 190 Table 4.50 Statistical results for GA by Games-Howell post hoc test (case 2) --------------------- 191 Table 4.53 Statistical results for PS by Games-Howell post hoc test (case 2) --------------------- 191 Table 4.60 Statistical results for TLBO by Tukey HSD post hoc test (case 3) ----------------------- 192 Table 4.63 Statistical results for Jaya by Tukey HSD post hoc test (case 3) ------------------------ 192 Table 4.65 Statistical results for GA by Games-Howell post hoc test (case 3) --------------------- 192 XIII List of Figures Figure 2.2: Distribution of marks for a group of learners (Rao et al., 2011) ------------------------- 18 Figure 2.4: Flowchart of Jaya algorithm (Rao, 2016b) ----------------------------------------------------- 24 Figure 2.5: Roulette Wheel Selections (Talbi, 2009) ------------------------------------------------------- 27 Figure 2.6: Tournament selection strategy (Talbi, 2009) ------------------------------------------------- 28 Figure 2.7: Linear Rank-based selection ---------------------------------------------------------------------- 28 Figure 2.8: Example of one point, two points, and uniform crossover methods (Sastry et al., 2005) ------------------------------------------------------------------------------------------------------------------ 29 Figure 2.9: The different simulation granularities; from left to right: macroscopic, microscopic, sub-microscopic, within the circle: mesoscopic. (SUMO user documentation)--------------------- 37 Figure 4.1: Framework of the traffic signals timing optimization (Hu et. al, 2015) ---------------- 63 Figure 4.2: Nablus city center road network ---------------------------------------------------------------- 68 Figure 4.3: Case study 2------------------------------------------------------------------------------------------- 69 -------------------------------------------------------------------------------------------------------------------------- 70 Figure 4.4: Case study 3------------------------------------------------------------------------------------------- 70 Figure 4.5: Traffic signal cycle with 4 phases ---------------------------------------------------------------- 72 Figure 4.6: (a) Two-phase junction, (b) Cycle program --------------------------------------------------- 72 Figure 4.7: State diagram of the given two-phase junction ---------------------------------------------- 73 Figure 4.8: Solution representation ---------------------------------------------------------------------------- 74 Figure 4.9: Traffic signal optimization model ---------------------------------------------------------------- 75 Figure 4.10: Network file creation in SUMO ----------------------------------------------------------------- 77 Figure 4.11: SUMO operation ----------------------------------------------------------------------------------- 78 Figure 4.12: Optimization strategy for traffic signal timing ---------------------------------------------- 80 Figure 5.1: The mean results of TLBO by changing Psize on case 1 phase duration 10-60 ------- 89 Figure 5.2: Convergence curves of TLBO by changing Psize on case 1 phase duration 10-60 --- 90 Figure 5.3: The mean results of WTLBO by changing Psize on case 1 phase duration 10-60 ---- 91 Figure 5.4: Convergence curves of WTLBO by changing Psize on case1 phase duration10-60 - 92 Figure 5.5. The mean results of Jaya by changing Psize on case 1 phase duration 10-60 -------- 94 Figure 5.6: Convergence curves of Jaya by changing Psize on case 1 phase duration 10-60 ---- 95 Figure 5.7: The mean results of GA by changing Psize on case 1 phase duration 10-60 ---------- 97 Figure 5.8: Convergence curves of GA by changing Psize on case 1 phase duration 10-60 ----- 98 Figure5.9. The mean results of PSO by changing Psize on case1 phase duration10-60 --------- 100 Figure 5.10: Convergence curves of PSO by changing Psize on case 1 phase duration 10-60 100 XIV Figure 5.11: The best results of TLBO, WTLBO, Jaya, GA, PSO on case 1 phase duration 10-60 ------------------------------------------------------------------------------------------------------------------------ 103 Figure 5.12: Convergence speed of TLBO, WTLBO, GA, PSO and Jaya on case study1 phase duration 10-60 ---------------------------------------------------------------------------------------------------- 104 Figure 5.13: The mean results of TLBO by changing Psize on case 1 phase duration 10-100 - 106 Figure 5.14: Convergence curves of TLBO by changing Psize on case1 phase duration 10-100 ------------------------------------------------------------------------------------------------------------------------ 106 Figure 5.15: The mean results of WTLBO by changing Psize on case 1 phase duration 10-100108 Figure 5.16: Convergence curves of WTLBO by changing Psize on case1 phase duration10-100 ------------------------------------------------------------------------------------------------------------------------ 109 Figure 5.17: The mean results of Jaya by changing Psize on case 1 phase duration 10-100 --- 111 Figure 5.18: Convergence curves of Jaya by changing Psize on case 1 phase duration 10-100112 Figure 5.19: The mean results of GA by changing Psize on case 1 phase duration 10-100 ---- 114 Figure 5.20: Convergence curves of GA by changing Psize on case 1 phase duration 10-100 115 Figure 5.21: The mean results of PSO by changing Psize on case1 phase duration10-100----- 117 Figure 5.2: Convergence curves of PSO by changing Psize on case 1 phase duration 10-60 -- 117 Figure 5.23: The best results of TLBO, WTLBO, Jaya, GA, PS on case 1 phase duration 10-100121 Figure 5.24: Convergence speed of TLBO, WTLBO, GA, PS and Jaya on case study1 phase duration 10-60 ---------------------------------------------------------------------------------------------------- 122 Figure 525: The mean results of TLBO by changing Psize on case 2 --------------------------------- 124 Figure 5.26: Convergence curves of TLBO by changing Psize on case2 (log scale) --------------- 125 Figure 5.27: The mean results of WTLBO by changing Psize on case 1 phase duration 10-100126 Figure 5.28: Convergence curves of WTLBO by changing Psize on case2 -------------------------- 127 Figure 5.29: The mean results of Jaya by changing Psize on case 2 ---------------------------------- 129 Figure 5.30: Convergence curves of Jaya by changing Psize on case 2 (log scale) --------------- 130 Figure 5.31: The mean results of GA by changing Psize on case 2 ----------------------------------- 131 Figure 5.32: Convergence curves of GA by changing Psize on case 2 ------------------------------- 132 Figure 5.33: The mean results of PSO by changing Psize on case 2 ---------------------------------- 134 Figure 5.34: Convergence curves of PSO by changing Psize on case 2 ------------------------------ 135 Figure 5.35: The best results of TLBO, WTLBO, Jaya, GA, PSO on case 2 --------------------------- 137 Figure 5.36: Convergence speed of TLBO, WTLBO, GA, PSO and Jaya on case study 2 --------- 138 Figure 5.37: The mean results of TLBO by changing Psize on case 3 -------------------------------- 141 Figure.5.38: Convergence curves of TLBO by changing Psize on case 3 ---------------------------- 142 Figure 5.40: The mean results of Jaya by changing Psize on case 3 ---------------------------------- 144 Figure 5.41: Convergence curves of Jaya by changing Psize on case 3 ----------------------------- 145 XV Figure 5.42: The mean results of GA by changing Psize on case 3 ----------------------------------- 146 Figure 5.43: Convergence curves of GA by changing Psize on case 3 ------------------------------- 146 Figure 5.44: The mean results of PSO by changing Psize on case 3 ---------------------------------- 147 Figure 5.45: Convergence curves of PSO by changing Psize on case 3 ----------------------------- 149 Figure 5.46: The best results of TLBO, WTLBO, Jaya, GA, PSO on case 3 --------------------------- 151 Figure 5.47: Convergence speed of TLBO, WTLBO, GA, PSO and Jaya on case study 2 --------- 151 Figure 5.49: The total number of times each algorithm was able to outperform others ------- 158 Figure 5.50: Convergence speed of TLBO, WTLBO, GA, PSO and Jaya algorithms (a) Case 1 phase 1(b) Case 1 phase 2 (c) Case 3 (d) Case 4 ---------------------------------------------------------- 159 XVI List of Abbreviations ACO Ant Colony Optimization ATT Average Travel Time CORSIM Corridor Simulation GA Genetic Algorithm GSA Gravitational Search Algorithm HC Hill Climbing HCM Highway Capacity Manual HS Harmony Search MA Memetic Algorithm MOTION Method for the Optimization of Traffic Signals in Online Controlled Networks OPAC Optimized Policies for Adaptive Control PASSER Progression Analysis and Signal System Evaluation Routine Psize Population Size PSO Particle Swarm Optimization RHODES Real-time Hierarchical Optimized Distributed and Effective System SA Simulated Annealing SCATS Sydney Coordinated Adaptive Traffic System SCOOT Split Cycle and Offset Optimization Technique SUMO Simulation of Urban Mobility TLBO Teaching Learning Based Optimization TRANSYT TRAffic Network Study Tool TS Tabu Search TSIS Traffic Software Integrated System TSOP Traffic Signals Optimization Problem WTLBO Weighted Teaching Learning Based Optimization XVII Optimization of Traffic Signals Timing Using Parameter-less Metaheuristic Optimization Algorithms By Thaer A. Thaher Supervisor Dr. Baker Abdulhaq Abstract Traffic congestion is a common challenge in urban areas, so several methods are used to reduce it. A powerful solution that can reduce the congestion problem is by developing a real-time traffic light control system with an optimization technique to minimize the overall traffic delay through optimizing the traffic signals timing. Researchers have proposed several simulation models and used various techniques to optimize the traffic signals timing. The purpose of this research is to evaluate and compare the performance of several meta-heuristic techniques in tackling the Traffic Signals Optimization Problem (TSOP). In this work, recently published algorithms that do not have specific parameters (the parameter-less) such as Teaching-Learning-Based Optimization (TLBO) and Jaya are applied to solve the traffic signals optimization problem. These algorithms have not been applied to the considered problem yet. A stochastic micro-simulator called 'Simulation of Urban Mobility' (SUMO) is used as a tool to implement and evaluate the performance and convergence speed of each algorithm. Three road networks of different XVIII sizes: small, medium and large containing 13, 34 and 141 phases respectively are simulated to study the scalability of algorithms. The performance of TLBO and Jaya algorithms are compared to three algorithms that have some parameters that need to be set such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Weighted Teaching-Learning-Based Optimization (WTLBO). The study also considers the effect of common controlling parameters (i.e. the population size) on the performance of the evaluated algorithms. After conducting many experiments, the comparisons and discussions have shown that TLBO and Jaya outperformed WTLBO, GA, and PSO for small and medium-sized networks. Moreover, TLBO achieved the best performance and scalability for the complex network. 1 1. Introduction 1.1 Research Background and Motivation Traffic jams are becoming a major problem that faces most countries in the world, especially developing ones. There is a steady increase in the population rate and thus an increase in the number of roads, and vehicles that cause traffic congestion (Gao et al., 2016). As a result, drivers and travelers are facing many problems such as air pollution, time wasting, fuel consuming, frustration, economic loss and other serious problems (Abushehab et al., 2014). There is a number of suggested solutions to alleviate the problem. Urban planners tried to tackle this phenomenon through building new lanes, bridges and expanding them (Kumar & Sing, 2017). However, it did not meet the anticipated success. The first problem with this solution is that it is expensive, and it is impossible to do that in urban cities due to the residential areas and nearby buildings (Bazzan & Ana, 2007). Researchers are therefore resorting to the optimal utilization of the available infrastructure (Hu et al., 2015). In traffic systems, there is a relationship between the timing of the traffic lights and the total traveling time for all vehicles in the network, so the adjustment of signal timing can give more green time to an intersection with heavy traffic or shorten or even skip a phase that has little or no traffic 2 waiting. Thus, it may lead to increase or decrease the travel time for vehicles (Xie et al., 2014). when choosing the average travel time as a measure of efficiency for the traffic network, the best values for the time of traffic lights are those that give the minimum average travel time for all vehicles. Due to the limitation of the supplied resources from the current infrastructure, smart traffic light control, and coordination system are becoming highly required to guarantee that traffic moves as smoothly as possible (Gao et al., 2016). These smart systems can be developed by replacing the traditional traffic light systems with smart ones that self- adjust timing based on the historical data collected by detectors (sensors, cameras) (Aljaafreh & Al-Oudat, (2014). According to Warberg et al. (2008), the correct utilization of smart traffic signals might increase the road's capacity [The maximum number of vehicles obtainable on a given roadway over a period of time] in the Greater Copenhagen area by 5 to 10%. The desired objective of the problem is to obtain a global optimal scheduling of traffic lights which enhances the traffic conditions comprehensively (Hu et al., 2015). In urban networks, there are hundreds of intersections which are controlled by traffic lights. These traffic lights require a proper control and coordination to achieve the desired objective (Gao et al., 2016). However, how to optimize the timings of hundreds of 3 traffic signals, has become a complex and challenging problem (Hu et al., 2015). The traffic lights scheduling can be considered as an NP-hard problem (Sklenar et al., 2009). It is a real-world problem where the optimal solution is unknown (Adacher, 2012). It is difficult to develop a closed- form mathematical model to describe the stochastic behavior of traffic system (Yun & Park, 2006). In addition, the greater the number of traffic lights, the greater the problem search space, then the complexity of the search will be much higher (Talbi, 2009). The vast majority of the real-world optimization problems in several areas such as transportation, engineering, manufacturing, and so on are NP- hard problems (Talbi, 2009). For complex optimization problems (e.g. NP- hard or global optimization), exact algorithms are not appropriate to be used because the amount of required time to find the optimal solution may increase exponentially relative to the dimensions of the problem (Beheshti & Shamsuddin, 2013). Hence, heuristic methods are more suitable to solve complex problems with a high-dimensional search space where it tends to find a good solution in a reasonable amount of time (Talbi, 2009). Heuristic methods can be classified into two types: specific heuristic designed for specific purpose problems (problem-dependent) and metaheuristic developed to solve a wide range of problems (problem-independent) (Talbi, 2009; Beheshti & Shamsuddin, 2013) 4 Metaheuristics algorithms have shown superior performance in solving a very large variety of optimization problems such as scheduling problems, parameter optimization, feature selection, automatic clustering, Neural Network training and son on (Mafarja & Mirjalili, 2018; Torres- Jimenez & Pavon, 2014). Recently, those algorithms have become popular for solving the traffic signals scheduling problem (Garcia-Nieto et al, 2013; Abushehab et al., 2014). Metaheuristic techniques are classified into two categories according to the number of solution being processed in each iteration: single solution- based algorithms and population-based algorithms (Luke, 2013). Most of the population-based metaheuristic algorithms are inspired by naturally occurring phenomena (Talbi, 2009). They can be classified into four major groups: evolution-based (e.g. GA), swarm-based (e.g. PSO), physics-based (e.g. Simulated Annealing 'SA'), and human-based (e.g. Harmony Search 'HS') (Panimalar, 2017). Two contradictory approaches need to be balanced in all these techniques to achieve suitable performance: diversification (exploration of the search space) and intensification (exploitation of the best solution found) (Yang, 2010; Talbi, 2009). Metaheuristic algorithms have their own specific parameter(s) in addition to the common control parameters like population size, the number of generations and elite size (Rao, 2016). The effectiveness of algorithms is sensitive to parameters' values. The wrong choice for the values of 5 parameters will either increase the computational effort or lead to a wrong optimal solution. (Rao et al., 2012) Parameter values selection is either assumed according to past experience or tuned to suit each new problem (Neumuller & Wagner, 2011). However, finding good values for parameters is difficult and time- consuming. The search for the optimal parameter values can be seen as an optimization problem itself (Neumuller et al., 2012). For these reasons, the search is still ongoing to modify algorithms with adaptive parameters methods or find new algorithms that are free of parameters. Population size is a common parameter to all population-based techniques. It has a significant influence on the performance and convergence of metaheuristic algorithms, and therefore must be taken into consideration (Diaz-Gomez & Hougen, 2007 ; Roeva et. al, 2014; Mora- Melia et.al, 2017;). Several studies have examined the effect of population size on the effectiveness of algorithms, some studies have shown that small population size leads to the lack of sufficient diversity and will not provide good solutions (Koumousis & Katsaras, 2006), and other studies also have argued that large population size may leads to undesirable results (Lobo & Goldberg, 2004; Chen et. al, 2012 ; Roeva et al, 2014; Mora-Melia et al, 2017). Therefore, more investigation should be done to find an appropriate approximation for the population size parameter that yields better solutions. 6 Traffic system is a complex, dynamic, and adaptive system. It consists of interacting sub-systems which depends heavily on stochastic behaviors, and thus lead to unpredictable outcomes (López-Neri et al., 2010). Therefore, there is no closed mathematical form that can be used as a model which is capable of describing all the stochastic behavior of the traffic system components (Krajzewicz et al., 2002). Hence, simulation is an effective way for the experimental studies of the traffic system (Olstam, & Tapani, 2004). The process of Traffic Signals Optimization Problem (TSOP) consists of two sub-problems: the optimization algorithm and the simulation model which is used to evaluate the objective function (Adacher, 2012). In this study, a microscopic traffic simulator called SUMO 'Simulation of Urban Mobility' integrated with parameterless metaheuristic algorithms called TLBO and Jaya have been used to determine the best time for each traffic signal and thus minimize the delay time for vehicles. Recently, various optimization techniques have been used to solve the problem of traffic light optimization (Abushehab et al., 2014). However, due to the stochastic behavior of these techniques, there is no guarantee to find the optimal solution (Luke, 2013). Also, they may suffer from poor performance in solving some problems. Besides, the No-Free- Lunch (NFL) theorem confirms that there is no algorithm that can be 7 considered the best to solve all optimization problems (Wolpert & Macready, 1997). Therefore, the answer to "which algorithm is most appropriate to solve the problem" remains open (Abdalhaq & Abu Baker, 2014). These reasons motivated us to investigate the efficiency of recently published algorithms such as TLBO and Jaya in the field of traffic signals timing optimization for the first time in literature. 1.2 Research Objectives The main aim of this study is to develop a computational framework that is based on the integration of SUMO and an efficient metaheuristic optimizer which offers a better solution to TSOP and thus lead to minimize the average travel time of all vehicles. To achieve the main aim of this thesis, the following objectives were formulated:  To apply different metaheuristic algorithms to optimize the traffic signals timing.  To identify the effect of common controlling parameters such as population size on the performance of each algorithm for the optimization of traffic signals timing. And then estimate the most suitable population size for the considered algorithms.  To identify the scalability of the algorithms through evaluating them on simple and complex networks. 8 1.3 Research Hypotheses There are three research hypotheses that need to be tested at this phase of the research:  The choice of common controlling parameter(s) values such as population size has a great impact on the performance of the algorithms to optimize traffic signals timing.  The parameter-less algorithms such as TLBO and Jaya outperform the other traditional algorithms such as GA and PSO in solving the optimization of traffic signals timing problem.  The performance of the algorithms varies depending on the size and characteristics of the network to be resolved. 1.4 Significance of the Research The findings of this research will redound to the benefit of society, as well as specialists and researchers in the field of traffic system development. The growing of traffic congestion in urban traffic networks justifies the need for more effective approaches that alleviate this problem. Thus, the Ministry of Transport and Municipalities that apply the recommendations derived from the results of this study may alleviate traffic congestion and subsequent problems such as air pollution, fuel consumption, time wasting, and frustration. 9 In this study, recently published parameter-less algorithms (i.e. TLBO and Jaya) have been used to optimize the duration of traffic light phases in order to minimize the average of travel time for the vehicles. An improved version of TLBO called weighted TLBO (WTLBO), which is introduced by Satapathy et al (2013), is also tested. The performance and convergence rates of these algorithms have been compared with tuned GA and PSO algorithms selected from Abushehab et al. (2014) research. To study the scalability of each algorithm, the three different road networks, that have different characteristics and different number of traffic lights, have been simulated. The findings of this study will raise the awareness of researchers about a better solution for TSOP. It will also give them a perception of the effectiveness of the metaheuristic techniques that have been tested in this study, especially the parameter-less algorithms, and thus determine the most appropriate algorithm for the traffic signals timing optimization. 1.5 Thesis Structure This thesis consists of six chapters. The rest of the thesis is organized as follows: Chapter two introduces a theoretical background that covers an introduction to optimization problem and solution techniques. Then, the metaheuristic optimization techniques such as TLBO, Jaya, WTLBO, GA, 10 and PSO are reviewed. Furthermore, it introduces the modeling and simulation approaches to traffic systems. Chapter three introduces the literature review in modeling and simulation of traffic systems, and then it reviews the approaches that have been used to optimize traffic light timing, including mathematical optimization models, simulation-based approaches, and metaheuristic techniques. Chapter four explains the methodology which is used to answer the study questions. The methodology focuses on the use of a suitable microscopic traffic simulator integrated with an efficient metaheuristic optimization technique. In addition, chapter four presents the cases of the study, the model design of traffic signal optimization problem, the experimental setup, procedures, and statistical analysis. Chapter five presents the simulation results and data analysis in the form of descriptive and inferential statistics. Furthermore, the performance and convergence speed of each tested algorithm is also discussed. The last chapter summarizes the conclusions and recommendations. It also outlooks promising directions for future work. 11 2. Theoretical Background 2.1 Introduction to Optimization Optimization is the process of finding the best solutions that give the maximum or minimum of a function (Chong & Zak, 2013). The optimum search methods are known as mathematical programming methods. In every optimization problem, there are the following elements: 1) search space which is the set of possible solutions. 2) cost function (objective function) which is the model that is used to evaluate solutions. 3) constraints (possibly empty) which is a set of conditions for the input variables that are required to be satisfied. (Neumüller& Wagner, 2011) An optimization problem has the following form: (2.1) Where:  : R n R is the objective function to be minimized or maximized.  = [x1, x2, ……., xn] T R n is an n-vector of parameters (decision variables)  Ω: is a subset of R n which is called constraint set or feasible set. The constraints are called functional constraints when can be defined by some functions. It takes the form: = {x : h(x) = 0 , g(x) =0 } 12 The above optimization problem can be defined as finding the best values of decision variables for vector x from all candidate vectors in which minimize/maximize the objective function f. The optimization problem is either constraint or unconstraint. A previous standard is a general form for a constraint problem. If = R n then the problem is unconstraint. (Chong & Zak, 2013) A variety of real-world problems can be formulated as an optimization problem. Indeed, optimization techniques are widely used to solve many real-world problems in several areas, such as automatic control systems, electronic design, chemical, mechanical, and civil design problems (Boyd & Vandenberghe, 2015, p.3). Furthermore, they are also used to solve traffic problems such as network designs and TSOP (Garcia- Nieto et al). The technique selection depends on the nature and the characteristics of the problem to be solved (Talbi, 2009, p. 3-9). Optimization methods can be classified in several ways (see Figure 2.1), one of these classifications divides them into exact methods and heuristic methods depending on the complexity of the problem (Beheshti & Shamsuddin, 2013). Exact methods, such as dynamic programming, constraint programming, backtracking methods, branch-and-X methods (branch-and-bound, branch-and-cut, branch-and-price) guarantee finding the optimal solution for the problem being solved, they are suitable to solve small instances of difficult problems where the required time increases 13 polynomially relative to the dimensions of the problem (Rothlauf, 2013, P.45). Whereas heuristic methods do not guarantee that globally optimal solution can be found in some class of problems, they can find "near optimal" solution in a reasonable amount of time (Talbi, 2009, P.21). In combinatorial optimization problems with a high-dimensional search space, finding all possible solutions are consuming time and resources. By searching over a large set of feasible solutions, heuristic methods can often find good solutions with less computational effort and therefore they are appropriate to solve this class of problems (Beheshti & Shamsuddin, 2013). In general, heuristic methods can be classified into two types: specific heuristic and metaheuristic. Specific heuristic methods are problem-dependent and they are developed to solve very specific purpose problems. On the other hand, metaheuristic methods are a high-level problem-independent, so they are suitable to solve a wide range of problems (Talbi, 2009, P.21). 2.2 Metaheuristic Optimization Techniques Metaheuristic techniques are a kind of stochastic optimization methods where some degree of randomness and probability is employed to find the (near) optimal solutions (Neumüller & Wagner, 2011). These methods explore the search space to find good solutions without guaranteeing the optimal solution. They are suitable for (I knew it when I see it) problems (Luke, 2013). In such problems, we do not have previous 14 information about how the best solution seems. When we are given a candidate solution, its goodness or suitability can be evaluated using the objective function. (Luke, 2013) Metaheuristic algorithms can be classified in many ways; one of the most popular categorizations is depending on the number of solutions being processed in each iteration. Single solution based (S-based) algorithms are algorithms that manipulate one solution in each iteration in the optimization process, while the population-based (P-based) algorithms manipulate a set of solutions (called population) in each iteration of the optimization process (Luke, 2013). Simulated Annealing (SA), Tabu Search (TS), and Great Deluge (GD) are examples of the S-based Metaheuristic algorithms. Genetic Algorithm (GA), Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO) are examples of P-based Metaheuristic algorithms. Moreover, depending on the nature of inspiration, where most of the population-based metaheuristic algorithms are nature-inspired (Talbi, 2009), they can be classified into four major groups: evolution-based (e.g. GA, ES), swarm-based (e.g. PSO, TLBO, Jaya, and ACO, and), physics- based (e.g. SA, GSA), and human-based (e.g. HS). (Arockia, 2017). In p-based metaheuristic algorithms, the optimization process is accomplished in two main phases: exploration (or diversification), and exploitation (or intensification). In exploration, a large scale of regions of 15 the search space is examined to generate diverse solutions, so that reducing the chance of getting trap into a local minimum (Beheshti & Shamsuddin, 2013). On the other hand, exploitation means to examine the promising regions more carefully to find better solutions (Talbi, 2009). However, a proper trade-off between these two components is required to achieve the global optimality (Yang, 2010, P.5). Metaheuristic algorithms are probabilistic algorithms and thus require their own specific parameters in addition to the common controlling parameters (Rao & Patel, 2012). These algorithms are highly sensitive to the parameter settings. Missing to fine tune the values for those parameters will negatively affect the performance of the employed algorithm (Neumuller et al. 2012). Considering this fact, recently published parameter-less algorithms called TLBO and Jaya have been introduced and shown a good performance in solving a variety of problems (Rao et al., 2011; Rao, 2016). In this study, to solve the TSOP, the performance of parameter-less algorithms (e.g., TLBO and Jaya) was compared to the performance of algorithms that have their own parameters (e.g., WTLBO, GA, and PSO). 16 Figure 2.1: Optimization techniques classification 2.2.1 Parameter-less Algorithms Different from other evolutionary and swarm intelligence based algorithms, these algorithms are free of any specific parameters and require only common controlling parameters like population size, number of iterations, and elite size. This category contains two recently published algorithms: TLBO and Jaya. (Rao, 2016b) 2.2.1.1 Teaching-Learning-Based Optimization (TLBO) Algorithm TLBO is a population-based heuristic optimization method introduced by Rao et al. (2011). It simulates the teaching-learning process of the classroom, where learners represent the population, while the subjects which are given to learners represent the decision variables (Rao et 17 al., 2011). The learners’ results are equivalent to the fitness value of the optimization problem. The best learner (The learner who has the highest knowledge in the entire population according to the fitness value) is chosen as the teacher. In TLBO, the optimization process is divided. The first one is called 'Teacher Phase' and the second one is called 'Learner Phase'. In the teacher phase, the learning process depends on the teacher himself/herself, but in the learner phase, the learning process is done through the interaction between learners. The two phases are explained in the next section (Rao, 2015). Teacher Phase In this phase, the teacher relies on his/her ability to transfer knowledge to the learners to raise their grades and thus to improve the mean results of the class (Rao et al., 2011). As shown in Fig 2.2, the teacher TA makes an effort to shift the current mean of the learner MA towards his/her level and gets a new mean MB (Rao et al., 2012). 18 Figure 2.2: Distribution of marks for a group of learners (Rao et al., 2011) The existing solution is modified according to Eqs. (2.2) and (2.3). The new solution is accepted if it gives better function value; otherwise, we keep the old one (Rao, 2016a). = (2.2) = + (2.3) where: i: represents the current iteration. j: represents the subject (j=1 ….m) k: represents the learner (k=1 …. n) r: is a uniformly distributed random number within (0,1). Xj,kbest,i: represents the result of the teacher (i.e. best learner) in subject j TF: is the Teaching Factor which randomly calculated as in Eq. (2.4) Mj,i: represents the mean result of all learners in subject j. Difference_Meanj,i represents The difference between the teacher result and the current mean result of the learners in each subject Xj,k,i : represents the result of learner k in subject j. :is the updated value of the existing . (2.4) The teaching factor (TF) determines the value of mean to be change (Satapathy et al., 2013). After performing several experiments on several benchmark functions, it is concluded that the efficiency of the algorithm is better when the value of TF is either 1 or 2 (Rao et al., 2011). Its value is calculated randomly by the algorithm using Eq. (2.4), so it is not an input parameter (Rao et al., 2011). 19 It can be observed that r and TF are both random parameters which are used for a stochastic purpose. The values of these parameters affect the performance of the algorithm (Rao et al., 2012). However, their values are calculated during the manipulation of the algorithm, and therefore do not need to be tuned. Thus, TLBO is called an algorithm-specific parameter- less algorithm (Rao et al. 2012; Rao, 2016). However, Rao and Patel (2012) have introduced an improved version of TLBO with the concept of an adaptive TF where its value is not always 1 or 2 but varies in automatically between [0,1]. Learner phase This phase simulates learning through interactions among learners. A learner can gain knowledge through discussion and communication with another learner who has a better knowledge. For a given learner Xp, another learner Xq ,which is different from it (i.e. p q), is randomly chosen. The new values for learner Xp are updated as in Eq. (2.5). 1 = if (2.5a) + if (2.5b) where , are the function values for learners Xp and Xq respectively. , is the updated value of the existing . The new solution is accepted if it gives a better function value, otherwise we keep the old one. 1 The equation (4) is for minimization problems, the reverse is true for maximization. 20 The pseudo code for TLBO operation is illustrated in Algorithm 2.1, and the flow chart shown in figure 2.3. Algorithm 2.1: TLBO (Zou et al., 2015) Initialize N (number of learners), D (number of dimensions), and termination criteria Generate initial population (the learners) Calculate the fitness value for each learner X * = the best solution While (termination criteria is not met); {Teacher Phase} Choose the best learner as XTeacher calculate the mean for each design variable for each learner Calculate TF using Eq. (2.4) Update the existing solution according to Eqs. (2.2) and (2.3) end for Evaluated the new learners Accept the new solutions if it is better than the old one {Learner Phase} for each learner Randomly select another learner that is different from it Use Eq (2.5) to update the existing solution end for Evaluate the new learners Accept the new solution if it is better than the old one Update X* if there is a better solution end while Return X * 21 Figure 2.3: Flowchart of TLBO algorithm (Rao et. al, 2011) 22 2.2.1.2 Jaya Algorithm Ventaka Rao (2016b) proposed a new optimization algorithm and called it Jaya. This algorithm is very similar to TLBO; both are classified as algorithm-specific parameter-less algorithms, but unlike TLBO, Jaya has only one phase and it is relatively simple to apply (Rao, 2016b; Pandey, 2016) Jaya algorithm has a victorious nature (Pandey, 2016). It always tries to get closer to the best solution and tries to move away from the worst solution (Rao, 2016b). For this reason, the algorithm was named Jaya (which is a Sanskrit word meaning victory). To illustrate the algorithm's work, suppose that we have 'm' number of design variables (i.e. j=1,2,……, m), the population size 'n' (i.e. k=1, 2, …., n). Suppose that the best and the worst respectively indicate the best solution and the worst solution obtained so far. Each variable of every candidate solution is updated using Eq. (2.6). ( | |) (2.6) where i represents the current iteration, represents the value of the j th variable for the k th solution in the i th iteration, r1j,i and r2j,i are two uniformly distributed random numbers in the range of [0,1] for the j th variable in the i th iteration, and respectively represent 23 the value of the j th variable for the best and worst solutions. is the updated value of the existing . The new solution is accepted if it gives better function value; otherwise, we keep the old one. It is clear from Eq. (2.6) that the obtained solution always moves towards the best solution by the expression ( ( | |)) and moving away from the worst solution by the expression ( ) (Rao, 2016b). The absolute value of the variable is used instead of a signed variable for the exploration purpose (Rao et al., 2016). The new solution is accepted if it gives a better function value; otherwise we keep the old one. The pseudo code of Jaya is shown in Algorithm 2.2, and the flow chart is shown in figure 2.4. Algorithm 2.2: Jaya algorithm (Pandey, 2016) S1 Initialize S2 Until the termination condition not satisfied, Repeat S3 to S5 S3 Evaluate the best and worst solution Set Set S4 Modify the solution ( | |) S5 if ( solution corresponding to better than that correspnding to ) Update the previous solution Else No update in the previous solution S6 Display the optimum result 24 Figure 2.4: Flowchart of Jaya algorithm (Rao, 2016b) 2.2.2 Algorithms that Require Parameters Unlike parameter-less algorithms, these algorithms require their own specific parameters in addition to the common controlling parameters like population size and the number of generations which are common in all population-based heuristic algorithms. For example, GA requires three main parameters (selection operator, mutation probability, and crossover probability); PSO requires inertia weight, cognitive, and social parameters; 25 ABC uses limit, and a number of onlooker bees, employed bees, scout bees; and other algorithms such as ACO, HS, DE, etc. use specific parameters (Rao, 2016). We will briefly introduce the algorithms which were used in this research such as GA, PSO, and WTLBO in the next section. 2.2.2.1 Genetic Algorithm Genetic algorithm is a probabilistic technique that was originally developed by John Holland in the late 1960s and early 1970s (Holland,1975). It simulates the phenomenon of natural evolution and hence it is classified within the evolutionary optimization methods (Chong & Zak, 2013). GA is a population-based method which uses multiple solutions at the same time. It starts with an initial set of individuals that represents the candidate solutions, and it then involves a set of operations to generate a new set of individuals. These operations are called selection, crossover, and mutation (Chong & Zak, 2013). The algorithm starts by selecting two pairs of individuals (called parents) according to their fitness scores. Individuals with high fitness have more chance to be selected for reproduction. The selected parents will be improved by the evolutionary operators (crossover and mutation) in the next iteration of the optimization process to form new solutions (offspring). 26 In the second stage, the crossover operation takes a pair of parents and recombine them to give a pair of offspring. Pairs of parents for crossover are chosen randomly from the selected group. After a crossover is performed, mutation take place by randomly changing the new offspring with a given probability. Mutation occurs to maintain diversity within the population and thus prevent premature convergence. The steps of traditional GA are shown in Algorithm 2.3 (Neumüller & Wagner, 2011). The performance is influenced mainly by these two operators Algorithm 2.3: GA algorithm 1: 2: evaluate 3: while termination criteria not met do 4: 5: 6: Mutate 7: Evaluate 8: (update population) 9: end while 10: return (best solution) Selection Operator There are different strategies for the selection operator which affects the convergence speed of GA (Goldberg & Deb, 1991). The common selection strategies are: roulette wheel selection, tournament selection, and rank-based selection (Talbi, 2009). 27 Roulette wheel selection is the most common selection method (Talbi, 2009). Each individual is assigned a probability of selection that is proportional to its relative fitness. For each individual i, the probability is calculated as follows: ∑ (2.7) Where, n is the population size and is the fitness of individual i. Therefore, the individual with better fitness has more opportunity to be selected as shown in Figure 2.5 (Beheshti & Shamsuddin, 2013). However, due to the possible presence of individual with high fitness that is always selected, this cause a premature convergence to a local optimum (Jebari, 2013). Figure 2.5: Roulette Wheel Selections (Talbi, 2009) In Tournament selection method, a set of k individuals are randomly selected from the population; where k is the tournament group. The fittest individual is then selected after the tournament is applied to the k individuals (Figure 2.6). This process is repeated µ times until µ individuals are selected. 28 Figure 2.6: Tournament selection strategy (Talbi, 2009) The main idea of Rank-based selection depends on using the rank of individuals instead of using their fitness. The best individual has rank n (population size) while the worst one has rank 1. Each individual is assigned a probability of selection using the following liner formula (Jebari, 2013): (2.8) where, n is the population size and is the rank of individual i. Therefore, all the individuals have an opportunity to be selected (Beheshti & Shamsuddin, 2013) and hence reducing the problem of premature convergence (Figure 2.7). individual A B C fitness 4 1 5 rank 2 1 3 probability 0.34 0.16 0.5 Figure 2.7: Linear Rank-based selection In addition to the above selection methods, there are other methods that can be used such as exponential rank selection (Jebari, 2013), 29 stochastic universal sampling (Talbi, 2009), competitive selection, and variable life span. Crossover Operator This is the first stage of evolutionary operators where a pair of parents are recombined to generate a pair of offspring. There are several methods to perform the crossover process such as one point, two points, and uniform crossover as shown in Figure 2.8 (Chong & Zak, 2013). Figure 2.8: Eexample of one point, two points, and uniform crossover methods (Sastry et al., 2005) Mutation Operator It is the process of randomly changing some parts of individuals with a given probability. This operator helps to have better exploration process and thus escape from local optima (Mehboob et al., 2016). 30 2.2.2.2 Particle Swarm Optimization (PSO) Swarm optimization is a stochastic optimization method which mimics the social behaviors of creatures that usually live in groups like bird flocking and fish schooling (Talbi, 2009). It was developed by Kennedy and Eberhart (1995). PSO is a population-based optimization method, in which the population of particles is called a swarm. Each particle in the population is associated with two victors; position victor that represents its location according to the swarm, and the velocity that controls the direction of the next move of this particle (Luke, 2013). During the optimization process each particle is evaluated using a fitness function, the fittest particle is denoted as global best (gBest), and the position that gives the best fitness value for a specific particle is denoted as a local best (pBest). Then, pBest (self-experiences) and gBest (social experiences) are used to update the position of the current particle hoping to get a better position than the current one (Garcia-Nieto et al, 2013). Each dimension of the velocity component is updated according to Eq. (2.9), while each dimension of the particle position is updated according to the Eq. (2.10) (Kennedy and Eberhart, 1995) (2.9) Inertia wight self-experience social-experience (2.10) 31 where: xi: the i th dimension of particle position xvi: the i th dimension of the velocity component r: a uniformly distributed random real number within [0, 1]. pbesti: particle best value found so far of dimension i gbesti: global best value found so far of dimension i w, cp, cg: tunable parameters. w (inertia weight), cp (weight of local information), cg (weight of global information) In Eq. (2.9) The inertia weight parameter (w) controls the balance between exploration and exploitation. A smaller value of w assists the local exploitation, while a larger value of w encourages the global exploration (Kennedy, 1997; Beheshti & Shamsuddin, 2013). Therefore, this parameter has received increased attention in the research by introducing a dynamically adjusted inertia weight using different updating mechanisms such as linear and nonlinear decreasing methods (Arasomwan & Adewumi, 2013; Alkhraisat & Rashaideh, 2016). The work of PSO can be summarized in Algorithm 2.4 (Kennedy & Eberhart, 1995). Algorithm 2.4: PSO algorithm 1. (𝜃) // initial swarm usually random 2. for each particle 𝜃: for each dimension i // calculate velocity according to equation (2.9) // update particle position according to equation (2.10) 3. While stop criteria not reached, Go to step 02 32 2.2.2.3 Weighted Teaching-Learning Based Optimization Satapathy et al (2013) proposed an improved version of traditional TLBO algorithm to improve the convergence speed. The authors added A new parameter called (weight) to the learning equations of TLBO, and hence the new algorithm was called Weighted TLBO (WTLBO). The principle of adding a new parameter was based on the natural phenomena of the learner’s brain in forgetting the lessons learned in the last session. The value of the weight parameter (w) is linearly reduced from wmax to wmin according to Eq. (2.11). ( ) (2.11) Where w-max and w-min are a predetermined maximum and minimum values respectively, max-iteration is the maximum number of iterations, i is the current iteration. Hence, the learning equations (2.4) and (2.5) in TLBO become as following: = w * + (2.12) if (2.13a) + if (2.13b) WTLBO algorithm was compared to TLBO, PSO, DE algorithms using several benchmark functions. The results showed that WTLBO is faster than other algorithms (Satapathy et al, 2013). 33 2.3 Conclusion Metaheuristic optimization techniques are suitable to solve complex and hard problems which cannot be solved by traditional optimization methods. They do not guarantee the optimal solution but they can find good solutions in a reasonable time even in large spaces of solutions. Many algorithms have been developed, some of which are suitable for solving a specific type of problems while the others are not. However, According to No-Free-Lunch (NFL) theorem, there is no optimization algorithm that is good enough to be suited for all optimization problems (Wolpert & Macready, 1997). 2.4 Modeling and Simulation of Traffic Systems 2.4.1 Introduction A traffic system is a complex, dynamic and adaptive system. It consists of a number of interacting agents such as vehicles, pedestrians, traffic lights and some other sub-systems which lead to emergent outcomes that are often difficult (or impossible) to be predicted. (López-Neri et al., 2010). Traffic conditions depend on the integrated and complex relationships between various variables such as passengers' behaviors, road laws, weather conditions, infrastructure, and other unpredictable conditions. Traffic cannot be described just by departure times and paths 34 used during a period of time. It depends heavily on the travelers' behavior. (Krajzewicz et al., 2002). This complexity makes it difficult to describe traffic using mathematical formulas. Therefore, there is no closed mathematical form that can be used as a model which is capable of describing all the stochastic behavior of the traffic system components (Krajzewicz et al., 2002). So, simulation is characterized as a powerful and cost-efficient tool to design, analyze, evaluate roads and to develop plans and proposals for their improvement. (Olstam, & Tapani, 2004) Nowadays, the availability of data and the high processing power of computers makes it easier for researchers to simulate road networks much faster than real environment and thus an experiment that is conducted using simulations yields results in much less time than the same experiment when conducted in reality. (Bazzan & Ana, 2007; Kotushevski & Hawick, 2009). Many model-based simulation packages such as VISSIM (PTV AG, 2015), CORSIM (FHWA, 2006), AIMSUN (Barceló, & Casas, 2006), PARAMICS (Ozbay et al., 2005) and SUMO (Krajzewicz et al., 2012) have been developed for traffic. Traffic models can be classified based on several properties: Scale of independent variables (discrete, continuous and semi-discrete), level of details (microscopic, sub-microscopic, macroscopic, mesoscopic), the scale 35 of applications (networks, stretches, links, intersections), representation of the processes (deterministic, stochastic) (Hoogendoorn & Bovy, 2001). The detail-level classification is commonly used because it specifies important criteria to be considered when choosing a traffic model such as accuracy, computation time, ability to achieve the objective, and suitability for large networks. In the following section, we discuss the modeling approaches based on the level of details. 2.4.2 Traffic Modeling Approaches Based on the Level of Details In traffic flow models, there are different approaches to simulation models which are classified based on the level of details through which the system components are described. These models are macroscopic, microscopic, mesoscopic and sub-microscopic models (Hoogendoorn & Bovy, 2001; Abdalhaq & Abu Baker, 2014). The four approaches are represented in Figure 2.9. 2.4.2.1 Microscopic Models The microscopic traffic flow model simulates the behavior of each individual vehicle-driver unit and its interactions with other vehicles in the street. This model is concerned with describing the network accurately and in details (Ehlert et al., 2017). The dynamic variables of the models represent microscopic properties like the position, velocity, and acceleration of single vehicles. Hence, a high computation time is needed 36 to evaluate these parameters (Abushehab et al., 2014). This model assumes that there are two factors which determine the behavior of the vehicle: the vehicle's physical abilities to move and the driver's controlling behavior (Chowdhury et al., 2000). 2.4.2.2 Macroscopic Models The macro-simulation has founded under the assumption that traffic streams are comparable to the fluid stream. Therefore, it ignores the behavior of the individual vehicle and concerns only with the traffic flow in a road network using aggregated quantities such as flow, density, and average speed (Mccrea & Moutari, 2010; Mitsakis et al., 2014). The lack of details used to describe the traffic system makes this model less complex than microscopic model, and therefore less computational time. It is also relatively easy to implement and allows users to execute several scenarios in a short time Therefore, in general, it is the most suitable for modeling large networks in real time or even faster (Olstam, & Tapani,2004; Burghout, 2004). However, the main drawback of this model is the lack of accuracy which limited its application in the cases where the interaction of vehicles is not crucial to the results of simulation (Olstam, & Tapani,2004) 2.4.2.3 Mesoscopic Models The mesoscopic model combines the characteristics of the two previous models. It describes the traffic using both levels: the aggregate level of macroscopic models and the individual interactions behavior of 37 microscopic models (Burghout, 2004). This model approximates the positions and behavior of vehicles but less accuracy than microscopic model (Olstam, & Tapani,2004). These models can be represented in several forms. One of these forms is a queue-server form (Mahut, 2001). 2.4.2.4 Sub-microscopic Models The last class model of traffic simulation models is sub-microscopic. This model is similar to the microscopic one, but it describes more details about the vehicle-driver unit like the engine's rotation speed in connection with the vehicle speed or the driver's favored gear. However, this model needs longer computation time compared to simple microscopic model and therefore it is suitable for small networks (Krajzewicz et al., 2002; Hoogendoorn & Bovy, 2001). Figure 2.9: The different simulation granularities; from left to right: macroscopic, microscopic, sub-microscopic, within the circle: mesoscopic. (SUMO user documentation) 38 Although macroscopic and mesoscopic models are simpler and faster than microscopic models, their use is limited to certain cases where the interaction of individual vehicles is not decisive to the desired results. For example, they are inappropriate to analyze the merging areas. Besides, the accurate modeling of the adaptive signal control can be difficult in both macroscopic and mesoscopic models because when the positions of the vehicle are not known (i.e. macroscopic) or inaccurate (i.e. mesoscopic) it is difficult to simulate the activations of detectors used in the adaptive control system (Olstam, & Tapani,2004). Moreover, the availability of data and high-performance computing environment makes the use of microscopic simulators less challenging to model large-scale networks accurately. For these reasons, we have used a microscopic traffic simulator (called SUMO) in this work. 2.4.3 SUMO Simulator: "Simulation of Urban Mobility" (SUMO) is a microscopic road traffic simulation package which is available as an open source under the GPL License since 2001 (Krajzewicz, 2010). It was developed by the Institute of transportation systems at the German Aerospace Center (DLR). The main objective of developing SUMO was to provide researchers and engineers in the field of traffic with a tool to propose plans, implement and evaluate their own algorithms. SUMO is a multimodal, space-continuous and time-discrete simulation platform (DLR and contributors, n.d). See Table 2.1 for the main features of SUMO. (Abdalhaq & Abu Baker, 2014) 39 Table 2.1: SUMO features (Abdalhaq & Abu Baker, 2014) Category Features Simulation Complete workflow (network and routes import, DUA, simulation) Simulation Collision-free vehicle movement Different vehicle types Multi-lane streets with lane changing Junction-based right-of-way rules Hierarchy of junction types A fast OpenGL graphical user interface Manages networks with several 10.000 edges (streets) Fast execution speed (up to 100.000 vehicle updates/s on a 1GHz machine) Interoperability with other application at runtime using Traci Network-wide, edge-based, vehicle-based, and detector-based outputs Network Many network formats (VISUM, Vissim, Shapefiles, OSM, Tiger, RoboCup, XML-Descriptions) may be imported Missing values are determined via heuristics Routing Microscopic routes - each vehicle has an own one Dynamic User Assignment High portability Only standard c++ and portable libraries are used Packages for Windows main Linux distributions exist High interoperability through the usage of XML-data only SUMO as an open source software is widely used and popular because its source code is available for research, study, and modifications. This feature provides an additional help and a continuous support from other contributors (Kotushevski & Hawick, 2009). Various sub-models were implemented in SUMO; each has a specific task in the simulation. These models are the car following Krauss model (Krauss,1998), lane change Krajzewicz model (Gawron,1998), route choice model, user assignment model and the traffic light model. SUMO is not only for traffic simulation, but it is a software package which includes several applications based on their purpose (i.e. network generation, demand generation, and simulation). This helps to prepare and perform the simulation of a traffic scenario. The main applications that are included in SUMO are listed in Table 2.2. (Krajzewicz et al., 2012) 40 Table 2.2: Main applications included in SUMO (Pattberg,n.d.) Purpose Application Name Short Description Simulation SUMO The microscopic simulation with no visualization; command line application SUMO-GUI The microscopic simulation with a graphical user interface Network generation NETCONVERT Network importer and generator; reads road networks from different formats and converts them into the SUMO-format NETEDIT A graphical network editor. NETGENERATE Generates abstract networks for the SUMO- simulation Vehicles and Routes DUAROUTER Computes fastest routes through the network, importing different types of demand description. Performs the DUA JTRROUTER Computes routes using junction turning percentages DFROUTER Computes routes from induction loop measurements MAROUTER Performs macroscopic assignment OD2TRIPS Decomposes O/D-matrices into single vehicle trips POLYCONVERT Imports points of interest and polygons from different formats and translates them into a description that may be visualized by SUMO-GUI ACTIVITYGEN Generates a demand based on mobility wishes of a modeled population SUMO is a microscopic simulation of vehicular traffic. Each vehicle behavior is simulated individually, and defined at least by a unique name, departure time, and the vehicle's route through the network. Moreover, the vehicle can be described in more details such as speed, position, type, and the amount of pollution or noise emission. See (Krajzewicz et al, 2012). These details are required in this research to achieve the desired simulation output (i.e. calculate the average travel time for vehicles). So, for the achievement of our study’s objective, a microscopic simulator was selected instead of a macroscopic one. http://www.sumo.dlr.de/userdoc/SUMO.html http://www.sumo.dlr.de/userdoc/SUMO-GUI.html http://www.sumo.dlr.de/userdoc/NETCONVERT.html http://www.sumo.dlr.de/userdoc/NETEDIT.html http://www.sumo.dlr.de/userdoc/NETGENERATE.html http://www.sumo.dlr.de/userdoc/DUAROUTER.html http://www.sumo.dlr.de/userdoc/JTRROUTER.html http://www.sumo.dlr.de/userdoc/DFROUTER.html http://www.sumo.dlr.de/userdoc/MAROUTER.html http://www.sumo.dlr.de/userdoc/OD2TRIPS.html http://www.sumo.dlr.de/userdoc/POLYCONVERT.html http://www.sumo.dlr.de/userdoc/SUMO-GUI.html http://www.sumo.dlr.de/userdoc/ACTIVITYGEN.html 41 3. Literature Review 3.1 Traffic Lights Timing Optimization The timing of traffic signals in roads and intersections has a significant impact on congestion. The correct scheduling for the duration of green and red lights is one of the most cost-effective techniques for facilitating the mobility within the urban traffic system. (Schneeberger & Park,2003) Finding the proper duration of traffic lights phases is a complex optimization problem due to the unstable and random behavior of the urban traffic process (Sklenar et. al, 2009; Hu et. al., 2015). In addition, the complexity of the problem depends on the size of the network and the number of traffic lights. Hence, it could be difficult to solve such an optimization problem by traditional mathematical optimization techniques (Damy, 2015). The research on traffic signal optimization has been conducted since the early 1960s (Lu, 2015). In 1967, traffic was monitored using digital- computers installed in several cities (Denos & Gazis, 1967). Research is ongoing in this area to find innovative ways and to implement new algorithms to solve traffic signal timings optimization. Many researches have been conducted to tackle the TSOP where different approaches have been used, including mathematical optimization 42 models, and simulation-based approaches integrated with metaheuristic optimization techniques. (Warberg et al., 2008) 3.1.1 Mathematical Optimization Models In the late 1950s, Webster has developed the principle of traffic signal optimization methodology for isolated intersections (Webster, 1958). He has developed a single intersection mathematical model for estimating the delays for vehicles at fixed-time traffic signals and for computing the optimum settings of such signals to minimize the overall vehicular delay. Many researchers then have proposed mathematical optimization models for traffic signal timing, such as Miller (1963), Gazis (1964), DAns and Gazis (1975), Michalopoulos and Stephanopoulos (1978), Akcelik (1981), Lieberman et al (2000), Ceder and Reshetnik (2001), Li (2010), Jiao and Sun (2014). (Jiao, Z. Li, Liu, D. Li, & Y. Li, 2015). The main weakness in the use of mathematical models in this area is that it was used to optimize junctions as isolated units. (Abushehab et al, 2014) 3.1.2 Simulation-based Approaches The traffic system is complex and random, so simulation is the most effective way of analyzing the different problems and gathering quantitative information about traffic system that changes dynamically (Olstam, & Tapani, 2004). Research studies about traffic simulation 43 focused on two types of simulation models: macroscopic and microscopic models (Garcia-Nieto et al, 2013). 3.1.2.1 Off-line Optimization Tools Off-line optimization tools are software packages which are based on historical data about traffic flow and therefore the scheduled time remains constant and does not change depending on the variety and stochastic aspects of traffic flow (Lu, 2015). A variety of software packages have been developed to optimize traffic signal timing plans, such as SYNCHRO (Husch & Albeck, 2006) which is the most common software package used locally by municipalities, TRAffic Network Study Tool (TRANSYT) (Hale, 2005), Progression Analysis and Signal System Evaluation Routine (PASSER) (PASSER V, 2002), and the Traffic Software Integrated System - Corridor Simulation (TSIS/CORSIM) (Kaman Science Corporation, 1996). These programs consist of two main parts: an optimizer that uses an optimization technique to search for the optimal settings which improve the system performance. In addition to a traffic simulation model, which is used to evaluate and assess the objective functions during the optimization process. (Álvarez & Hadi, 2014). TRANSYT, SYNCHRO, and PASSER are based on embedded macroscopic simulation models (Álvarez & Hadi, 2014), while 44 TSIS/CORSIM is based on a microscopic simulation model (Lu, 2015). The use of deterministic and macroscopic simulation-based signal optimization methods could lead to trap at the local optimum or even not good solution (Schneeberger & Park,2003). In addition, macroscopic models are limited in describing the behavior of each individual vehicle- driver unit and its interactions with other vehicles in the street. Rouphail et al (2000) study indicated that the performance of the microscopic simulation-based approach is much better than the macroscopic simulation-based approach to solve the traffic light timing optimization problem (Schneeberger & Park,2003). 3.1.2.2 On-line Optimization Tools Because urban traffic contains a variety of stochastic behaviors and time to time demand variations, some adaptive and real-time traffic control systems have been developed to adjust the traffic signal settings automatically to adapt to traffic conditions. Examples of these systems are Split Cycle and Offset Optimization Technique (SCOOT) (Robertson, & Bretherton, 1991), Sydney Coordinated Adaptive Traffic System (SCATS) (Lowrie,1982), Optimized Policies for Adaptive Control (OPAC) (Gartner, 1990), Real-time Hierarchical Optimized Distributed and Effective System (RHODES) (Mirchandani, & Head, 2001.), Method for the Optimization of Traffic Signals in Online Controlled Networks (MOTION) (Busch, & Kruse, 2001), and Balancing Adaptive Network Control Method 45 (BALANCE). However, there are other control systems in addition to the mentioned examples, yet SCOOT and SCATS are the most widely used internationally. (Jiao et al, 2015; Lu, 2015) For more details about the components and the mission of each optimization tool, and the difference between them, look at (Lu, 2015; Ratrout, & Reza, 2014) 3.2 Review of TLBO and Jaya algorithms TLBO and Jaya algorithms have been widely used in different real-world applications of engineering and science and have showed effectiveness in problem-solving (Rao, 2016a, 2016b). Table 3.1 presents examples of recently published papers related to TLBO and Jaya algorithms (Rao, 2016a). 46 Table 3.1: Recently published papers related to TLBO and Jaya # Algorithm Authors Year Description 1 TLBO Zou et al. 2015 An improved TLBO algorithm (LETLBO) with learning experience of other learners has been introduced. 2 TLBO Yu et al. 2015 A self-adaptive multi-objective TLBO (SA-MTLBO) has been proposed. 3 TLBO Xu et al. 2015 Proposed an effective TLBO algorithm to solve the flexible job shop scheduling problem. 4 Jaya Rao et. al 2016 Dimensional optimization of a micro-channel heat sink using Jaya algorithm 5 TLBO Qu et al 2017 An improved TLBO based memetic algorithm for aerodynamic shape optimization 6 Jaya Rao & More 2017 Optimal design and analysis of mechanical draft cooling tower using improved Jaya algorithm 7 Jaya Rao & Saroj 2017