Multifactorial evolutionary algorithms for clustered minimum routing cost tree problems in the multi domain network

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY MASTER THESIS Multifactorial Evolutionary Algorithms for Clustered Minimum Routing Cost Tree Problems in the Multi-domain Network TA BAO THANG Data science and Artificial intelligence Supervisor: School: Assoc Prof Huynh Thi Thanh Binh School of Information and Communication Technology HA NOI, 2022 HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY MASTER THESIS Multifactorial Evolutionary Algorithms for Clustered Minimum Routing Cost Tree Problems in the Multi-domain Network TA BAO THANG Data science and Artificial intelligence Supervisor: Assoc Prof Huynh Thi Thanh Binh Supervisor’s Signature School: School of Information and Communication Technology HA NOI, 2022 CỘNG HÒA XÃ HỘI CHỦ NGHĨA VIỆT NAM Độc lập – Tự – Hạnh phúc BẢN XÁC NHẬN CHỈNH SỬA LUẬN VĂN THẠC SĨ Họ tên tác giả luận văn: Tạ Bảo Thắng Đề tài luận văn: Tiếng Việt: Giải thuật tiến hóa đa nhân tố giải tốn phân cụm có chi phí định tuyến nhỏ nhất mạng đa miền Tiếng Anh: Multifactorial Evolutionary Algorithms for Clustered Minimum Routing Cost Tree Problems in the Multi-domain Network Chuyên ngành: Khoa học liệu Trí tuệ nhân tạo Mã số SV: 20202647M Tác giả, Người hướng dẫn khoa học Hội đồng chấm luận văn xác nhận tác giả sửa chữa, bổ sung luận văn theo biên họp Hội đồng ngày 28/04/2022 với nội dung sau: - Sửa lại lỗi tả, hành văn, ngữ pháp, ký hiệu luận văn - Bổ xung thông tin độ lệch chuẩn kết thực nghiệm Giáo viên hướng dẫn Ngày 26 tháng 05 năm 2022 Tác giả luận văn CHỦ TỊCH HỘI ĐỒNG Declaration of Authorship and Topic Sentences Personal information Full name: Ta Bao Thang Phone number: +84344277998 Email: thang.tb202647M@sis.hust.edu.vn Major: Data Science and Artificial Intelligence Topic: Multifactorial evolutionary algorithms for clustered minimum routing cost tree problems in the multi-domain network Contributions • Develop a new encoding and decoding scheme for two clustered tree problems: Clustered Minimum Routing Cost Tree (CluMRCT) and Clustered Shortest Path Tree (CluSPT) The proposed method allows evolutionary algorithms to function on complete and sparse graphs • Design efficient multifactorial evolutionary algorithms to solve CluSPT and CluMRCT problems simultaneously • Evaluate the efficiency of the proposed algorithms and encoding methods on various instances The results proved that the proposed methods outperformed all existing approaches in terms of solution quality and convergence trend Declaration of Authorship I declare that my thesis, titled ”Multifactorial Evolutionary Algorithms for Clustered Minimum Routing Cost Tree Problems in the Multi-domain Network”, is the work of myself and my supervisor Associate Professor Huynh Thi Thanh Binh All papers, sources, tables used in this thesis have been thoroughly cited Supervisor confirmation Hanoi, April 2022 Supervisor Associate Professor Huynh Thi Thanh Binh Acknowledgments This thesis would not have been possible without the assistance and support of many people and organizations First and foremost, I would like to express my gratitude to my supervisor, Associate Professor Huynh Thi Thanh Binh I am fortunate to have been her student She taught me the fundamentals of conducting research and encouraged me to develop my own ideas Her words always have the power to unleash my potential by pushing me to constantly try a little more challenging than the best I can achieve Thank you for this extensive instruction and your trust over such a long period Second, I would like to thank Dr Pham Dinh Thanh, Ph.D student Do Tuan Anh, and Ph.D student Tran Thi Huong for their unconditional support during the last four years at the Modelling, Simulation, and Optimization Laboratory (MSO Lab) I appreciate their specialization and open-mindedness, which allowed me to discuss and talk about anything, whether research, programming, or anything else I learned a lot from them I hope we will be able to undertake more collaborative work in the near future I am also grateful to my friends who assisted me in improving the quality of my thesis Finally, I would like to thank Vingroup JSC, the Vingroup Innovation Foundation, and the School of Information and Communication Technology (SoICT) for supporting my studies during the Master’s program I was funded by Vingroup JSC and supported by the Master, Ph.D Scholarship Programme of Vingroup Innovation Foundation (VINIF), Institute of Big Data, code VINIF.2020.ThS.BK.01 and VINIF.2021.ThS.BK.01 for two years, 2021 and 2022 These supports allow me to entirely focus on my scientific research Abstract Real-world network architectures seldom exist in isolation Many of them are either repetitive or share domain-specific similarities A good network architecture for one system can also be helpful for another Therefore, knowledge drawn from solving previous network design problems may be reused to solve new problems more quickly and efficiently Meanwhile, traditional optimization algorithms often solve only one problem at a time from scratch and assume zero prior knowledge about these problems at hand It makes the capabilities of solvers not automatically grow with experience This thesis proposes multitasking evolutionary algorithms to solve multiple clustered tree problems in multi-domain networks simultaneously The thesis focuses on two clustered tree problems: Clustered Shortest Path Tree (CluSPT) and Clustered Minimum Routing Cost Tree (CluMRCT) Both are NP-Hard and representative cases of Client-Sever and Peer-to-Peer topologies in multi-domain networks, respectively The proposed algorithms help reduce the total time for optimization completion and facilitate online knowledge transfers between problems during the optimization process, thereby yielding superior results to traditional single-task optimization methods Keywords: Evolutionary Algorithms, Multitasking Evolutionary Algorithm, Multifactorial Evolutionary Algorithm, Clustered Tree Problems Author Ta Bao Thang Contents Theoretical Basis 1.1 Overview of Meta-heuristic Algorithm 1.2 Multifactorial Evolutionary Algorithm Problem Formulation 2.1 Problem formulation 2.2 Related Works Multitask Algorithm for Clustered Shortest Path Tree 11 3.1 Individual Encoding 11 3.2 Individual Decoding 13 3.3 Repairing Method 15 3.4 Algorithmic Structure 17 3.4.1 Unified search space 17 3.4.2 Individual Initialization Method 20 3.4.3 Crossover Operator 20 3.4.4 Mutation Operator 21 3.4.5 Mapping Individual Method 21 Multitask Algorithm for Clustered Minimum Routing Cost Tree 23 4.1 Individual Encoding 23 4.2 Individual Decoding 24 4.3 Algorithmic Structure 27 4.3.1 Knowledge Transfer Method 29 4.3.2 Fireflies’ Movement-based Mutation 31 Experiments 33 5.1 Dataset 33 5.2 Experimental criteria 33 5.3 5.4 Results and Discussions on Clustered Shortest Path Tree 34 5.3.1 Comprehensive comparisons between the proposed algorithm and several state-of-the-art approaches 34 5.3.2 Analyze the effect of the input graph size on the performance of the proposed algorithm 38 5.3.3 Analyze the effectiveness of the proposed multi-parent crossover 38 Results and Discussions on Clustered Minimum Routing Cost Tree 40 5.4.1 Analyze the effectiveness of the proposed encoding and decoding method 41 5.4.2 Analyze the effectiveness of proposed hybridization strategy 42 5.4.3 Comprehensive comparisons between the proposed algorithm and several state-of-the-art approaches 43 Conclusion 47 A 57 A.1 Experimental results of the Clustered Shortest-Path Tree (CluSPT) problem 57 A.2 Experimental results of the Clustered Minimum Routing Cost Tree (CluMRCT) problem 57 [9] Iago A Carvalho and Marco A Ribeiro A node-depth phylogenetic-based artificial immune system for multi-objective network design problems Swarm and Evolutionary Computation, 50:100491, 2019 [10] Rohitash Chandra, Abhishek Gupta, Yew-Soon Ong, and Chi-Keong Goh Evolutionary multi-task learning for modular training of feedforward neural networks In International Conference on Neural Information Processing, pages 37–46 Springer, 2016 [11] Gonggui Chen, Jie Qian, Zhizhong Zhang, and Zhi Sun Multi-objective optimal power flow based on hybrid firefly-bat algorithm and constraints-prior objectfuzzy sorting strategy IEEE Access, 7:139726–139745, 2019 [12] Yen Hung Chen The clustered and bottleneck clustered selected-internal steiner tree problems In The Second Malta Conference in Graph Theory and Combinatorics 2017, page 44, Qawra, St Paul’s Bay, 2017 The Second Malta Conference in Graph Theory and Combinatorics [13] Zhiwen Cheng, Haohao Song, Jiquan Wang, Hongyu Zhang, Tiezhu Chang, and Mingxin Zhang Hybrid firefly algorithm with grouping attraction for constrained optimization problem Knowledge-Based Systems, 220:106937, 2021 [14] Tran Cong Dao, Tran Huy Hung, Nguyen Thi Tam, and Huynh Thi Thanh Binh A multifactorial evolutionary algorithm for minimum energy cost data aggregation tree in wireless sensor networks In 2021 IEEE Congress on Evolutionary Computation (CEC), pages 1656–1663 IEEE, 2021 [15] Alexandre CB Delbem, Telma W de Lima, and Guilherme P Telles Efficient forest data structure for evolutionary algorithms applied to network design IEEE transactions on evolutionary computation, 16(6):829–846, 2012 [16] Mattia D’Emidio, Luca Forlizzi, Daniele Frigioni, Stefano Leucci, and Guido Proietti On the clustered shortest-path tree problem In Proceedings of the 17th Italian Conference on Theoretical Computer Science, Lecce, Italy, September 79, 2016., pages 263–268, Lecce, Italy, 2016 Italian Conference on Theoretical Computer [17] Thanh Pham Dinh, Binh Huynh Thi Thanh, Trung Tran Ba, and Long Nguyen Binh Multifactorial evolutionary algorithm for solving clustered tree problems: competition among cayley codes Memetic Computing, 12(3):185–217, 2020 [18] Benjamin Doerr, Huu Phuoc Le, R´egis Makhmara, and Ta Duy Nguyen Fast genetic algorithms In Proceedings of the Genetic and Evolutionary Computation Conference, pages 777–784, 2017 52 [19] Ke-Lin Du and MNS Swamy Particle swarm optimization In Search and optimization by metaheuristics, pages 153–173 Springer, 2016 [20] Farhad Soleimanian Gharehchopogh and Hojjat Gholizadeh A comprehensive survey: Whale optimization algorithm and its applications Swarm and Evolutionary Computation, 48:1–24, 2019 [21] A Gupta, Y Ong, and L Feng Multifactorial evolution: Toward evolutionary multitasking IEEE Transactions on Evolutionary Computation, 20(3):343–357, June 2016 [22] Abhishek Gupta, Yew-Soon Ong, and Liang Feng Multifactorial evolution: toward evolutionary multitasking IEEE Transactions on Evolutionary Computation, 20(3):343–357, 2015 [23] Phan Thi Hong Hanh, Pham Dinh Thanh, and Huynh Thi Thanh Binh Evolutionary algorithm and multifactorial evolutionary algorithm on clustered shortest-path tree problem Information Sciences, 553:280–304, 2021 [24] Tran Thi Huong, Huynh Thi Thanh Binh, et al A multi-task approach for maximum survival ratio problem in large-scale wireless rechargeable sensor networks In 2021 IEEE Congress on Evolutionary Computation (CEC), pages 1688–1695 IEEE, 2021 [25] James Kennedy and Russell Eberhart Particle swarm optimization In Proceedings of ICNN’95-International Conference on Neural Networks, volume 4, pages 1942–1948 IEEE, 1995 [26] Marylu L Lagunes, Oscar Castillo, Jose Soria, and Fevrier Valdez Optimization of a fuzzy controller for autonomous robot navigation using a new competitive multi-metaheuristic model Soft Computing, 25(17):11653–11672, 2021 [27] Chen-Wan Lin and Bang Ye Wu On the minimum routing cost clustered tree problem Journal of Combinatorial Optimization, 33(3):1106–1121, 2017 [28] Zengwei Lyu, Zhenchun Wei, Jie Pan, Hua Chen, Chengkai Xia, Jianghong Han, and Lei Shi Periodic charging planning for a mobile wce in wireless rechargeable sensor networks based on hybrid pso and ga algorithm Applied Soft Computing, 75:388–403, 2019 [29] M´ario Mestria, Luiz Satoru Ochi, and Simone de Lima Martins Grasp with path relinking for the symmetric euclidean clustered traveling salesman problem Computers & Operations Research, 40(12):3218–3229, 2013 53 [30] Venkataraman Muthiah-Nakarajan and Mathew Mithra Noel Galactic swarm optimization: A new global optimization metaheuristic inspired by galactic motion Applied Soft Computing, 38:771–787, 2016 [31] Young-Soo Myung, Chang-Ho Lee, and Dong-Wan Tcha On the generalized minimum spanning tree problem Networks, 26(4):231–241, 1995 [32] Mohammad H Nadimi-Shahraki, Shokooh Taghian, and Seyedali Mirjalili An improved grey wolf optimizer for solving engineering problems Expert Systems with Applications, 166:113917, 2021 [33] Bach Hoai Nguyen, Bing Xue, and Mengjie Zhang A survey on swarm intelligence approaches to feature selection in data mining Swarm and Evolutionary Computation, 54:100663, 2020 [34] Tim Paulden and David K Smith Recent advances in the study of the dandelion code, happy code, and blob code spanning tree representations In 2006 IEEE International Conference on Evolutionary Computation, pages 2111– 2118 IEEE, 2006 [35] B Pitchaimanickam and G Murugaboopathi A hybrid firefly algorithm with particle swarm optimization for energy efficient optimal cluster head selection in wireless sensor networks Neural Computing and Applications, 32(12):7709– 7723, 2020 [36] Petric˘a C Pop The generalized minimum spanning tree problem: An overview of formulations, solution procedures and latest advances European Journal of Operational Research, 283(1):1–15, 2020 [37] A Rahmani and SA MirHassani A hybrid firefly-genetic algorithm for the capacitated facility location problem Information Sciences, 283:70–78, 2014 [38] R Venkata Rao, Vimal J Savsani, and DP Vakharia Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems Computer-Aided Design, 43(3):303–315, 2011 [39] Esmat Rashedi, Hossein Nezamabadi-Pour, and Saeid Saryazdi Gsa: a gravitational search algorithm Information sciences, 179(13):2232–2248, 2009 [40] Franz Rothlauf Representations for genetic and evolutionary algorithms In Representations for Genetic and Evolutionary Algorithms, pages 9–32 Springer, 2006 [41] Franz Rothlauf On the bias and performance of the edge-set encoding IEEE transactions on evolutionary computation, 13(3):486–499, 2009 54 [42] Franz Rothlauf, David E Goldberg, and Armin Heinzl Network random keys—a tree representation scheme for genetic and evolutionary algorithms Evolutionary Computation, 10(1):75–97, 2002 [43] Ramon Sagarna and Yew-Soon Ong Concurrently searching branches in software tests generation through multitask evolution In 2016 IEEE Symposium Series on Computational Intelligence (SSCI), pages 1–8 IEEE, 2016 [44] Daniela S´anchez, Patricia Melin, and Oscar Castillo Optimization of modular granular neural networks using a firefly algorithm for human recognition Engineering Applications of Artificial Intelligence, 64:172–186, 2017 [45] Mojtaba Shakeri, Abhishek Gupta, Yew-Soon Ong, Xu Chi, and Allan Zhang NengSheng Coping with big data in transfer optimization In 2019 IEEE International Conference on Big Data (Big Data), pages 3925–3932 IEEE, 2019 [46] Razi Sheikholeslami, Behnam Gholipour Khalili, Ali Sadollah, and JoongHoon Kim Optimization of reinforced concrete retaining walls via hybrid firefly algorithm with upper bound strategy KSCE Journal of Civil Engineering, 20(6):2428–2438, 2016 [47] Fang Shen, Jing Liu, and Kai Wu Evolutionary multitasking fuzzy cognitive map learning Knowledge-Based Systems, 192:105294, 2020 [48] Kay Chen Tan, Liang Feng, and Min Jiang Evolutionary transfer optimizationa new frontier in evolutionary computation research IEEE Computational Intelligence Magazine, 16(1):22–33, 2021 [49] Ta Bao Thang, Nguyen Binh Long, Ngo Viet Hoang, and Huynh Thi Thanh Binh Adaptive knowledge transfer in multifactorial evolutionary algorithm for the clustered minimum routing cost problem Applied Soft Computing, 105:107253, 2021 [50] P D Thanh, D A Dung, T N Tien, and H T T Binh An effective representation scheme in multifactorial evolutionary algorithm for solving cluster shortest-path tree problem In 2018 IEEE Congress on Evolutionary Computation (CEC), pages 1–8, Rio de Janeiro, Brazil, July 2018 Institute of Electrical and Electronics Engineers (IEEE) [51] P D Thanh, H Thi Thanh Binh, D D Dac, N Binh Long, and L M Hai Phong A heuristic based on randomized greedy algorithms for the clustered shortest-path tree problem In 2019 IEEE Congress on Evolutionary Computation (CEC), pages 2915–2922, Wellington, New Zealand, June 2019 Institute of Electrical and Electronics Engineers (IEEE) 55 [52] Pham Dinh Thanh, Huynh Thi Thanh Binh, and Tran Ba Trung An efficient strategy for using multifactorial optimization to solve the clustered shortest path tree problem Applied Intelligence, 50(4):1233–1258, 2020 [53] H Thi Thanh Binh, P Dinh Thanh, T Ba Trung, and L Phuong Thao Effective multifactorial evolutionary algorithm for solving the cluster shortest path tree problem In 2018 IEEE Congress on Evolutionary Computation (CEC), pages 1–8, Rio de Janeiro, Brazil, July 2018 Institute of Electrical and Electronics Engineers (IEEE) [54] Surafel Luleseged Tilahun, Jean Medard T Ngnotchouye, and Nawaf N Hamadneh Continuous versions of firefly algorithm: a review Artificial Intelligence Review, 51(3):445–492, 2019 [55] Tran Ba Trung, Le Tien Thanh, Ly Trung Hieu, Pham Dinh Thanh, and Huynh Thi Thanh Binh Multifactorial evolutionary algorithm for clustered minimum routing cost problem In Proceedings of the Tenth International Symposium on Information and Communication Technology, pages 170–177, 2019 [56] Ting-Chen Wang and Rung-Tzuo Liaw Multifactorial genetic fuzzy data mining for building membership functions In 2020 IEEE Congress on Evolutionary Computation (CEC), pages 1–8 IEEE, 2020 [57] Yinyan Zhang, Shuai Li, and Bin Xu Convergence analysis of beetle antennae search algorithm and its applications Soft Computing, 25(16):10595–10608, 2021 [58] Miodrag Zivkovic, Nebojsa Bacanin, K Venkatachalam, Anand Nayyar, Aleksandar Djordjevic, Ivana Strumberger, and Fadi Al-Turjman Covid-19 cases prediction by using hybrid machine learning and beetle antennae search approach Sustainable Cities and Society, 66:102669, 2021 56 Appendix A A.1 Experimental results of the CluSPT problem A.2 Experimental results of the CluMRCT problem 57 Table A.1: Results obtained by G-MFEA, HB-RGA and K-MFEA on Type HB-RGA K-MFEA Std Avg Time Std Avg Time Std Avg Time Small instances G-MFEA 10berlin52 10eil51 10eil76 10kroB100 10pr76 10rat99 10st70 15berlin52 15eil51 15eil76 15pr76 15st70 25eil101 25kroA100 25lin105 25rat99 50eil101 50kroA100 50kroB100 50lin105 50rat99 5berlin52 5eil51 5eil76 5pr76 5st70 232.4 10.0 5.1 1316.3 3160.9 41.9 32.2 125.7 7.1 10.5 3927.6 17.4 5.3 477.8 415.4 21.5 0.8 214.7 190.4 81.9 6.2 360.5 21.8 27.6 4770.1 42.7 43971.0 1723.2 2208.4 141951.4 525733.1 7562.1 3131.7 26437.7 1313.8 2921.8 708944.9 4147.3 4686.1 147716.8 98502.9 6867.8 3828.1 160029.9 133325.8 145951.8 8016.8 23106.9 1792.3 2658.4 589778.1 4562.8 0.04 0.04 0.05 0.06 0.04 0.05 0.04 0.03 0.03 0.04 0.04 0.03 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.06 0.05 0.03 0.03 0.05 0.06 0.04 0.0 0.0 0.0 46.7 126.6 3.8 0.5 36.2 2.3 4.0 1279.4 8.8 27.5 940.2 1643.9 91.4 143.4 6392.8 8365.5 2779.2 274.1 0.0 0.0 0.0 0.0 0.0 43724.1 1713.2 2203.3 140597.9 522340.4 7524.0 3095.7 26351.7 1309.1 2913.1 706505.5 4135.5 4727.9 149708.1 100585.3 7022.3 4178.1 179506.1 157831.1 154680.7 9002.1 22746.4 1769.4 2630.8 585008.0 4520.1 0.67 0.92 1.60 2.35 1.67 2.35 1.40 1.07 1.00 1.62 1.63 1.40 2.38 2.37 2.50 2.33 3.15 3.13 3.13 3.33 3.15 1.02 0.95 1.83 1.82 1.57 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 43724.1 1713.2 2203.3 140522.2 522213.8 7520.2 3095.2 26312.0 1306.4 2909.1 704600.6 4120.1 4679.0 147195.0 97944.7 6841.5 3825.3 159647.2 133104.5 145829.1 8007.4 22746.4 1769.4 2630.8 585008.0 4520.1 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.08 0.08 0.08 0.08 0.05 0.05 0.00 0.00 0.00 0.00 Large instances Instance 10a280 10gil262 10lin318 10pcb442 10pr439 25a280 25gil262 25lin318 25pcb442 25pr439 50a280 50gil262 50lin318 50pcb442 50pr439 322.2 134.4 10513.5 5097.7 12781.9 169.9 175.4 3322.6 3296.9 12654.5 64.5 46.8 1153.7 1257.8 5439.3 28515.8 27788.0 825808.2 750362.1 1930766.4 30228.5 30711.1 595489.0 748031.6 1531976.6 36471.0 26680.8 691897.5 914652.8 2167713.8 0.31 0.27 0.37 0.87 1.32 0.23 0.22 0.31 0.54 0.89 0.22 0.22 0.31 0.57 0.93 143.3 8.2 1520.4 566.5 4246.4 280.9 257.4 8101.4 5183.4 24526.8 1275.7 1223.9 18179.5 28334.3 72915.1 28079.4 27645.7 814264.5 742678.9 1911815.3 30654.1 30953.2 601118.8 762707.5 1556475.7 39872.5 30004.0 748203.2 990436.0 2375177.6 14.72 12.78 18.55 39.38 42.50 11.17 11.67 16.65 31.28 29.62 12.15 12.12 16.80 31.00 25.13 0.0 0.0 0.0 0.0 28.7 0.0 0.0 0.0 0.0 28.3 0.0 0.0 24.0 8.8 1.3 27925.2 27637.5 809750.0 741195.8 1904718.9 29902.4 30325.7 584554.0 740892.6 1511197.2 36266.9 26523.3 688748.6 910487.5 2152987.9 0.03 0.03 0.03 0.03 0.05 0.05 0.07 0.07 0.07 0.07 0.13 0.13 0.15 0.15 0.15 58 Table A.2: Results obtained by G-MFEA, HB-RGA and K-MFEA on Types and HB-RGA Instance G-MFEA K-MFEA Std Avg Time Std Avg Time Std Avg Time 6i300 6i350 Type 6i400 6i450 6i500 375.5 327.8 400.3 564.3 426.4 19836.6 21713.4 29913.7 36463.5 38225.9 0.55 0.73 1.05 1.34 1.95 34 42.8 48 80.2 63.8 19320.3 21261.3 29437.5 35795.9 37631.4 23.42 33.2 46.6 60.45 82.3 0 0 19264.5 21217.2 29348.2 35681.5 37516.1 0.03 0.03 0.03 0.03 0.05 4i200a 4i200h 4i200x1 4i200x2 4i200z Type 4i400a 4i400h 4i400x1 4i400x2 4i400z 14.5 609.8 1014.5 1372.5 1890.4 115.2 3129.1 2305.2 3430.8 3216.8 97974.1 88285.1 124825.9 115432 133697.8 214230.5 260183.1 191145.3 162685.6 224677.4 0.35 0.36 0.35 0.37 0.38 2.53 2.41 2.32 2.35 2.22 0 0.5 1.7 90.7 23416.1 19392.6 10691.3 97959.6 87675.3 123670.2 114012 131685.2 214115 256291.2 222805.4 195580.8 244894.6 11.43 11.63 11.67 12.03 11.57 64.53 62.68 36.93 64.03 36.95 0 0 0 0 0 97959.6 87675.3 123670 114012 131684 214115 256201 188197 159255 221424 0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 59 Table A.3: Results obtained by G-MFEA, HB-RGA and K-MFEA on Type HB-RGA Std Avg Time Std Avg Time Std Avg Time Small Instances K-MFEA 10i120-46 10i30-17 10i45-18 10i60-21 10i65-21 10i70-21 10i75-22 10i90-33 5i120-46 5i30-17 5i45-18 5i60-21 5i65-21 5i70-21 5i75-22 5i90-33 7i30-17 7i45-18 7i60-21 7i65-21 541.5 12.6 77.2 1257.5 290.3 311.2 371.2 526.4 617.2 8.7 161.5 440.4 331.6 182.7 787.1 11.1 461.8 75.6 34.3 94596.7 13289.2 23344.8 35002 37677 38855 65783.1 52617.6 62393.2 14399.9 14893 28584.2 31684.7 35384.4 34993.8 52916 20450 20973.8 36339.5 34881.9 0.08 0.02 0.03 0.03 0.04 0.03 0.05 0.05 0.11 0.02 0.02 0.03 0.03 0.04 0.05 0.06 0.02 0.02 0.03 0.04 77.4 1.8 0.5 120.6 35.3 32.4 43.8 0 3.9 0 0.3 0 0 94034.3 13276.6 22892.2 33702.8 37353.6 38187.3 65397.3 51975.6 61495.3 14399.9 14884.3 28422.7 30911.7 35052.8 34692.5 51977.3 20438.9 20512 36263.9 34847.6 2.77 0.58 0.85 1.2 1.32 1.43 1.67 2.03 3.65 0.62 0.88 1.18 1.4 1.57 1.83 2.28 0.57 0.8 1.13 1.33 0 0 0 0 0 0 0 0 0 0 93925 13276.6 22890.4 33694.8 37353.1 38059.5 65361.9 51931.2 61451.5 14399.9 14884.3 28422.7 30907.8 35052.8 34692.5 51977 20438.9 20512 36263.9 34847.6 0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 Large Instances Instance G-MFEA 10i300-109 10i400-206 10i500-305 15i300-110 15i400-207 15i500-306 20i300-111 20i400-208 20i500-307 25i300-112 25i400-209 25i500-308 5i300-108 5i400-205 5i500-304 981.3 1844.1 4809.7 439.6 1230.7 1895.2 1037.6 790.7 1340 459.7 1128.9 1068.8 2098.8 5785.2 2679.4 114274 211253 356961 114532 166796 306930 158564 226964 204679 118122 233016 301907 179797 216015 185810 0.33 0.6 0.99 0.28 0.47 0.8 0.24 0.39 0.64 0.22 0.38 0.61 0.67 1.17 2.11 140.9 308.9 1032.2 423 526.7 820.7 618.9 685.6 972.2 1091.2 2903.9 1549.4 34.8 482.9 210.2 113017 208087 351930 113359 165855 304949 157990 227070 203911 119401 236457 304047 177221 209971 182416 16.98 31.85 52.5 15.83 28.27 42.77 15.3 26.78 39.17 14.38 23.27 24.6 26.78 52.22 90.62 0 0 0 0 14.3 0 0 1619.6 112681 207522 349675 112097 164118 300734 156348 224013 200343 116194 229914 299498 177186 209390 183977 0.03 0.03 0.03 0.03 0.03 0.03 0.05 0.05 0.05 0.05 0.05 0.05 0.02 0.02 0.6 60 Table A.4: Results obtained by G-MFEA, HB-RGA and K-MFEA on Type HB-RGA Std Avg Time Std Avg Time Std Avg Time Small Instances K-MFEA 10berlin52-2x5 12eil51-3x4 12eil76-3x4 12pr76-3x4 12st70-3x4 15pr76-3x5 16eil51-4x4 16eil76-4x4 16lin105-4x4 16st70-4x4 18pr76-3x6 20eil51-4x5 20eil76-4x5 20st70-4x5 25eil101-5x5 25eil51-5x5 25eil76-5x5 25rat99-5x5 28kroA100-4x7 30kroB100-5x6 35kroB100-5x5 36eil101-6x6 42rat99-6x7 4berlin52-2x2 4eil51-2x2 4eil76-2x2 4pr76-2x2 6berlin52-2x3 6pr76-2x3 6st70-2x3 8berlin52-2x4 9eil101-3x3 9eil51-3x3 9eil76-3x3 9pr76-3x3 250.8 3.2 2.4 2876.8 16.5 6300.1 1.6 11.4 633.1 26.8 3666.1 3.7 6.7 6.3 12.9 1.6 1.7 18.6 403.3 229 709.7 1.4 3.5 108 17.1 25.8 3304.3 164.9 7343.7 26.8 115.4 18.9 8.5 18.2 5234.5 27723 1702.3 2653.2 603474 4144.6 532897 1304 2053.8 125685 2966.1 646399 2287.9 2392.6 2945.7 3622 1476.2 2194.8 11419 134532 199206 129832 3852.1 8906 23396 1915.6 2974.6 445997 32296 656229 3503.5 26970 3154.3 1921.3 2956.6 560230 0.04 0.03 0.04 0.05 0.03 0.06 0.02 0.04 0.06 0.03 0.04 0.03 0.03 0.03 0.05 0.02 0.03 0.05 0.05 0.05 0.05 0.04 0.05 0.03 0.03 0.05 0.06 0.03 0.05 0.04 0.03 0.06 0.03 0.04 0.04 1.6 0.1 387.8 3.6 995.9 2.9 12.2 237.6 13.8 1976.8 6.5 11.7 24.2 21.3 19.9 26.1 51 1841.7 1613 1905.3 52.4 206.5 0 0 232.2 12.2 2.6 1.9 1.2 164.1 27473 1699.1 2650.8 600818.7 4110.1 526166.2 1305.6 2052.2 125289.8 2949.2 641700.1 2295.2 2402.2 2967 3670.5 1507.3 2245.2 11485.9 138342.8 202209.8 132840.4 3981.6 9393.5 23287.9 1898.5 2948.7 442693 32128.6 648507.9 3476.7 26795.4 3120.2 1909.9 2938.6 553849.7 0.83 0.93 1.57 1.65 1.43 1.63 1.67 2.4 1.45 1.68 1.05 1.68 1.47 2.5 1.18 1.73 2.33 2.38 2.5 2.48 2.68 2.75 1.1 0.97 1.98 2.02 1.13 1.73 1.4 0.93 2.32 0.92 1.57 1.63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 27471.4 1699 2650.8 600008.6 4106.5 524335.2 1301.4 2036 125052.2 2932.6 638164.5 2283.7 2385.9 2934.8 3603.5 1474.6 2193.1 11395.8 133101.6 197934.6 129078.7 3850.7 8902.1 23287.9 1898.5 2948.7 442693 32128.6 648275.7 3476.7 26783.2 3117.6 1907.7 2937.4 553400.6 0.02 0.02 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.07 0.07 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 Large Instances Instance G-MFEA 18pr439-3x6 20pr439-4x5 25a280-5x5 25gil262-5x5 25pcb442-5x5 36pcb442-6x6 42a280-6x7 49lin318-7x7 9a280-3x3 9gil262-3x3 9lin318-3x3 9pcb442-3x3 9pr439-3x3 22121 14847 133.8 254.5 4799.5 2634.1 78.9 1934.1 240 204.9 5059.1 6294.5 33240 1E+06 2E+06 42151 31080 752960 869008 44159 574040 29497 21454 725328 769413 2E+06 2.19 1.87 0.24 0.2 0.59 0.53 0.2 0.28 0.36 0.32 0.47 1.05 2.86 5057.5 6748.9 265.7 256.7 9817.3 14520 970.9 24091 59.9 55.3 970.9 784.7 5858 1488675.8 2000099.7 42388.8 31372.9 762391.2 901697.8 46000.9 633218.4 29105 20993.1 719450.3 761269.1 1809146.2 57.18 50.65 13.1 11.6 28.68 30.92 12.95 15.55 14.55 14.27 20.27 41.25 56.98 1010 0 0 15.3 0 0 30246 1472798 1978001 41690.3 30649.5 740883.3 860993.5 43896.8 569755.3 28947.5 20935.9 716850.2 760238.3 1830999.9 0.07 0.07 0.07 0.07 0.07 0.1 0.1 0.12 0.02 0.02 0.02 0.02 0.47 61 Table A.5: Averaged Experimental results (unit: 104 ) on Type where +, =, and − denote the number of tasks that each algorithm was better, equal, and worse than the MFEA-FA algorithm Type Small 10berlin52 10eil51 10eil76 10kroB100 10pr76 10rat99 15eil51 15eil76 15pr76 15st70 25eil101 25kroA100 25lin105 25rat99 50eil101 50kroA100 50kroB100 50lin105 50rat99 5berlin52 5eil51 5eil76 5pr76 5st70 97.77 5.96 13.55 1156.95 3069.46 57.15 6.06 13.60 3000.89 18.10 25.04 1159.30 843.37 57.16 24.42 1141.42 1123.48 827.50 55.80 99.10 5.83 13.69 3085.03 18.50 98.04 6.01 13.69 1164.37 3085.23 57.24 6.09 13.73 3014.83 18.21 25.10 1162.29 845.67 57.43 24.49 1145.70 1129.70 833.02 55.99 99.47 5.89 13.76 3092.13 18.74 98.20 6.05 13.77 1185.42 3115.37 58.91 6.11 13.81 3034.80 18.37 25.27 1172.87 849.89 57.80 24.65 1150.73 1136.80 840.48 56.34 99.88 5.99 14.01 3141.04 19.00 98.99 6.22 14.24 1228.13 3191.55 61.41 6.20 14.24 3107.19 18.76 25.92 1197.28 863.98 59.38 24.94 1167.79 1153.02 849.84 56.99 101.43 6.14 14.47 3221.78 19.72 111.80 6.81 17.00 1428.31 3673.23 71.99 6.78 16.47 3467.38 20.80 32.09 1441.86 1027.04 73.19 40.09 1871.68 1825.25 1305.92 96.99 119.04 7.12 18.56 4031.20 24.77 130.77 10.15 22.30 2156.44 4459.71 102.90 11.25 23.47 6202.15 27.86 39.20 1719.86 1223.61 108.95 32.09 1801.27 1458.65 986.38 78.46 151.69 9.72 24.19 5206.66 29.14 112.85 6.82 17.63 1443.02 3752.87 73.39 6.93 16.56 3590.22 21.32 33.11 1480.17 1100.24 96.84 47.00 3001.47 2096.26 2318.67 140.45 126.46 7.47 14.33 4306.56 18.70 10a280 10gil262 10lin318 10pcb442 25a280 25gil262 25lin318 25pcb442 25pr439 686.56 522.48 13475.18 25726.67 693.37 517.39 13785.01 25385.28 58964.24 689.76 525.43 13561.14 25982.65 695.95 518.73 13805.79 25492.69 59127.60 717.95 711.13 740.21 538.84 538.52 556.36 13775.51 13765.71 14041.03 26682.85 26580.75 27372.44 711.55 712.44 727.93 529.28 527.71 540.83 14109.62 14103.31 14353.40 26130.60 26158.82 26705.14 60568.95 60405.97 61791.03 1323.29 1015.71 26739.68 53872.95 1047.95 811.72 20762.37 44667.08 97122.85 1140.98 865.45 16561.32 37782.67 1037.05 830.55 22139.26 35569.45 71744.72 1335.04 1028.36 27075.91 54764.69 1024.44 836.45 21130.29 45195.79 102280.58 0/0/33 0/0/33 0/0/33 0/0/33 0/0/33 0/0/33 0/0/33 +/=/- 62 98.15 6.06 13.81 1193.01 3114.39 59.47 6.10 13.84 3042.64 18.39 25.42 1172.96 850.71 58.02 24.61 1149.68 1132.90 834.95 56.26 99.81 5.98 13.99 3133.45 19.00 PFA aMFEA-II R-Star E-MFEA Type Large Instances MFEA-FA PMFEA PBA PWOA Table A.6: Averaged Experimental results (unit: 106 ) on Type and Type where +, =, and − denote the number of tasks that each algorithm was better, equal, and worse than the MFEA-FA algorithm Type 6i300 6i350 6i400 6i450 6i500 4.45 5.97 7.95 9.86 12.29 4.48 6.03 8.02 9.92 12.44 4.51 6.09 8.10 10.04 12.56 4.50 6.07 8.09 9.99 12.51 4.59 6.19 8.24 10.17 12.82 6.92 9.65 13.59 17.38 22.43 6.16 8.33 10.90 13.64 16.75 7.14 10.06 14.01 17.84 22.67 Type Instances MFEA-FA PMFEA PBA PWOA PFA aMFEA-II R-Star E-MFEA 4i200a 4i200x1 4i200z 4i400a 4i400h 4i400x1 4i400x2 4i400z 16.01 15.16 15.23 64.81 61.37 61.26 61.15 61.22 16.13 15.36 15.40 65.46 62.15 62.20 62.23 62.07 16.52 15.63 15.67 66.60 63.77 63.35 63.48 63.03 16.24 15.63 15.61 66.05 62.86 63.31 63.04 63.30 17.36 16.09 16.16 69.80 65.61 65.71 65.51 65.62 57.16 37.45 39.07 277.04 198.71 200.34 202.75 200.16 31.80 23.29 23.53 124.67 93.90 91.31 91.30 91.79 57.75 36.29 37.29 273.78 204.97 202.32 204.31 202.08 0/0/13 0/0/13 0/0/13 +/=/- 0/0/13 0/0/13 0/0/13 0/0/13 63 Table A.7: Averaged Experimental results (unit: 105 ) on Type where +, =, and − denote the number of tasks that each algorithm was better, equal, and worse than the MFEA-FA algorithm Type Small 10i120-46 10i45-18 10i60-21 10i65-21 10i70-21 10i90-33 5i120-46 5i30-17 5i45-18 5i60-21 5i65-21 5i70-21 5i75-22 5i90-33 7i60-21 7i65-21 59.21 7.07 14.95 17.73 20.42 27.69 46.08 3.30 5.96 14.27 16.31 18.99 19.50 24.76 15.95 17.53 59.42 7.09 15.00 17.81 20.58 27.89 46.34 3.32 5.98 14.45 16.52 19.17 19.62 24.93 16.06 17.73 60.59 7.16 15.11 18.09 20.73 28.24 46.99 3.33 6.01 14.59 16.64 19.27 19.69 25.32 16.15 17.88 60.67 7.13 15.20 18.03 20.78 28.40 46.72 3.31 6.02 14.50 16.56 19.32 19.73 25.13 16.23 17.99 62.52 7.34 15.54 18.55 21.35 29.27 48.19 3.35 6.15 14.90 17.06 19.74 20.19 25.95 16.67 18.69 81.78 8.39 17.99 21.10 24.85 34.71 69.26 3.57 7.11 17.28 20.01 23.12 26.08 33.68 18.00 21.10 91.72 11.00 25.93 28.57 32.08 51.38 68.27 4.91 9.48 22.70 25.62 31.42 40.75 46.61 23.62 26.02 81.97 8.52 18.53 21.39 25.46 35.04 69.34 3.68 7.14 17.47 21.43 24.10 27.60 34.07 18.48 21.21 Type Large Instances MFEA-FA PMFEA PBA PWOA PFA aMFEA-II R-Star E-MFEA 10i300-109 10i400-206 10i500-305 15i400-207 15i500-306 20i300-111 20i400-208 20i500-307 25i300-112 25i400-209 25i500-308 5i300-108 5i400-205 213.90 546.45 967.53 579.83 960.85 350.95 652.57 764.41 326.57 633.56 929.27 328.04 354.50 215.30 550.87 974.37 583.32 964.69 352.20 654.96 767.76 329.39 637.70 933.34 330.51 357.54 221.17 559.93 986.15 592.73 980.01 360.97 665.93 783.68 336.59 650.40 952.97 332.67 361.57 220.16 559.94 983.73 594.55 977.42 360.45 668.16 784.32 336.41 650.02 951.41 331.55 360.92 227.74 572.61 1006.97 608.02 994.48 368.10 682.21 798.44 344.02 662.78 969.65 337.06 370.22 443.36 964.19 1582.14 1009.49 1590.81 574.29 1022.39 1298.73 522.89 1072.98 1563.32 605.78 784.24 320.89 983.93 1378.58 1020.45 1196.18 652.00 1011.83 1071.68 480.77 1090.83 1709.38 499.68 451.81 452.75 990.13 1457.32 1031.35 1643.67 590.89 1059.14 1226.60 529.90 1107.40 1626.59 613.39 793.14 0/0/29 0/0/29 0/0/29 0/0/29 0/0/29 0/0/29 0/0/29 +/=/– 64 Table A.8: Averaged Experimental results (unit: 104 ) on Type Small where +, =, and − denote the number of tasks that each algorithm was better, equal, and worse than the MFEA-FA algorithm Type Small Instances 10berlin52-2x5 12eil51-3x4 12eil76-3x4 12pr76-3x4 12st70-3x4 15pr76-3x5 16eil51-4x4 16eil76-4x4 16lin105-4x4 16st70-4x4 18pr76-3x6 20eil51-4x5 20eil76-4x5 20st70-4x5 25eil101-5x5 25eil51-5x5 25eil76-5x5 25rat99-5x5 28kroA100-4x7 30kroB100-5x6 35kroB100-5x5 36eil101-6x6 42rat99-6x7 4berlin52-2x2 4eil51-2x2 4eil76-2x2 4pr76-2x2 6berlin52-2x3 6pr76-2x3 6st70-2x3 8berlin52-2x4 9eil101-3x3 9eil51-3x3 9eil76-3x3 +/=/- MFEA-FA PMFEA PBA PWOA PFA aMFEA-II R-Star E-MFEA 104.23 6.05 13.61 3102.25 18.33 3083.45 5.85 13.86 875.24 18.49 3152.99 5.95 13.83 18.28 25.12 5.93 13.55 58.09 1180.99 1157.08 1159.35 24.58 56.50 98.80 5.85 13.38 3087.64 99.50 3154.20 18.66 104.28 25.15 6.06 13.68 104.54 6.07 13.65 3119.03 18.51 3090.30 5.89 13.96 879.42 18.58 3163.79 5.97 13.90 18.33 25.27 5.94 13.64 58.26 1184.18 1160.56 1162.05 24.66 56.80 99.48 5.90 13.44 3104.72 100.17 3156.32 18.79 104.51 25.22 6.12 13.73 104.81 6.12 13.82 3141.21 18.70 3125.89 5.92 14.01 884.48 18.82 3178.75 5.99 13.99 18.53 25.49 5.95 13.69 58.85 1189.35 1170.81 1176.32 24.80 57.06 99.88 5.96 13.67 3140.81 100.34 3203.74 19.03 105.06 25.62 6.13 13.88 105.66 6.23 14.31 3212.90 19.15 3187.83 6.01 14.41 906.21 19.13 3236.57 6.05 14.33 18.86 26.12 5.99 13.92 60.15 1216.45 1193.14 1200.81 25.23 57.87 101.51 6.13 14.20 3224.22 101.85 3261.73 19.68 106.44 26.52 6.31 14.34 122.22 7.12 16.37 3647.61 21.43 3930.51 6.67 16.99 1123.68 20.99 3558.04 6.91 16.69 21.16 33.11 6.95 16.97 72.61 1531.14 1495.87 1492.70 34.29 80.76 153.20 7.04 17.69 4052.88 130.47 3843.30 23.00 124.67 33.85 6.92 16.99 204.44 10.72 26.44 5096.88 37.83 5119.53 10.53 30.20 1745.17 37.57 5622.21 10.39 29.92 30.26 53.46 11.79 29.47 109.76 1819.28 2201.24 2206.75 50.83 115.44 155.99 9.49 23.51 4707.58 178.64 4467.75 30.21 195.46 49.25 10.63 25.36 123.59 7.21 17.16 3709.93 21.19 4012.60 6.74 17.02 1162.25 21.45 3533.94 6.95 17.10 21.81 35.36 7.03 17.66 73.46 1533.21 1518.01 1403.96 33.66 80.11 146.84 7.45 17.40 3964.85 133.89 4032.39 23.62 124.81 34.72 6.97 17.15 0/0/34 0/0/34 0/0/34 0/0/34 0/0/34 0/0/34 0/0/34 65 104.71 6.12 13.90 3143.43 18.66 3117.54 5.90 14.09 886.61 18.76 3186.32 5.98 14.07 18.48 25.54 5.95 13.68 59.02 1191.85 1169.77 1175.00 24.90 57.08 99.85 5.94 13.63 3130.99 100.41 3198.05 19.08 104.90 25.68 6.15 13.93 Table A.9: Experimental results (unit: 106 ) on Type Large where +, =, and − denote the number of tasks that each algorithm was better, equal, and worse than the MFEA-FA algorithm Type Large Instances 18pr439-3x6 20pr439-4x5 25a280-5x5 25gil262-5x5 25pcb442-5x5 36pcb442-6x6 42a280-6x7 49lin318-7x7 9a280-3x3 9gil262-3x3 9lin318-3x3 9pcb442-3x3 +/=/- MFEA-FA PMFEA PBA PWOA PFA aMFEA-II R-Star E-MFEA 582.33 589.37 7.05 5.23 254.96 253.14 6.89 134.82 7.04 5.21 138.13 259.08 585.70 593.19 7.07 5.25 256.06 253.50 6.92 134.89 7.09 5.24 138.89 263.00 595.45 603.56 7.26 5.38 262.75 259.98 7.06 136.89 7.26 5.38 141.14 268.42 606.73 615.62 7.45 5.51 268.42 264.95 7.21 139.36 7.49 5.57 143.83 275.55 1116.22 1473.50 11.45 8.20 434.79 461.70 11.87 240.87 14.03 10.60 299.56 596.70 1259.31 1137.12 1301.77 1485.29 11.86 11.67 9.04 8.23 437.28 446.10 442.83 408.80 12.26 10.78 276.50 257.83 11.56 14.18 8.66 10.82 230.85 293.79 422.58 579.18 0/0/12 0/0/12 0/0/12 0/0/12 0/0/12 0/0/12 66 594.21 603.42 7.28 5.38 262.64 259.64 7.06 137.18 7.25 5.39 140.79 268.05 0/0/12 ... algorithms for clustered minimum routing cost tree problems in the multi- domain network Contributions • Develop a new encoding and decoding scheme for two clustered tree problems: Clustered Minimum Routing. .. TECHNOLOGY MASTER THESIS Multifactorial Evolutionary Algorithms for Clustered Minimum Routing Cost Tree Problems in the Multi- domain Network TA BAO THANG Data science and Artificial intelligence Supervisor:... tuyến nhỏ nhất mạng đa miền Tiếng Anh: Multifactorial Evolutionary Algorithms for Clustered Minimum Routing Cost Tree Problems in the Multi- domain Network Chuyên ngành: Khoa học liệu Trí tuệ