Development of meta heuristic of optimization methods for mechanics problems

MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITYUNIVERSITY OF TECHNOLOGY AND EDUCATION Ph.D THESIS LAM PHAT THUAN DEVELOPMENT OF META-HEURISTIC OPTIMIZATION METHODS FOR MECHANICS PROBLEMS MAJOR: ENGINEERING MECHANICS S K A0 0 Ho Chi Minh City, 05/2021 MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION LAM PHAT THUAN DEVELOPMENT OF META-HEURISTIC OPTIMIZATION METHODS FOR MECHANICS PROBLEMS PHD THESIS MAJOR: ENGINEERING MECHANICS Ho Chi Minh City, 05/2021 THE WORK IS COMPLETED AT HCM CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION LAM PHAT THUAN DEVELOPMENT OF META-HEURISTIC OPTIMIZATION METHODS FOR MECHANICS PROBLEMS MAJOR: ENGINEERING MECHANICS - 13252010105 Supervisor 1: Assoc Prof NGUYEN HOAI SON Supervisor 2: Assoc Prof LE ANH THANG PhD thesis is protected in front of EXAMINATION COMMITTEE FOR PROTECTION OF DOCTORAL THESIS HCM CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION Date……month……year…… Originality Statement I, Lam Phat Thuan, hereby assure that this thesis is my own work The data and results stated in this thesis are honest and have not been published by any works Ho Chi Minh City, May 2021 Lam Phat Thuan Acknowledgements This thesis has been carried out in the Faculty of Civil Engineering, HCM City University of Technology and Education, Viet Nam The process of conducting this thesis brings excitement but has quite a few challenges and difficulties And I can say without hesitation that it has been finished thanks to the encouragement, support and help of my professors and colleagues First of all, I would like to express my deepest gratitude to Assoc Prof Dr Nguyen Hoai Son and Assoc Prof Le Anh Thang, especially Assoc Prof Dr Nguyen Hoai Son from GACES Group, Ho Chi Minh City University of Technology and Education, Vietnam for having accepted me as their PhD student and for the enthusiastic guidance and mobilization during my research Secondly, I would like also to acknowledge Msc Ho Huu Vinh for his troubleshooting and the cooperation in my study Furthermore, I am grateful to Faculty of Civil Engineering for their great support to help me have good environment to my research Thirdly, I take this chance to thank all my nice colleagues at the Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, for their professional advice and friendly support Finally, this thesis is dedicated to my parents who have always given me valuable encouragement and assistance Lam Phat Thuan i Abstract Almost all design problems in engineering can be considered as optimization problems and thus require optimization techniques to solve During the past few decades, many optimization techniques have been proposed and applied to solve a wide range of various optimization problems Among them, meta-heuristic algorithms have gained huge popularity in recent years in solving design optimization problems of many types of structure with different materials These meta-heuristic algorithms include genetic algorithms (GA), particle swarm optimization (PSO), bat algorithm (BA), cuckoo search (CS), differential evolution (DE), firefly algorithm (DA), harmony search (HS), flower pollination algorithm (FPA), ant colony optimization (ACO), bee algorithms (BA), Jaya algorithm and many others Among the methods mentioned above, the Differential Evolution is one of the most widely used methods Since it was first introduced in 1997 by Storn and Price, many studies have been carried out to improve and apply DE in solving structural optimization problems The DE has demonstrated excellently performance in solving many different engineering problems Besides the Differential Evolution algorithm, the Jaya algorithm recently proposed by Rao in 2016 is also an effective and efficient methods that has been widely applied to solve many optimization problems and showed its good performance It gains dominate results when being tested with benchmark test functions in comparison with other meta-heuristic methods However, like many other population-based optimization algorithms, one of the disadvantages of DE and Jaya is that the computational time obtaining optimal solutions is much slower than the gradient-based optimization methods This is because DE and Jaya takes a lot of time evaluating the fitness of individuals in the population To overcome this disadvantage, Artificial Neuron Networks (ANN) are studied to combine with the meta-heuristic algorithms, such as Differential Evolution, to form a new approach which has the ability to solve the design optimization effectively Moreover, one of the most important issues in engineering design is that the optimal designs are often effected by uncertainties which can be occurred from various sources, such as ii manufacturing processes, material properties and operating environments These uncertainties may cause structures to improper performance as in the original design, and hence may result in risks to structures Therefore, reliability-based design optimization (RBDO) can be considered as an important and comprehensive strategy for finding an optimal design In this thesis, an improved version of Differential Evolution has been first time utilized to solve for optimal fiber angle and thickness of the stiffened composite Secondly, the Artificial Neural Network is integrated to the optimization process of the improved Differential Evolution algorithm to form a new algorithm call ABDE (ANN-based Differential Evolution) algorithm This new algorithm is then applied to solve optimization problems of the stiffened composite plate structures Thirdly, an elitist selection technique is utilized to modify the selection step of the original Jaya algorithm to improve the convergence of the algorithm and formed a new version of the original Jaya called iJaya algorithm The improved Jaya algorithm is then applied to solve for optimization problem of the Timoshenko composite beam and obtained very good results Finally, the so-called called (SLMD-iJaya) algorithm which is the combination of the improved Jaya algorithm and the Global Single-Loop Deterministic Methods (SLDM) has been proposed as a new tool set for solving the Reliability-Based Design Optimization problems This new method is applied to look for optimal design of Timoshenko composite beam structures with certain level of reliability iii Contents Originality Statement i Acknowledgements i Abstract ii Contents iv Nomenclature vii List of Tables xii List of Figures xiii Chapter 1: LITERATURE REVIEW .1 1.1 An overview on research direction of the thesis .1 1.2 Motivation of the research 1.3 Goals of the thesis 1.4 Research scope of the thesis 1.5 Outline 1.6 Contributions of the thesis Chapter 2: FUNDAMENTAL THEORY OF COMPOSITE STRUCTURE IN DESIGN AND OPTIMIZATION 10 2.1 Introduction to Composite Materials 10 2.1.1 Basic concepts and applications of Composite Materials .10 2.1.2 Overview of Composite Material in Design and Optimization 16 2.2 Analysis of Timoshenko composite beam 18 2.2.1 Exact analytical displacement and stress 18 2.2.2 Boundary-condition types .22 2.3 Analysis of stiffened composite plate .23 Chapter 3: RELIABILITY-BASED OPTIMIZATION METHODS WITH IJAYA AND IMPROVED DIFFERENTIAL EVOLUTION .29 3.1 Overview of Metaheuristic Optimization 29 3.1.1 Meta-heuristic Algorithm in Modeling .30 3.1.2 Meta-heuristic Algorithm in Optimization 33 iv 3.2 Solving Optimization problems using improved Differential Evolution 43 3.2.1 Brief on the Differential Evolution algorithm [12], [128] .43 3.2.2 The modified algorithm Roulette-Wheel-Elitist Differential Evolution 44 3.3 Solving Optimization problems using improved Jaya algorithm 45 3.3.1 Jaya Algorithm 45 3.2.2 Improvement version of Jaya algorithm 47 3.4 Reliability-based design optimization using a global single loop deterministic method .48 3.4.1 Reliability-based optimization problem formulation 50 3.4.2 A global single-loop deterministic approach 51 Chapter 4: FUNDAMENTAL THEORY OF NEURAL NETWORK 55 4.1 Fundamental theory of Neural Network 55 4.1.1 Basic concepts on Neural Networks [145] 57 4.1.2 Neural Network Structure 58 4.1.3 Neural Network Design Steps 62 4.1.4 Levenberg-Marquardt training algorithm .63 4.1.5 Over fitting, Over training 65 4.2 Artificial Neural Network based meta-heuristic optimization methods 67 Chapter 5: DEVELOPMENTS OF META-HEURISTIC OPTIMIZATION METHODS 70 5.1 Verification of iDE algorithm 70 5.1.1 A 10-bars planar truss structure: 70 5.1.2 A 200-bars truss structure Error! Bookmark not defined 5.1.3 A 72-bar space truss structure 74 5.1.4 A 120-bar space truss structure: .77 5.2 Static analysis of the stiffened composite plate .79 v 5.3 The effective of the improved Differential Evolution algorithm 81 5.4 Optimization of stiffened composite plate .82 5.4.1 Thickness optimization of stiffened Composite plate 82 5.4.2 Artificial neural network-based optimization of stiffened composite plate 84 5.5 Deterministic optimization of composite beam .87 5.5.1 Optimal design with variables: b and h 89 5.5.2 Optimal design with variables: b and ti 92 5.6 Reliability-based optimization design of Timoshenko composite beam 95 5.6.1 Verification of SLDM-iJaya .96 5.6.2 Reliability-based lightweight design 97 Chapter 6: CONCLUSIONS AND RECOMMENDATIONS 102 6.1 Conclusions and Remarks 102 6.2 Recommendations and future works .106 REFERENCES 107 List of Publications 122 vi [44] M H Sadr and H G Bargh, “Optimization of laminated composite plates for maximum fundamental 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Computational Mechanics 2017 pp 229-242 (Part of the Lecture Notes in Mechanical Engineering book series (LNME)) Link: https://link.springer.com/chapter/10.1007/978-981-10-7149-2_16 Q Nguyen, S Nguyen-Hoai, T Chuong-Thiet, T Lam-Phat Optimization of the Longitudinal Cooling Fin by Levenberg–Marquardt Method Proceedings of the International Conference on Advances in Computational Mechanics 2017 pp 217227 (Part of the Lecture Notes in Mechanical Engineering book series (LNME)) Link: https://link.springer.com/chapter/10.1007/978-981-10-7149-2_15 National Journal Lam Phat Thuan, Nguyen Nhat Phi Long, Nguyen Hoai Son, Ho Huu Vinh, Le Anh Thang Global Optimization of Laminzation Composite Beams Using An Improved Differential Evolution Algorithm Journal of Science and Technology in Civil Engineering NUCE 2020 14 (1): 54–64 International Conference 122 Thuan Lam-Phat, Son Nguyen-Hoai, Vinh Ho-Huu, Trung Nguyen-Thoi Optimization of stiffened composite plate using adjusted different evolution algorithm Proceeding of the international conference on computational methods (Vol.3, 2016), Berkeley, CA, USA National Conference Thuan Lam-Phat, Son Nguyen-Hoai, Vinh Ho-Huu, Trung Nguyen-Thoi Optimization analysis of stiffened composite plate by adjusted different evolution Hội nghị Khoa học – Cơng nghệ tồn quốc khí 2015 Lâm Phát Thuận, Nguyễn Hồi Sơn, Lê Anh Thắng, Hồ Hữu Vịnh Tối ưu hóa góc hướng sợi Composite gia cường dùng thuật toán Differential Evolution kết hợp mạng thần kinh nhân tạo Hội nghị học toan quốc lần thứ X, 8-9/12/2017) Other papers T Nguyen-Thoi, T Rabczuk, T Lam-Phat, V Ho-Huu, P Phung-Van (2014) Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3) Theoretical and Applied Fracture Mechanics Vol.72, 150-163 Link: https://www.sciencedirect.com/science/article/pii/S016784421400041X Nguyen-Thoi, T., Ho-Huu, V., Dang-Trung, H., Bui-Xuan, T., Lam-Phat, T (2013) Optimization analysis of stiffened composite plate by sequential quadratic programming Journal of Science and Technology, Vol 51(4B), p 156-165 10 Nguyen Thoi Trung, Bui Xuan Thang, Ho Huu Vinh, Lam Phat Thuan, Ngo Thanh Phong An Effective Algorithm For Reliability-Based Optimization Of Stiffened 123 Mindlin Plate Vietnam Journal of Mechanics, VAST, Vol 35, No (2013), pp 335 – 346 124 ... algorithms and meta- heuristic optimization methods to tackle such nonlinear optimization problems Meta- heuristic algorithms have gained huge popularity in recent years These meta- heuristic algorithms... ENGINEERING MECHANICS Ho Chi Minh City, 05/2021 THE WORK IS COMPLETED AT HCM CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION LAM PHAT THUAN DEVELOPMENT OF META- HEURISTIC OPTIMIZATION METHODS FOR MECHANICS PROBLEMS. ..MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION LAM PHAT THUAN DEVELOPMENT OF META- HEURISTIC OPTIMIZATION METHODS FOR MECHANICS PROBLEMS PHD THESIS