A customized bilevel optimization approach for solving large-scale truss design problems

References

• Achtziger, W., and M. Stolpe. 2007. “Truss Topology Optimization with Discrete Design Variables—Guaranteed Global Optimality and Benchmark Examples.” Structural and Multidisciplinary Optimization 34 (1): 1–20.
   Web of Science ®Google Scholar
• Ahrari, A., and A. A. Atai. 2013. “Fully Stressed Design Evolution Strategy for Shape and Size Optimization of Truss Structures.” Computers & Structures 123: 58–67.
   Web of Science ®Google Scholar
• Ahrari, A., and K. Deb. 2016. “An Improved Fully Stressed Design Evolution Strategy for Layout Optimization of Truss Structures.” Computers & Structures 164: 127–144.
   Web of Science ®Google Scholar
• Ahrari, A., A. A. Atai, and K. Deb. 2015. “Simultaneous Topology, Shape and Size Optimization of Truss Structures by Fully Stressed Design Based on Evolution Strategy.” Engineering Optimization 47 (8): 1063–1084.
   Web of Science ®Google Scholar
• AISC (American Institute of Steel Construction) Manual Committee. 1989. Manual of Steel Construction: Allowable Stress Design. 9th ed. Chicago, IL: American Institute of Steel Construction.
   Google Scholar
• Alimoradi, A., C. M. Foley, and S. Pezeshk. 2010. “Benchmark Problems in Structural Design and Performance Optimization: Past, Present, and Future-Part I.” State of the Art and Future Challenges in Structure. ASCE Publication.
   Google Scholar
• Allison, J. T., and D. R. Herber. 2014. “Special Section on Multidisciplinary Design Optimization: Multidisciplinary Design Optimization of Dynamic Engineering Systems.” AIAA Journal 52 (4): 691–710.
   Web of Science ®Google Scholar
• Bartz-Beielstein, T., M. Preuss, K. Schmitt, and H. P. Schwefel. 2010. Challenges for Contemporary Evolutionary Algorithms. Dortmund: Techn. Univ., Fak. für Informatik.
   Google Scholar
• Bendsøe, M. P., A. Ben-Tal, and J. Zowe. 1994. “Optimization Methods for Truss Geometry and Topology Design.” Structural Optimization 7 (3): 141–159.
   Web of Science ®Google Scholar
• Bendsøe, M. P., and N. Kikuchi. 1988. “Generating Optimal Topologies in Structural Design Using a Homogenization Method.” Computer Methods in Applied Mechanics and Engineering 71(2): 197–224.
   Web of Science ®Google Scholar
• Beyer, H. G., and B. Sendhoff. 2008. “Covariance Matrix Adaptation Revisited—The CMSA Evolution Strategy.” In Parallel Problem Solving from Nature–PPSN X. Berlin: Springer.
   Google Scholar
• Burns, S. A. (Ed.). 2002. Recent Advances in Optimal Structural Design (chapter 5). Reston, VA: ASCE Publications.
   Google Scholar
• Cao, H., X. Qian, Z. Chen, and H. Zhu. 2017. “Enhanced Particle Swarm Optimization for Size and Shape Optimization of Truss Structures.” Engineering Optimization 49 (11): 1939–1956.
   Web of Science ®Google Scholar
• Cheng, M. Y., D. Prayogo, Y. W. Wu, and M. M. Lukito. 2016. “A Hybrid Harmony Search Algorithm for Discrete Sizing Optimization of Truss Structure.” Automation in Construction 69: 21–33.
   Web of Science ®Google Scholar
• Deb, K., and S. Gulati. 2001. “Design of Truss-Structures for Minimum Weight Using Genetic Algorithms.” Finite Elements in Analysis and Design 37 (5): 447–465.
   Web of Science ®Google Scholar
• Deb, K., and C. Myburgh. 2017. “A Population-based Fast Algorithm for a Billion-dimensional Resource Allocation Problem with Integer Variables.” European Journal of Operational Research 261 (2): 460–474.
   Google Scholar
• Degertekin, S. O., L. Lamberti, and I. B. Ugur. 2019. “Discrete Sizing/Layout/Topology Optimization of Truss Structures with an Advanced Jaya Algorithm.” Applied Soft Computing 79: 363–390.
   Web of Science ®Google Scholar
• Feury, C. 1980. “An Efficient Optimality Criteria Approach to The Minimum Weight Design of Elastic Structures.” Computers & Structures 11 (3): 163–173.
   Web of Science ®Google Scholar
• Feury, C., and M. Geradin. 1978. “Optimality Criteria and Mathematical Programming in Structural Weight Optimization.” Computers & Structures 8 (1): 7–17.
   Web of Science ®Google Scholar
• Gholizadeh, S. 2013. “Layout Optimization of Truss Structures by Hybridizing Cellular Automata and Particle Swarm Optimization.” Computers & Structures 125: 86–99.
   Web of Science ®Google Scholar
• Hansen, N., A. Auger, S. Finck, and R. Ros. 2010. Real-Parameter Black-Box Optimization Benchmarking 2010: Experimental Setup. RR-7215. Rocquencourt: INRIA.
   Google Scholar
• Hansen, N., and A. Ostermeier. 2001. “Completely Derandomized Self-Adaptation in Evolution Strategies.” Evolutionary Computation 9 (2): 159–195.
   PubMed Web of Science ®Google Scholar
• Hasançebi, O. 2007. “Optimization of Truss Bridges Within a Specified Design Domain Using Evolution Strategies.” Engineering Optimization 39 (6): 737–756.
   Web of Science ®Google Scholar
• Hasançebi, O., and S. K. Azad. 2014. “Discrete Size Optimization of Steel Trusses Using a Refined Big Bang–Big Crunch Algorithm.” Engineering Optimization 46 (1): 61–83.
   Web of Science ®Google Scholar
• Hasançebi, O., and S. K. Azad. 2015. “Adaptive Dimensional Search: A New Metaheuristic Algorithm for Discrete Truss Sizing Optimization.” Computers & Structures 154: 1–16.
   Web of Science ®Google Scholar
• Hasançebi, O., S. D. Çarbaş, F. Erdal, and M. P. Saka. 2009. “Performance Evaluation of Metaheuristic Search Techniques in the Optimum Design of Real Size Pin Jointed Structures.” Computers & Structures 87 (5): 284–302.
   Web of Science ®Google Scholar
• Hasançebi, O., and F. Erbatur. 2002. “Layout Optimisation of Trusses Using Simulated Annealing.” Advances in Engineering Software 33 (7): 681–696.
   Web of Science ®Google Scholar
• Herber, D. R., and J. T. Allison. 2019a. “Nested and Simultaneous Solution Strategies for General Combined Plant and Control Design Problems.” Journal of Mechanical Design 141 (1): 011402.
   Web of Science ®Google Scholar
• Herber, D. R., and J. T. Allison. 2019b. “A Problem Class with Combined Architecture, Plant, and Control Design Applied to Vehicle Suspensions.” Journal of Mechanical Design 141 (10): 101401.
   Web of Science ®Google Scholar
• Kaveh, A., and M. I. Ghazaan. 2016. “Optimum Design of Large-Scale Truss Towers Using Cascade Optimization.” Acta Mechanica 227 (9): 2645–2656.
   Web of Science ®Google Scholar
• Kaveh, A., and M. I. Ghazaan. 2018a. “A New Hybrid Meta-heuristic Algorithm for Optimal Design of Large-Scale Dome Structures.” Engineering Optimization 50 (2): 235–252.
   Web of Science ®Google Scholar
• Kaveh, A., and M. I. Ghazaan. 2018b. Meta-Heuristic Algorithms for Optimal Design of Real-Size Structures. Cham: Springer International Publishing.
   Google Scholar
• Kaveh, A., and S. M. Javadi. 2019. “Chaos-Based Firefly Algorithms for Optimization of Cyclically Large-Size Braced Steel Domes with Multiple Frequency Constraints.” Computers & Structures 214: 28–39.
   Web of Science ®Google Scholar
• Kaveh, A., and V. R. Mahdavi. 2014. “Colliding Bodies Optimization Method for Optimum Discrete Design of Truss Structures.” Computers & Structures 139: 43–53.
   Web of Science ®Google Scholar
• Kaveh, A., B. Mirzaei, and A. Jafarvand. 2015. “An Improved Magnetic Charged System Search for Optimization of Truss Structures with Continuous and Discrete Variables.” Applied Soft Computing 28: 400–410.
   Web of Science ®Google Scholar
• Kaveh, A., and S. Talatahari. 2011. “Optimization of Large-Scale Truss Structures Using Modified Charged System Search.” International Journal of Optimization in Civil Engineering 1 (1): 15–28.
   Google Scholar
• Kicinger, R., T. Arciszewski, and K. De Jong. 2005. “Evolutionary Computation and Structural Design: A Survey of the State-of-the-Art.” Computers & Structures 83 (23): 1943–1978.
   Web of Science ®Google Scholar
• King, W. S., S. M. Wu, and L. Duan. 2013. “Laboratory Load Tests and Analysis of Bailey Bridge Segments.” Journal of Bridge Engineering 18 (10): 957–968.
   Web of Science ®Google Scholar
• Lamberti, L., and C. Pappalettere. 2011. “Metaheuristic Design Optimization of Skeletal Structures: A Review.” Computational Technology Reviews 4 (1): 1–32.
   Google Scholar
• Lee, K. S., Z. W. Geem, S. H. Lee, and K. W. Bae. 2005. “The Harmony Search Heuristic Algorithm for Discrete Structural Optimization.” Engineering Optimization 37 (7): 663–684.
   Web of Science ®Google Scholar
• Liang, J. J., B. Y. Qu, P. N. Suganthan, and Q. Chen. 2014. Problem Definitions and Evaluation Criteria for the CEC 2015 Competition on Learning-Based Real-Parameter Single Objective Optimization. Technical Report 201411A, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report. Singapore: Nanyang Technological University.
   Google Scholar
• Lu, Z., I. Whalen, V. Boddeti, Y. Dhebar, K. Deb, E. D. Goodman, and W. Banzhaf. 2019. “NSGA-Net: Neural Architecture Search Using Multi-objective Genetic Algorithm.” In Proceedings of Genetic and Evolutionary Computation Conference (GECCO-2019), 419–427. New York, NY: ACM.
   Google Scholar
• Luh, G. C., and C. Y. Lin. 2008. “Optimal Design of Truss Structures Using Ant Algorithm.” Structural and Multidisciplinary Optimization 36 (4): 365–379.
   Web of Science ®Google Scholar
• Luh, G. C., and C. Y. Lin. 2011. “Optimal Design of Truss-Structures Using Particle Swarm Optimization.” Computers & Structures 89 (23–24): 2221–2232.
   Web of Science ®Google Scholar
• Martini, K. 2017. “Rational and Irregular: Questioning Traditional Concepts of Efficiency and Esthetics in Structural Design.” Journal of Structural Engineering 143 (6): 02517001. doi:10.1061/(ASCE)ST.1943-541X.0001748.
   Web of Science ®Google Scholar
• Miguel, L. F., R. H. Lopez, and L. F. Miguel. 2013. “Multimodal Size, Shape, and Topology Optimisation of Truss Structures Using the Firefly Algorithm.” Advances in Engineering Software 56: 23–37.
   Web of Science ®Google Scholar
• Mueller, K., M. Gustafson, and J. Ericksen. 2012. “A Practicing Engineer’s View of Benchmark Problems in Structural Optimization.” In Proceeding of 20th Analysis and Computation Specialty Conference, 288–299. Chicago, IL: ASCE.
   Google Scholar
• Mueller, C., and J. Ochsendorf. 2013. “From Analysis to Design: A New Computational Strategy for Structural Creativity.” In Proceeding of the Second International Workshop on Design in Civil and Environmental Engineering, edited by Mary Kathryn Thompson, 46–56. Worcester, MA: DCEE.
   Google Scholar
• Myburgh, C. and Deb, K. 2017. “Use of Derived Heuristics in Improved Performance of Evolutionary Optimization for Real-World Applications.” Proceedings of Congress on Evolutionary Computation (CEC-2017) Conference, 830–837. New York: ACM.
   Google Scholar
• Panagant, N., and S. Bureerat. 2018. “Truss Topology, Shape and Sizing Optimization by Fully Stressed Design Based on Hybrid Grey Wolf Optimization and Adaptive Differential Evolution.” Engineering Optimization 50 (10): 1645–1661.
   Web of Science ®Google Scholar
• Rahami, H., A. Kaveh, and Y. Gholipour. 2008. “Sizing, Geometry and Topology Optimization of Trusses via Force Method and Genetic Algorithm.” Engineering Structures 30 (9): 2360–2369.
   Web of Science ®Google Scholar
• Rasmussen, M. H., and M. Stolpe. 2008. “Global Optimization of Discrete Truss Topology Design Problems Using a Parallel Cut-and-Branch Method.” Computers & Structures 86 (13): 1527–1538.
   Web of Science ®Google Scholar
• Razani, R. 1965. “Behavior of Fully Stressed Design of Structures and its Relationshipto Minimum-Weight Design.” AIAA Journal 3 (12): 2262–2268.
   Web of Science ®Google Scholar
• Rojas Labanda, S., M. Stolpe, and O. Sigmund. 2015. “Mathematical Programming Methods for Large-Scale Topology Optimization Problems.” PhD Thesis. DTU Wind Energy, Denmark.
   Google Scholar
• Ros, R., and N. Hansen. 2008. “A Simple Modification in CMA-ES Achieving Linear Time and Space Complexity.” In Parallel Problem Solving from Nature–PPSN X, 296–305. Berlin: Springer.
   Google Scholar
• Rozvany, G. I., M. Zhou, and T. Birker. 1992. “Generalized Shape Optimization Without Homogenization.” Structural Optimization 4 (3–4): 250–252.
   Web of Science ®Google Scholar
• Sadollah, A., H. Eskandar, A. Bahreininejad, and J. H. Kim. 2015. “Water Cycle, Mine Blast and Improved Mine Blast Algorithms for Discrete Sizing Optimization of Truss Structures.” Computers & Structures 149: 1–16.
   Web of Science ®Google Scholar
• Saka, M. P. 1990. “Optimum Design of Pin-Jointed Steel Structures with Practical Applications.” Journal of Structural Engineering 116 (10): 2599–2620.
   Web of Science ®Google Scholar
• Schevenels, M., S. McGinn, A. Rolvink, and J. Coenders. 2014. “An Optimality Criteria Based Method for Discrete Design Optimization Taking Into Account Buildability Constraints.” Structural and Multidisciplinary Optimization 50 (5): 755–774.
   Web of Science ®Google Scholar
• Shrestha, S. M., and J. Ghaboussi. 1998. “Evolution of Optimum Structural Shapes Using Genetic Algorithm.” Journal of Structural Engineering 124 (11): 1331–1338.
   Web of Science ®Google Scholar
• Sigmund, O. 2011. “On the Usefulness of Non-gradient Approaches in Topology Optimization.” Structural and Multidisciplinary Optimization 43 (5): 589–596.
   Web of Science ®Google Scholar
• Sinha, A., P. Malo, and K. Deb. 2018. “A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications.” IEEE Transactions on Evolutionary Computation 22 (2): 276–295.
   Web of Science ®Google Scholar
• Souza, R. R., L. F. Miguel, A. J. Torii, and L. F. Miguel. 2016. “A Backtracking Search Algorithm for the Simultaneous Size, Shape and Topology Optimization of Trusses.” Latin American Journal of Solids and Structures 13 (15): 2922–2951.
   Web of Science ®Google Scholar
• Stolpe, M. 2016. “Truss Optimization with Discrete Design Variables: A Critical Review.” Structural and Multidisciplinary Optimization 53: 349–374.
   Web of Science ®Google Scholar
• Tang, W., L. Tong, and Y. Gu. 2005. “Improved Genetic Algorithm for Design Optimization of Truss Structures with Sizing, Shape and Topology Variables.” International Journal for Numerical Methods in Engineering 62 (13): 1737–1762.
   Web of Science ®Google Scholar
• Tejani, G. G., V. J. Savsani, V. K. Patel, and P. V. Savsani. 2018. “Size, Shape, and Topology Optimization of Planar and Space Trusses Using Mutation-Based Improved Metaheuristics.” Journal of Computational Design and Engineering 5 (2): 198–214.
   Web of Science ®Google Scholar
• Topping, B. H. V. 1983. “Shape Optimization of Skeletal Structures: A Review.” Journal of Structural Engineering 109 (8): 1933–1951.
   Web of Science ®Google Scholar
• Van Mellaert, R., G. Lombaert, and M. Schevenels. 2016. “Global Size Optimization of Statically Determinate Trusses Considering Displacement, Member, and Joint Constraints.” Journal of Structural Engineering 142 (2): 04015120.
   Web of Science ®Google Scholar
• Wang, Q., and J. S. Arora. 2007. “Optimization of Large-Scale Truss Structures Using Sparse SAND Formulations.” International Journal for Numerical Methods in Engineering 69 (2): 390–407.
   Web of Science ®Google Scholar
• Wu, S. J., and P. T. Chow. 1995. “Steady-State Genetic Algorithms for Discrete Optimization of Trusses.” Computers & Structures 56 (6): 979–991.
   Web of Science ®Google Scholar
• Wu, C. Y., and K. Y. Tseng. 2010. “Truss Structure Optimization Using Adaptive Multi-population Differential Evolution.” Structural and Multidisciplinary Optimization 42 (4): 575–590.
   Web of Science ®Google Scholar
• Xie, Y. M., and G. P. Steven. 1993. “A Simple Evolutionary Procedure for Structural Optimization.” Computers & Structures 49 (5): 885–896.
   Web of Science ®Google Scholar