A new second-order approximation method for optimum design of structures

References

• Adeli, H., and N. T. Cheng. 1994. “Concurrent Genetic Algorithms for Optimization of Large Structures.” Journal of Aerospace Engineering 7 (3): 276–296. doi:10.1061/(ASCE)0893-1321(1994)7:3(276).
   Web of Science ®Google Scholar
• Adeli, H., and O. Kamal. 1986. “Efficient Optimization of Space Trusses.” Computers and Structures 24 (3): 501–511. Pergamon. doi: 10.1016/0045-7949(86)90327-5.
   Web of Science ®Google Scholar
• Akin, A., and M. P. Saka. 2015. “Harmony Search Algorithm Based Optimum Detailed Design of Reinforced Concrete Plane Frames Subject to ACI 318-05 Provisions.” Computers and Structures 147: 79–95.
   Google Scholar
• Arora, J. S. 1989. Introduction to Optimum Design. New York: McGraw-Hill.
   Google Scholar
• Arora, J. S., and E. J. Haug. 1976. “Efficient Optimal Design of Structures by Generalized Steepest Descent Programming.” International Journal for Numerical Methods in Engineering 10 (4): 747–766. doi:10.1002/nme.1620100404.
   Web of Science ®Google Scholar
• Barthelemy, J.-F. M., and R. T. Haftka. 1993. “Approximation Concepts for Optimum Structural Design — A Review.” Structural Optimization 5 (3): 129–144. Springer-Verlag. doi: 10.1007/BF01743349.
   Google Scholar
• Bekdas, G., and S. M. Nigdeli. 2016. “Bat Algorithm for Optimization of Reinforced Concrete Columns.” PAMM 16 (1): 681–682. doi:10.1002/pamm.201610329.
   Google Scholar
• Belegundu, A. D., and J. S. Arora. 1985. “A Study of Mathematical Programmingmethods for Structural Optimization. Part II: Numerical Results.” International Journal for Numerical Methods in Engineering 21 (9): 1601–1623. Wiley-Blackwell. doi: 10.1002/nme.1620210905.
   Web of Science ®Google Scholar
• Camp, C. V. 2007. “Design of Space Trusses Using Big Bang–Big Crunch Optimization.” Journal of Structural Engineering 133 (7): 999–1008. doi:10.1061/(ASCE)0733-9445(2007)133:7(999).
   Web of Science ®Google Scholar
• Camp, C. V., and B. J. Bichon. 2004. “Design of Space Trusses Using Ant Colony Optimization.” Journal of Structural Engineering 130 (5): 741–751. doi:10.1061/(ASCE)0733-9445(2004)130:5(741).
   Web of Science ®Google Scholar
• Camp, C. V., B. J. Bichon, and S. P. Stovall. 2005. “Design of Steel Frames Using Ant Colony Optimization.” Journal of Structural Engineering 131 (3): 369–379. doi:10.1061/(ASCE)0733-9445(2005)131:3(369).
   Web of Science ®Google Scholar
• Chao, N. H., S. J. Fenves, and A. W. Westerberg. 1981. Application of Reduced Quadratic Programming Technique to Optimal Structural Design. Defense Technical Information Center: ADP000067. Defense Technical Information Center: ADP000067. http://www.dtic.mil/docs/citations/ADP000067
   Google Scholar
• Chung, T. T., Q. H. Jiang, and J. R. Zhu. 2013. “Enhanced Two-Point Exponential Approximation for Structural Optimization.” Applied Mechanics and Materials 397–400: 1021–1024. (September). Trans Tech Publications. doi:10.4028/www.scientific.net/AMM.397-400.1021.
   Google Scholar
• Dantzig, G. 1947. Simplex Algorithm for Linear Programming. NJ, Princeton University Press: Princeton.
   Google Scholar
• Degertekin, S. O. 2008. “Optimum Design of Steel Frames Using Harmony Search Algorithm.” Structural and Multidisciplinary Optimization 36 (4): 393–401. Springer-Verlag. doi: 10.1007/s00158-007-0177-4.
   Web of Science ®Google Scholar
• Degertekin, S. O. 2012. “Improved Harmony Search Algorithms for Sizing Optimization of Truss Structures.” Computers & Structures 92–93 (February). Pergamon: 229–241. doi:1016/J.COMPSTRUC.2011.10.022.
   Google Scholar
• Degertekin, S. O., and M. S. Hayalioglu. 2013. “Sizing Truss Structures Using Teaching-Learning-Based Optimization.” Computers & Structures 119: 177–188. (April). Pergamon. doi:10.1016/J.COMPSTRUC.2012.12.011.
   Web of Science ®Google Scholar
• Degertekin, S. O., L. Lamberti, and M. S. Hayalioglu. 2017. “Heat Transfer Search Algorithm for Sizing Optimization of Truss Structures.” Latin American Journal of Solids and Structures 14 (3): 373–397. doi:10.1590/1679-78253297.
   Web of Science ®Google Scholar
• Degertekin, S. O., M. P. Saka, and M. S. Hayalioglu. 2008. “Optimal Load and Resistance Factor Design of Geometrically Nonlinear Steel Space Frames via Tabu Search and Genetic Algorithm.” Engineering Structures 30 (1): 197–205. doi:10.1016/J.ENGSTRUCT.2007.03.014.
   Web of Science ®Google Scholar
• Dorigo, M., V. Maniezzo, and A. Colorni. 1992. “An Investigation of Some Properties of an Ant Algorithm.” In Proceeding of the Parallel Problem Solving from Nature Conference (PPSN 92), 509–520. Brussels, Belgium: Elsevier.
   Google Scholar
• Erbatur, F., O. Hasancebi, I. Tutuncil, and H. Kilci. 2000. “Optimal Design of Planar and Space Structures with Genetic Algorithms.” Computers and Structures 75 (2): 209–224. doi:10.1016/S0045-7949(99)00084-X.
   Google Scholar
• Fadel, G. M., M. F. Riley, and J. M. Barthelemy. 1990. “Two Point Exponential Approximation Method for Structural Optimization.” Structural Optimization 2 (2): 117–124. doi:10.1007/BF01745459.
   Google Scholar
• Farshi, B., and A. Alinia-ziazi. 2010. “Sizing Optimization of Truss Structures by Method of Centers and Force Formulation.” International Journal of Solids and Structures 47 (18–19): 2508–2524. Pergamon: . 10.1016/J.IJSOLS TR.2010.05.009. .
   Web of Science ®Google Scholar
• Feng, D. U., Q.-Y. Dong, and L. Hong-Shuang. 2017. “Truss Structure Optimization with Subset Simulation and Augmented Lagrangian Multiplier Method.” Algorithms 10 (4): 128. doi:10.3390/a10040128.
   Web of Science ®Google Scholar
• Fleury, C. 1988. “A Convex Linearization Method Using Second-Order Information.” Proceedings of Fourth SAS-World Conference 2: 374–383.
   Google Scholar
• Fleury, C. 1989a. “First and Second Order Convex Approximation Strategies in Structural Optimization.” Structural Optimization 1 (1): 3–10. Springer-Verlag. doi: 10.1007/BF01743804.
   Google Scholar
• Fleury, C. 1989b. “CONLIN: An Efficient Dual Optimizer Based on Convex Approximation Concepts.” Structural Optimization 1 (2): 81–89. doi:10.1007/BF01637664.
   Google Scholar
• Fleury, C. 1989c. “Efficient Approximation Concepts Using Second Order Information.” International Journal for Numerical Methods in Engineering 28 (9): 2041–2058. doi:10.1002/nme.1620280905.
   Web of Science ®Google Scholar
• Fleury, C., and V. Braibant. 1986. “Structural Optimization: A New Dual Method Using Mixed Variables.” International Journal for Numerical Methods in Engineering 23 (3): 409–428. doi:10.1002/nme.1620230307.
   Web of Science ®Google Scholar
• Gandomi, A. H., X. S. Yang, and A. H. Alavi. 2013. “Cuckoo Search Algorithm: A Metaheuristic Approach to Solve Structural Optimization Problems.” Engineering with Computers 29 (1): 17–35. doi:10.1007/s00366-011-0241-y.
   Web of Science ®Google Scholar
• Geem, Z. W., J. H. Kim, and G. V. Loganathan. 2001. “A New Heuristic Optimization Algorithm: Harmony Search.” Simulation 76 (2): 60–68. doi:10.1177/003754970107600201.
   Google Scholar
• Gholizadeh, S., and H. Poorhoseini. 2015. “Optimum Design of Steel Frame Structures by a Modified Dolphin Echolocation Algorithm.” Structural Engineering and Mechanics 55 (3): 535–554. Techno-Press. doi: 10.12989/sem.2015.55.3.535.
   Web of Science ®Google Scholar
• Grandhi, R. 1993. “Structural Optimization with Frequency Constraints – A Review.” AIAA Journal 31 (12): 2296–2303. doi:10.2514/3.11928.
   Web of Science ®Google Scholar
• Habibi, A. R. 2012. “New Approximation Method for Structural Optimization.” Journal of Computing in Civil Engineering 26 (2): 236–247. doi:10.1061/(ASCE)CP.1943-5487.0000133.
   Web of Science ®Google Scholar
• Haftka, R., and C. P. Shore. 1979. “Approximation Methods for Combined Thermal/structural Design.” NASA Technical Paper. https://ntrs.nasa.gov/search.jsp?R=19790017256
   Google Scholar
• Haftka, R. T., and Z. Gurdal. 1992. Elements of Structural Optimization. 3rd ed. Dordrecht: Kluwer: Solid Mechanics And Its Applications. doi:10.1007/978-94-011-2550-5.
   Google Scholar
• Harless, R. I. 1980. “A Method for Synthesis of Optimal Weight Structures.” Computers and Structures 12 (6): 791–804. Pergamon. doi: 10.1016/0045-7949(80)90016-4.
   Google Scholar
• Hasançebi, O. 2008. “Adaptive Evolution Strategies in Structural Optimization: Enhancing Their Computational Performance with Applications to Large-Scale Structures.” Computers and Structures 86 (1–2): 119–132. 10.1016/J.COMP STRUC.2007.05.012.
   Google Scholar
• Hasançebi, O., and F. Erbatur. 2002. “On Efficient Use of Simulated Annealing in Complex Structural Optimization Problems.” Acta Mechanica 157 (1–4): 27–50. Springer-Verlag. doi: 10.1007/BF01182153.
   Web of Science ®Google Scholar
• Holzleitner, L., and K. G. Mahmoud. 1999. “Structural Shape Optimization Using MSC/NASTRAN and Sequential Quadratic Programming.” Computers and Structures 70 (5): 487–514. doi:10.1016/S0045-7949(98)00179-5.
   Google Scholar
• Horowitz, B., and S. M. B. Afonso. 2002. “Quadratic Programming Solver for Structural Optimisation Using SQP Algorithm.” Advances in Engineering Software 33 (7–10): 669–674. Elsevier. doi: 10.1016/S0965-9978(02)00066-2.
   Web of Science ®Google Scholar
• Jalili, S., and Y. Hosseinzadeh. 2015. “A Cultural Algorithm for Optimal Design of Truss Structures.” Latin American Journal of Solids and Structures 12 (9): 1721–1747. Associação Brasileira de Ciências Mecânicas. doi: 10.1590/1679-78251547.
   Web of Science ®Google Scholar
• Jansen, P. W., and R. E. Perez. 2011. “Constrained Structural Design Optimization via a Parallel Augmented Lagrangian Particle Swarm Optimization Approach.” Computers & Structures 89 (13–14): 1352–1366. Pergamon Press, Inc.. doi: 10.1016/j.compstruc.2011.03.011.
   Web of Science ®Google Scholar
• Jawed, A. H., and A. J. Morris. 1984. “Approximate Higher-Order Sensitivities in Structural Design.” Engineering Optimization 7 (2): 121–142. 10.1080/03052158408960 634.
   Web of Science ®Google Scholar
• Jawed, A. H., and A. J. Morris. 1985. “Higher-Order Updates for Dynamic Responses in Structural Optimization.” Computer Methods in Applied Mechanics and Engineering 49 (2): 175–201. North-Holland. doi: 10.1016/0045-7825(85)90059-3.
   Web of Science ®Google Scholar
• Kaveh, A., and T. Bakhshpoori. 2013. “Optimum Design of Steel Frames Using Cuckoo Search Algorithm with Lévy Flights.” The Structural Design of Tall and Special Buildings 22 (13): 1023–1036. doi:10.1002/tal.754.
   Web of Science ®Google Scholar
• Kaveh, A., and T. Bakhshpoori. 2015. “Subspace Search Mechanism and Cuckoo Search Algorithm for Size Optimization of Space Trusses.” Steel and Composite Structures 18 (2): 289–303.
   Web of Science ®Google Scholar
• Kaveh, A., and T. Bakhshpoori. 2016. “A New Metaheuristic for Continuous Structural Optimization: Water Evaporation Optimization.” Structural and Multidisciplinary Optimization 54: 1. doi:10.1007/s00158-015-1396-8.
   Web of Science ®Google Scholar
• Kaveh, A., T. Bakhshpoori, and E. Afshari. 2014. “An Efficient Hybrid Particle Swarm and Swallow Swarm Optimization Algorithm.” Computers & Structures 143: 40–59. (September). Elsevier. doi:10.1016/j.compstruc.2014.07.012.
   Web of Science ®Google Scholar
• Kaveh, A., and M. Khayatazad. 2013. “Ray Optimization for Size and Shape Optimization of Truss Structures.” Computers & Structures 117: 82–94. (February). Pergamon. doi:10.1016/J.COMPSTRUC.2012.12.010.
   Web of Science ®Google Scholar
• Kaveh, A., and V. R. Mahdavi. 2014. “Colliding Bodies Optimization Method for Optimum Discrete Design of Truss Structures.” Computers and Structures 139: 43–53. doi:10.1016/j.compstruc.2014.04.006.
   Google Scholar
• Kaveh, A., and V. R. Mahdavi. 2015. “Colliding Bodies Optimization for Size and Topology Optimization of Truss Structures.” Structural Engineering and Mechanics 53 (5): 847–865. Techno-Press. doi: 10.12989/sem.2015.53.5.847.
   Web of Science ®Google Scholar
• Kaveh, A., and A. Nasrolahi. 2014. “A New Probabilistic Particle Swarm Optimization Algorithm for Size Optimization of Spatial Truss Structures.” International Journal of Civil Engineering 12 (1): 1–13.
   Google Scholar
• Khan, M. R., K. D. Willmert, and W. A. Thornton. 1979. “An Optimality Criterion Method for Large-Scale Structures.” AIAA Journal 17 (7): 753–761. doi:10.2514/3.61214.
   Web of Science ®Google Scholar
• Kicinger, R., T. Arciszewski, and K. D. Jong. 2005. “Evolutionary Computation and Structural Design: A Survey of the State-of-the-Art.” Computers and Structures 83 (23–24): 1943–1978.
   Google Scholar
• Kim, J. R., and D. H. Choi. 2008. “Enhanced Two-Point Diagonal Quadratic Approximation Methods for Design Optimization.” Computer Methods in Applied Mechanics and Engineering 197 (6–8): 846–856. North-Holland. doi: 10.1016/J.CMA.2007.09.014.
   Web of Science ®Google Scholar
• Kim, M. S., J. R. Kim, J. Y. Jeon, and D. H. Choi. 2001. “Efficient Mechanical System Optimization Using Two-Point Diagonal Quadratic Approximation in the Nonlinear Intervening Variable Space.” KSME International Journal 15 (9): 1257–1267.
   Google Scholar
• Lamberti, L. 2008. “An Efficient Simulated Annealing Algorithm for Design Optimization of Truss Structures.” Computers and Structures 86 (19–20): 1936–1953. doi:10.1016/j.compstruc.2008.02.004.
   Google Scholar
• Lamberti, L., and C. Pappalettere. 2000. “Comparison of the Numerical Efficiency of Different Sequential Linear Programming Based Algorithms for Structural Optimisation Problems.” Computers and Structures 76 (6): 713–728. doi:10.1016/S0045-7949(99)00185-6.
   Web of Science ®Google Scholar
• Lamberti, L., and C. Pappalettere. 2003. “Move Limits Definition in Structural Optimization with Sequential Linear Programming. Part II: Numerical Examples.” Computers and Structures 81 (4): 214–238.
   Google Scholar
• Lamberti, L., and C. Pappalettere. 2004. “Improved Sequential Linear Programming Formulation for Structural Weight Minimization.” Computer Methods in Applied Mechanics and Engineering 193 (33–35): 3493–3521. 10.1016/J. CMA.2003.12.040.
   Web of Science ®Google Scholar
• Lee, K. S., and Z. W. Geem. 2004. “A New Structural Optimization Method Based on the Harmony Search Algorithm.” Computers and Structures 82 (9–10): 781–798.
   Web of Science ®Google Scholar
• Li, L. J., Z. B. Huang, F. Liu, and Q. H. Wu. 2007. “A Heuristic Particle Swarm Optimizer for Optimization of Pin Connected Structures.” Computers and Structures 85 (7–8): 340–349. Pergamon Press, Inc.: . 10.1016/j.compstruc.2006.11.020. .
   Web of Science ®Google Scholar
• Mahmoud, K. G., H. W. Engl, and L. Holzleitner. 1994. “Optimum Structural Design Using MSC/NASTRAN and Sequential Quadratic Programming.” Computers and Structures 52 (3): 437–447. Pergamon. doi: 10.1016/0045-7949(94)90229-1.
   Google Scholar
• Miura, H., and L. A. Schmit. 1978. “Second Order Approximation of Natural Frequency Constraints in Structural Synthesis.” International Journal for Numerical Methods in Engineering 13 (2): 337–351. 10.1002/nme.1 620130209.
   Web of Science ®Google Scholar
• Mockus, J., R. Paulavičius, D. Rusakevičius, D. Šešok, and J. Žilinskas. 2017. “Application of Reduced-Set Pareto-Lipschitzian Optimization to Truss Optimization.” Journal of Global Optimization 67 (1–2): 425–450. Springer US. doi: 10.1007/s10898-015-0364-6.
   Web of Science ®Google Scholar
• Mortazavi, A., V. Togan, and A. Nuhoglu. 2017. “An Integrated Particle Swarm Optimizer for Optimization of Truss Structures with Discrete Variables.” Structural Engineering and Mechanics 61 (3): 359–370. Techno-Press. doi: 10.12989/sem.2017.61.3.359.
   Web of Science ®Google Scholar
• Perez, R. E., and K. Behdinan. 2007. “Particle Swarm Approach for Structural Design Optimization.” Computers & Structures 85 (19–20): 1579–1588. Pergamon. doi: 10.1016/J.COMPSTRUC.2006.10.013.
   Web of Science ®Google Scholar
• Rafiee, A., S. Talatahari, and A. Hadidi. 2013. “Optimum Design of Steel Frames with Semi-Rigid Connections Using Big Bang-Big Crunch Method.” Steel and Composite Structures 14 (5): 431–451.
   Web of Science ®Google Scholar
• Renwei, X., and L. Peng. 1987. “Structural Optimization Based on Second-Order Approximations of Functions and Dual Theory.” Computer Methods in Applied Mechanics and Engineering 65 (2): 101–114. North-Holland: . 10.10 16/0045–7825(87)90007–7. .
   Web of Science ®Google Scholar
• Rizzi, P. 1976. “Optimization of Multi-Constrained Structures Based on Optimality Criteria January.” https://ntrs.nasa. gov/search.jsp?R=19760047085
   Google Scholar
• Rosen, J. B., and S. Suzuki. 1965. “Construction of Nonlinear Programming Test Problems.” Commun. Assoc. Comput. Machina 8 (2): 113–125. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19650009341.pdf
   Web of Science ®Google Scholar
• Schmit, L. A. 1960. “Structural Design by Systematic Synthesis.” In Proceeding of the 2nd Conference on Electronic Computation, 105–122. Reston, VA: ASCE.
   Google Scholar
• Schmit, L. A. 1981. “Structural Synthesis – Its Genesis and Development.” AIAA Journal 19 (10): 1249–1263.
   Web of Science ®Google Scholar
• Schmit, L. A., and B. Farshi. 1974. “Some Approximation Concepts for Structural Synthesis.” AIAA Journal 12 (5): 692–699. Reston, Virigina. doi: 10.2514/3.49321.
   Web of Science ®Google Scholar
• Schmit, L. A., and C. Fleury. 1980. “Structural Synthesis by Combining Approximation Concepts and Dual Methods.” AIAA Journal 18 (10): 1252–1260. doi:10.2514/3.50877.
   Web of Science ®Google Scholar
• Schmit, L. A., and H. Miura. 1976. Approximation Concepts for Efficient Structural Synthesis Report. NASA-CR-2552. Washington, United States: NASA.
   Google Scholar
• Sedaghati, R. 2005. “Benchmark Case Studies in Structural Design Optimization Using the Force Method.” International Journal of Solids and Structures 42 (21–22): 5848–5871. doi:10.1016/J.IJSOLSTR.2005.03.030.
   Web of Science ®Google Scholar
• Shahrouzi, M., M. Aghabaglou, and F. Rafiee. 2017. “Observer-Teacher-Learner-Based Optimization: An Enhanced Meta-Heuristic for Structural Sizing Design.” Structural Engineering and Mechanics 62 (5): 537. Techno-Press. doi: 10.12989/SEM.2017.62.5.537.
   Web of Science ®Google Scholar
• Sonmez, M. 2011. “Artificial Bee Colony Algorithm for Optimization of Truss Structures.” Applied Soft Computing 11 (2): 2406–2418. Elsevier. doi: 10.1016/J.ASOC.2010.09.003.
   Web of Science ®Google Scholar
• Stander, N., J. A. Snyman, and J. E. Coster. 1995. “On the Robustness and Efficiency of the SAM Algorithm for Structural Optimization.” International Journal for Numerical Methods in Engineering 38 (1): 119–135. John Wiley & Sons, Ltd. doi: 10.1002/nme.1620380108.
   Web of Science ®Google Scholar
• Svanberg, K. 1987. “The Method of Moving Asymptotes – a New Method for Structural Optimization.” International Journal for Numerical Methods in Engineering 24 (2): 359–373. doi:10.1002/nme.1620240207.
   Web of Science ®Google Scholar
• Talatahari, S., M. Kheirollahi, C. Farahmandpour, and A. H. Gandomi. 2013. “A Multi-Stage Particle Swarm for Optimum Design of Truss Structures.” Neural Computing and Applications 23 (5): 1297–1309. Springer London. doi: 10.1007/s00521-012-1072-5.
   Web of Science ®Google Scholar
• Vanderplaats, G. N. 1995. DOT Users Manual, Version 4.20, Vanderplaats Research and Development (VR&D). Springs: Inc. Colorado.
   Google Scholar
• Vanderplaats, G. N. 1997. “Structural Design Optimization Status and Direction.” In 38th Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics. 10.2514/6.1997–1407.
   Google Scholar
• Vanderplaats, G. N. 1998. Numerical Optimization Techniques for Engineering Design. Colorado Springs, CO: Vanderplaats Research and Development.
   Google Scholar
• Vanderplaats, G. N., and F. Moses. 1973. “Structural Optimization by Methods of Feasible Directions.” Computers and Structures 3 (4): 739–755.
   Google Scholar
• Vanderplaats, G. N., H. L. Thomas, and Y. K. Shyy. 1991. “A Review of Approximation Concepts for Structural Synthesis.” Computing Systems in Engineering 2 (1): 17–25. Pergamon. doi: 10.1016/0956-0521(91)90036-5.
   Google Scholar
• Venkayya, V. B. 1971. “Design of Optimum Structures.” Computers and Structures 1 (1–2): 265–309. Pergamon. doi: 10.1016/0045-7949(71)90013-7.
   Google Scholar
• Vezvari, R., A. G. Mojtaba, and A. Nikoobinb. 2018. “Numbers Cup Optimization: A New Method for Optimization Problems.” Structural Engineering and Mechanics 66 (4): 465–476.
   Web of Science ®Google Scholar
• Wang, L., and R. V. Grandhi. 1994. “Efficient Safety Index Calculation for Structural Reliability Analysis.” Computers & Structures 52 (1): 103–111. Pergamon. doi: 10.1016/0045-7949(94)90260-7.
   Web of Science ®Google Scholar
• Wang, L., and R. V. Grandhi. 1995. “Improved Two-Point Function Approximations for Design Optimization.” AIAA Journal 33 (9): 1720–1727. doi:10.2514/3.12715.
   Web of Science ®Google Scholar
• Xu, S., and R. V. Grandhi. 1998. “Effective Two-Point Function Approximation for Design Optimization.” AIAA Journal 36 (12): 2269–2275. doi:10.2514/2.337.
   Web of Science ®Google Scholar