### 트러스 구조물의 최소중량설계를 위한 양자기반 화음탐색 알고리즘의 개발

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손수덕;이승재
Shon, Su-Deok;Lee, Seung-Jae

• 투고 : 2015.08.06
• 심사 : 2015.10.15
• 발행 : 2015.10.30
• 5 0

#### 초록

With the development of quantum computer, the quantum-inspired search method applying the features of quantum mechanics, i.e. indetermination, superposition, entanglement, etc, and its application to engineering-problems have emerged as one of the most interesting research topics. Unlike the study of the quantum computer, the quantum-inspired search algorithms have been developed based on the application of the existed meta-heuristic algorithm and the information superimposed quantum-bit approached via through quantum gate. In this process, it appears that the balance between the two features of exploration and exploitation, and continually accumulates evolutionary information. Thus, this study is to propose a quantum-inspired harmony search algorithm and to solve the structural optimization problem by the algorithm. For the optimization, we suggest the mathematical modeling of the truss which is possible to minimum weight design. In its model, the cost function is minimum weight and constraint function consists of the stress. To trace the accumulative and convergence process of evolutionary information, 3-bar and 10-bar truss are chosen as the numerical examples, and their results are analyzed. The optimized design result in the numerical examples shows it has better result in minimum weight design, compared to those of the other search methods. It is also observed that more accurate optional values can be acquired as the result by accumulating evolutionary information.

#### 키워드

양자기반 화음탐색 알고리즘;양자비트;양자게이트;트러스 구조물;최소중량설계

#### 참고문헌

1. Feynman, R. (1986). Quantum Mechanical computers. Foundations of Physics, 16, 507-531. https://doi.org/10.1007/BF01886518
2. Geem, Z.W., Kim, J.H. & Loganathan, G.V. (2001). A new heuristic optimization algorithm: harmony search. Simulation, 76(2), 60-68. https://doi.org/10.1177/003754970107600201
3. Ghosh, A. & Mukherjee, S. (2013). Quantum Annealing and Computation: A Brief Documentary Note. SCIENCE AND CULTURE (Indian Science News Association), 2013, 79, 485-500.
4. Grover, L. (1996). A fast quantum mechanical algorithm for database search. in Proc. of the 28th ACM Symposium on Theory of Computing, 212-219.
5. Grover, L. (1999). Quantum Mechanical Searching, in Proc. of the 1999 Congress on Evolutionary Computation, Piscataway, NJ: IEEE Press, 3, 2255-2261.
6. Han, K. (2003). Quantum-inspired Evolutionary Algorithm, Ph.D. dissertation, Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology, Daejeon, Korea.
7. Han, K. & Kim, J. (2002). Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Transaction on Evolutionary Computation, 6(6), 580-593. https://doi.org/10.1109/TEVC.2002.804320
8. Han, K. & Kim, J. (2004). Quantum-inspired evolutionary algorithms with new termination criterion, H${\varepsilon}$ gate, and two-phase scheme. IEEE Transaction on Evolutionary Computation, 8(2), 156-169. https://doi.org/10.1109/TEVC.2004.823467
9. Layeb, A. (2013). A hybrid quantum inspired harmony search algorithm for 0-1 optimization problems. Journal of Computational and Applied Mathematics, 253, 14-25. https://doi.org/10.1016/j.cam.2013.04.004
10. Lee, K. & Geem, Z.W. (2004). A new structural optimization method based on the harmony search algorithm. Computers and Structures, 82, 781-798. https://doi.org/10.1016/j.compstruc.2004.01.002
11. Mahdavi, M., Fesanghary, M. & Damangir, E. (2007). An improved harmony search algorithm for solving optimization problems. Applied Mathematics and Computation, 188, 1567-1579. https://doi.org/10.1016/j.amc.2006.11.033
12. Das, S., Mukhopadhyay, A., Roy, A., Abraham, A. & Panigrahi, B. (2011). Exploratory Power of the Harmony Search Algorithm: Analysis and Improvements for Global Numerical Optimization. IEEE Trans. on systems, man and cybernetics - Part B: Cybernetics, 41(1), 89-106. https://doi.org/10.1109/TSMCB.2010.2046035
13. Deutsch, D. (1989). Quantum computational networks, in Proc. of the Royal Society of London A, 425, 73-90. https://doi.org/10.1098/rspa.1989.0099
14. Moore, M. & Narayanan, A. (1995). Quantum-inspired Computing, Technical report, Department of Computer Science, University of Exeter, UK.
15. Omran, M. & Mahdavi, M. (2008). Global-best harmony search. Applied Mathematics and Computation, 198, 643-656. https://doi.org/10.1016/j.amc.2007.09.004
16. Pan Q., Suganthan, P., Liang, J. & Fatih Tasgetiren, M. (2010a). A local-best harmony search algorithm with dynamic subpopulations. Engineering Optimization, 42(2), 101-117. https://doi.org/10.1080/03052150903104366
17. Pan, Q., Suganthan, P., Fatih Tasgetiren, M. & Liang, J. (2010b). A self-adaptive global best harmony search algorithm for continuous optimization problems. Applied Mathematics and Computation, 216, 830-848. https://doi.org/10.1016/j.amc.2010.01.088
18. Schmit, Jr, L. & Miura, H. (1976). Approximation concepts for efficient structural synthesis. NASA CR-2552, Washington, DC: NASA.
19. Shon, S., Jo, H. & Lee S. (2015). An Arrangement Technique for Fine Regular Triangle Grid of Network Dome by using Harmony Search Algorithm. Journal of Korean Association for Spatial Structures, 15(2), 87-94. (Korean) https://doi.org/10.9712/KASS.2015.15.2.087
20. Shon, S. & Lee S. (2014). Structural Optimization of Planar Truss using Quantum-inspired Evolution Algorithm. Journal of Korea Institute of Safety Inspection, 18(4), 1-9. (Korean)
21. Shor, P. (1994). Algorithms for Quantum Computation: Discrete Logarithms and Factoring, in Proc. of the 35th Annual Symposium on Foundations of Computer Science, Piscataway, NJ: IEEE Press, 1994, 124-134.
22. Su, H. & Yang, Y. (2011). Free Search with Adaptive Differential Evolution Exploitation and Quantum-Inspired Exploration Differential evolution and quantum-inquired differential evolution for evolving Takagi-Sugeno fuzzy models. Expert Systems with Applications, 38, 6447-6451. https://doi.org/10.1016/j.eswa.2010.11.107
23. Wang, C. & Huang, Y. (2010). Self-adaptive harmony search algorithm for optimization. Expert Systems with Applications, 37, 2826-2837. https://doi.org/10.1016/j.eswa.2009.09.008
24. Yadav, P., Kumar, R., Panda, S. & Chang, C. (2012). An intelligent tuned Harmony Search algorithm for optimization. Information Sciences, 196, 47-72. https://doi.org/10.1016/j.ins.2011.12.035
25. Yin, J., Wang, Y. & Hu, J. (2012). Free Search with Adaptive Differential Evolution Exploitation and Quantum-Inspired Exploration. Journal of Network and Computer Applications, 35, 1035-1051. https://doi.org/10.1016/j.jnca.2011.12.004
26. Zhang, G. (2011). Quantum-inspired evolutionary algorithms: a survay and empirical study, J. Heuristics, 17, 303-351. https://doi.org/10.1007/s10732-010-9136-0

#### 과제정보

연구 과제 주관 기관 : 한국연구재단