Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
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Development of Improved Clustering Harmony Search and its Application to Various Optimization Problems

개선 클러스터링 화음탐색법 개발 및 다양한 최적화문제에 적용

  • Choi, Jiho (School of Civil, Environmental, and Architectural Engineering, Korea University) ;
  • Jung, Donghwi (Department of Civil Engineering, Keimyung University) ;
  • Kim, Joong Hoon (Department of Civil, Environmental, and Architectural Engineering, Korea University)
  • 최지호 (고려대학교 건축사회환경공학과) ;
  • 정동휘 (계명대학교 건축토목공학부) ;
  • 김중훈 (고려대학교 건축사회환경공학부)
  • Received : 2017.10.18
  • Accepted : 2018.03.09
  • Published : 2018.03.31
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Abstract

Harmony search (HS) is a recently developed metaheuristic optimization algorithm. HS is inspired by the process of musical improvisation and repeatedly searches for the optimal solution using three operations: random selection, memory recall (or harmony memory consideration), and pitch adjustment. HS has been applied by many researchers in various fields. The increasing complexity of real-world optimization problems has created enormous challenges for the current technique, and improved techniques of optimization algorithms and HS are required. We propose an improved clustering harmony search (ICHS) that uses a clustering technique to group solutions in harmony memory based on their objective function values. The proposed ICHS performs modified harmony memory consideration in which decision variables of solutions in a high-ranked cluster have higher probability of being selected than those in a low-ranked cluster. The ICHS is demonstrated in various optimization problems, including mathematical benchmark functions and water distribution system pipe design problems. The results show that the proposed ICHS outperforms other improved versions of HS.

본 연구에서는 최적화 기법의 하나인 화음탐색법 (HS: Harmony Search)에 클러스터링 기법을 적용하여 개선된 형태의 HS를 제안하였다. HS는 음악의 즉흥연주를 모방하여 개발되었으며 무작위선택, 기억회상, 음조조정의 세 가지 연산을 이용하여 최적해를 반복적으로 탐색해 나간다. 기존의 HS의 경우, 세 가지 연산 중 기억회상을 진행할 때 해집단의 저장 공간인 해저장소 (HM: Harmony Memory)에 있는 해를 선택하는데, 이 과정에서 적합도를 정량화한 목적함수 값에 상관없이 모두 동일한 확률로 해의 선택이 이루어지고, 이에 따라 최적의 해를 탐색하는 속도가 상대적으로 낮다. 본 연구에서 제안한 개선 클러스터링 화음탐색법 (ICHS: Improved Clustering Harmony Search)는 HM에서 목적함수의 값을 기준으로 클러스터링 기법을 적용하여 목적함수 값이 유사한 솔루션들이 하나의 해집단을 형성하도록 클러스터링을 수행한다. 이를 통해 만들어진 클러스터 중 상대적으로 목적함수 값이 우수한 클러스터에는 더 높은 선택 확률을 부여하여, 적합도가 높은 클러스터에 포함된 해의 결정변수가 선택될 확률을 높게 하는 역할을 한다. 본 연구에서는 ICHS의 효율성을 검증하기 위하여 개발 기법을 기존 논문에서 제시된 수학적 최적화 문제에 적용하였고 우수한 해탐색 성능을 확인할 수 있었다. 또한 실제 공학 문제에 대한 적용성 평가를 위해 개발 기법을 대규모 상수도관망 관경최적화 문제에 적용하였다. 상수도관망 최적설계에 대한 ICHS의 적용 결과, 기존 최적화 기법에 비해 우수한 해를 안정적으로 도출할 수 있는 것으로 나타났다.

Keywords

References

  1. R. Eberhart, and J. Kennedy, "A new optimizer using particle swarm theory", In Micro Machine and Human Science, 1995. MHS'95, Proceedings of the Sixth International Symposium, pp. 39-43, 1995. DOI: https://doi.org/10.1109/MHS.1995.494215
  2. S. Kirkpatrick and M. P. Vecchi, "Optimization by simulated annealing", Science, vol. 220, no. 4598, pp. 671-680, 1983. DOI: https://doi.org/10.1126/science.220.4598.671
  3. F. Glover, "Heuristics for integer programming using surrogate constraints", Decision Sciences, vol. 8, no. 1, pp. 156-166, 1977. DOI: https://doi.org/10.1111/j.1540-5915.1977.tb01074.x
  4. M. Dorigo, "Optimization, learning and natural algorithms", Ph. D. Thesis, Politecnico di Milano, Italy, 1992.
  5. J. H. Holland, "Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence", U Michigan Press, 1975.
  6. Z. W. Geem, J. H. Kim and G. V. Loganathan, "A new heuristic optimization algorithm: harmony search", Simulation, vol. 76, no. 2, pp. 60-68, 2001. DOI: https://doi.org/10.1177/003754970107600201
  7. K. R. Paik, J. H. Jeong, and J. H. Kim. "Use of a harmony search for optimal design of coffer dam drainage pipes", Journal of Korean Society of Civil Engineers, vol. 21, no. 2-B, pp. 119-128, 2001.
  8. C. W. Baek, "Development of Optimal Decision-Making System for Rehabilitation of Water Distribution Systems Using ReHS", Master degree thesis, Korea University, 2002.
  9. M. Mahdavi, Mohammad Fesanghary, and E. Damangir, "An improved harmony search algorithm for solving optimization problems", Applied mathematics and computation, 188.2, pp. 1567-1579, 2007. https://doi.org/10.1016/j.amc.2006.11.033
  10. Gil-Lopez, Sergio and I. Landa, "On the application of a novel grouping harmony search algorithm to the switch location problem", International Conference on Mobile Lightweight Wireless Systems. Springer Berlin Heidelberg, pp. 662-672, 2010.
  11. A. Askarzadeh, and A. Rezazadeh "A grouping-based global harmony search algorithm for modeling of proton exchange membrane fuel cell", International Journal of Hydrogen Energy, 36.8, pp. 5047-5053, 2011. DOI: http://doi.org/10.1016/j.ijhydene.2011.01.070
  12. A. Simpson, G. Dandy and L. Murphy "Genetic algorithms compared to other techniques for pipe optimisation", Journal of Water Resources Planning and Management, vol. 120, no. 4, pp. 423-443, 1994. DOI: https://doi.org/10.1061/(ASCE)0733-9496(1994)120:4(423)
  13. H. Maier, A. Simpson, A. Zecchin, W. Foong, K. Phang, H. Seah and C. Tan "Ant colony optimization for design of water distribution systems", Journal of Water Resources Planning and Management, vol. 129, no. 3, pp. 200-209, 2003. DOI: https://doi.org/10.1061/(ASCE)0733-9496(2003)129:3(200)
  14. I. Montalvo, J. Izquierdo, R. Perez and M. M. Tung, "Particle swarm optimization applied to the design of water supply systems", Computers and Mathematics with Applications, 56 pp. 769-776, 2008. DOI: https://doi.org/10.1016/j.camwa.2008.02.006
  15. Z. W. Geem, "Optimal cost design of water distribution networks using harmony search", Engineering Optimization, vol. 38, no. 3, pp. 259-277, 2006. DOI: https://doi.org/10.1080/03052150500467430
  16. A. Vasan and S. P. Simonovic, "Optimization of water distribution network design using differential evolution", Journal of Water Resources Planning and Management, vol. 136, no. 2, pp. 279-287, 2010. DOI: https://doi.org/10.1061/(ASCE)0733-9496(2010)136:2(279)
  17. J. Reca and J. Martinez "Genetic algorithms for the design of looped irrigation water distribution networks", Water resources research, vol. 42, no. 5, 2006. DOI: https://doi.org/10.1029/2005WR004383
  18. J. Reca, J. Martinez, C. Gil, and R. Banos. "Application of several meta-heuristic techniques to the optimization of real looped water distribution networks", Water Resources Management, vol. 22, no. 10, pp. 1367-1379, 2008. DOI: https://doi.org/10.1007/s11269-007-9230-8
  19. Z. W. Geem "Particle-swarm harmony search for water network design", Engineering Optimization, vol. 41, no. 4, pp. 297-311, 2009. DOI: https://doi.org/10.1080/03052150802449227
  20. A. Bolognesi, C. Bragalli, A. Marchi and S. Artina, "Genetic heritage evolution by stochastic transmission in the optimal design of water distribution networks", Advances in Engineering Software, 41 pp. 792-801, 2010. DOI: https://doi.org/10.1016/j.advengsoft.2009.12.020
  21. A. Sadollah, D. G. Yoo and J. H. Kim, "Improved mine blast algorithm for optimal cost design of water distribution systems", Engineering Optimization, vol. 47, no. 12, pp. 1-17, 2015. DOI: https://doi.org/10.1080/0305215X.2014.979815