# 제약조건 처리기법에 따른 하모니써치 알고리즘의 효율성 평가 : 관로 최소비용설계 문제의 적용

• Accepted : 2015.07.16
• Published : 2015.07.31
• 32 19

#### Abstract

The application of efficient constraint handling technique is fundamental method to find better solutions in engineering optimization problems with constraints. In this research four of constraint handling techniques are used with a meta-heuristic optimization method, harmony search algorithm, and the efficiency of algorithm is evaluated. The sample problem for evaluation of effectiveness is one of the typical discrete problems, optimal pipe size design problem of water distribution system. The result shows the suggested constraint handling technique derives better solutions than classical constraint handling technique with penalty function. Especially, the case of ${\varepsilon}$-constrained method derives solutions with efficiency and stability. This technique is meaningful method for improvement of harmony search algorithm without the need for development of new algorithm. In addition, the applicability of suggested method for large scale engineering optimization problems is verified with application of constraint handling technique to big size problem has over 400 of decision variables.

#### Keywords

Constraint Handling Technique;Harmony Search Algorithm;Optimal Pipe Size Design

#### References

1. Holland J. H. Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. U Michigan Press, 1975.
2. Glover F. "Heuristics for integer programming using surrogate constraints." Decision Sciences 8.1 (1977): 156-166. DOI: http://dx.doi.org/10.1111/j.1540-5915.1977.tb01074.x
3. Kirkpatrick S. and Vecchi M. P. "Optimization by simmulated annealing." science 220.4598 (1983): 671-680. https://doi.org/10.1126/science.220.4598.671
4. Dorigo M. "Optimization, learning and natural algorithms." Ph. D. Thesis, Politecnico di Milano, Italy 1992.
5. Eberhart R. C. and Kennedy J. "A new optimizer using particle swarm theory." Proceedings of the sixth international symposium on micro machine and human science. Vol. 1. 1995. DOI: http://dx.doi.org/10.1109/MHS.1995.494215
6. Storn R. and Kenneth V. "Minimizing the Real Functions of the ICEC'96 Contest by Differential Evolution." International Conference on Evolutionary Computation. 1996. DOI: http://dx.doi.org/10.1109/icec.1996.542711
7. Geem Z. W., Kim J. H. and Loganathan G. V. "A new heuristic optimization algorithm: harmony search." Simulation 76.2 (2001): 60-68. DOI: http://dx.doi.org/10.1177/003754970107600201 https://doi.org/10.1177/003754970107600201
8. Kim J. H., Geem Z. W. and Kim E. S. "Parameter Estimation Of The Nonlinear Muskingum Model Using Harmony Search." (2001): 1131-1138.
9. Nakrani S. and Tovey C. "On honey bees and dynamic server allocation in internet hosting centers." Adaptive Behavior 12.3-4 (2004): 223-240. https://doi.org/10.1177/105971230401200308
10. Yang X. S. "Firefly algorithm, Levy flights and global optimization." Research and Development in Intelligent Systems XXVI. Springer London, 2010a. 209-218. DOI: http://dx.doi.org/10.1007/978-1-84882-983-1_15
11. Yang X. S. "A new metaheuristic bat-inspired algorithm." Nature inspired cooperative strategies for optimization (NICSO 2010b). Springer Berlin Heidelberg, 2010. 65-74. DOI: http://dx.doi.org/10.1007/978-3-642-12538-6_6
12. Yang X. S. and Deb S. "Engineering optimisation by cuckoo search." International Journal of Mathematical Modelling and Numerical Optimisation 1.4 (2010): 330-343. DOI: http://dx.doi.org/10.1504/IJMMNO.2010.035430 https://doi.org/10.1504/IJMMNO.2010.035430
13. Eskandar H., Sadollah A., Bahreininejad A. and Hamdi M. "Water cycle algorithm-A novel metaheuristic optimization method for solving constrained engineering optimization problems." Computers &Structures 110 (2012): 151-166. DOI: http://dx.doi.org/10.1016/j.compstruc.2012.07.010
14. Sadollah A., Bahreininejad A., Eskandar H. and Hamdi M. "Mine blast algorithm for optimization of truss structures with discrete variables." Computers &Structures 102 (2012): 49-63. DOI: http://dx.doi.org/10.1016/j.compstruc.2012.03.013
15. Michalewicz Z. "A Survey of Constraint Handling Techniques in Evolutionary Computation Methods." Evolutionary Programming 4 (1995): 135-155.
16. Deb K. and Agrawal S. "A niched-penalty approach for constraint handling in genetic algorithms." Artificial Neural Nets and Genetic Algorithms. Springer Vienna, 1999. DOI: http://dx.doi.org/10.1007/978-3-7091-6384-9_40
17. Deb K. "An efficient constraint handling method for genetic algorithms." Computer methods in applied mechanics and engineering 186.2 (2000): 311-338. DOI: http://dx.doi.org/10.1016/S0045-7825(99)00389-8 https://doi.org/10.1016/S0045-7825(99)00389-8
18. Hilton A. B. C. and Culver T. B. "Constraint handling for genetic algorithms in optimal remediation design." Journal of Water Resources Planning and Management 126.3 (2000): 128-137. DOI: http://dx.doi.org/10.1061/(ASCE)0733-9496(2000)126:3(128) https://doi.org/10.1061/(ASCE)0733-9496(2000)126:3(128)
19. Runarsson T. P. and Yao X. "Stochastic ranking for constrained evolutionary optimization." Evolutionary Computation, IEEE Transactions on 4.3 (2000): 284-294. DOI: http://dx.doi.org/10.1109/4235.873238 https://doi.org/10.1109/4235.873238
20. Coello C. A. C. "Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art." Computer methods in applied mechanics and engineering 191.11 (2002): 1245-1287. DOI: http://dx.doi.org/10.1016/S0045-7825(01)00323-1 https://doi.org/10.1016/S0045-7825(01)00323-1
21. Coello C. A. C. and Montes E. M. "Constraint-handling in genetic algorithms through the use of dominance-based tournament selection." Advanced Engineering Informatics 16.3 (2002): 193-203. DOI: http://dx.doi.org/10.1016/S1474-0346(02)00011-3 https://doi.org/10.1016/S1474-0346(02)00011-3
22. Lampineni J. "A constraint handling approach for the differential evolution algorithm." Computational Intelligence, Proceedings of the World on Congress on. Vol. 2. IEEE, 2002. DOI: http://dx.doi.org/10.1109/cec.2002.1004459
23. Miettinen K., Makela M. M. and Toivanen J. "Numerical comparison of some penalty-based constraint handling techniques in genetic algorithms." Journal of Global Optimization 27.4 (2003): 427-446. DOI: http://dx.doi.org/10.1023/A:1026065325419 https://doi.org/10.1023/A:1026065325419
24. Pulido G. T. and Coello C. A. C. "A constraint-handling mechanism for particle swarm optimization." Evolutionary Computation, 2004. CEC2004. Congress on. Vol. 2. Ieee, 2004.
25. Chootinan P. and Chen A. "Constraint handling in genetic algorithms using a gradient-based repair method." Computers &operations research 33.8 (2006): 2263-2281. DOI: http://dx.doi.org/10.1016/j.cor.2005.02.002 https://doi.org/10.1016/j.cor.2005.02.002
26. Oyama A., Shimoyama K. and Fujii K. "New constraint-handling method for multi-objective and multi-constraint evolutionary optimization." Transactions of the Japan Society for Aeronautical and Space Sciences 50.167 (2007): 56-62. DOI: http://dx.doi.org/10.2322/tjsass.50.56 https://doi.org/10.2322/tjsass.50.56
27. Mallipeddi M. and Suganthan P. N. "Ensemble of constraint handling techniques." Evolutionary Computation, IEEE Transactions on 14.4 (2010): 561-579. DOI: http://dx.doi.org/10.1109/TEVC.2009.2033582 https://doi.org/10.1109/TEVC.2009.2033582
28. Zhang H. and Rangaiah G. P. "An efficient constraint handling method with integrated differential evolution for numerical and engineering optimization." Computers &Chemical Engineering 37 (2012): 74-88. DOI: http://dx.doi.org/10.1016/j.compchemeng.2011.09.018 https://doi.org/10.1016/j.compchemeng.2011.09.018
29. Yun J. J. and Lee H. K. "Job Shop Scheduling by Tabu Search Combined with Constraint Satisfaction Technique." Journal of the Society of Korea Industrial and Systems Engineering 25.71 (2002): 92-101.
30. Jung H. E., Jeon S. B. and Jo G. S. "A Web-based Spatial Layout Planning System with Constraint Satisfaction Problems." Journal of Koreaa Institute of Information Scientists and Engineering: Computing Practices and Letters 6.2 (2000): 216-224.
31. Baek C. W., Kim E. S., Park M. J. and Kim J. H. "Development of Optimal Decision-Making System for Rehabilitation of Water Distribution Systems Using ReHS." Journal of Korea Water Resources Association 38.3 (2005): 199-212. DOI: http://dx.doi.org/10.3741/JKWRA.2005.38.3.199 https://doi.org/10.3741/JKWRA.2005.38.3.199
32. Takahama T. and Sakai S. "Constrained optimization by ${\varepsilon}$ constrained differential evolution with dynamic ${\varepsilon}$-level control." Advances in Differential Evolution. Springer Berlin Heidelberg, 2008. 139-154. DOI: http://dx.doi.org/10.1007/978-3-540-68830-3_5
33. Rossman L. A. "EPANET 2: users manual." (2000).
34. Fujiwara O. and Khang D. B. "A two-phase decomposition method for optimal design of looped water distribution networks." Water resources research 26.4 (1990): 539-549. DOI: http://dx.doi.org/10.1029/WR026i004p00539 https://doi.org/10.1029/WR026i004p00539
35. Reca J., Martinez J., Gil C. and Banos R. "Application of several meta-heuristic techniques to the optimization of real looped water distribution networks." Water Resources Management 22.10 (2008): 1367-1379. DOI: http://dx.doi.org/10.1007/s11269-007-9230-8 https://doi.org/10.1007/s11269-007-9230-8
36. Zecchin, A. C., Simpson, A. R., Maier, H. R., Leonard, M., Roberts, A. J. and Berrisford, M. J. "Application of two ant colony optimisation algorithms to water distribution system optimisation." Mathematical and computer modelling 44.5 (2006): 451-468. https://doi.org/10.1016/j.mcm.2006.01.005
37. Geem, Z. W. "Particle-swarm harmony search for water network design." Engineering Optimization 41.4 (2009): 297-311. DOI: http://dx.doi.org/10.1080/03052150802449227 https://doi.org/10.1080/03052150802449227

#### Acknowledgement

Supported by : 한국연구재단