Journal of Applied Mathematics

Multiobjective Optimization Method Based on Adaptive Parameter Harmony Search Algorithm

P. Sabarinath, M. R. Thansekhar, and R. Saravanan

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Abstract

The present trend in industries is to improve the techniques currently used in design and manufacture of products in order to meet the challenges of the competitive market. The crucial task nowadays is to find the optimal design and machining parameters so as to minimize the production costs. Design optimization involves more numbers of design variables with multiple and conflicting objectives, subjected to complex nonlinear constraints. The complexity of optimal design of machine elements creates the requirement for increasingly effective algorithms. Solving a nonlinear multiobjective optimization problem requires significant computing effort. From the literature it is evident that metaheuristic algorithms are performing better in dealing with multiobjective optimization. In this paper, we extend the recently developed parameter adaptive harmony search algorithm to solve multiobjective design optimization problems using the weighted sum approach. To determine the best weightage set for this analysis, a performance index based on least average error is used to determine the index of each weightage set. The proposed approach is applied to solve a biobjective design optimization of disc brake problem and a newly formulated biobjective design optimization of helical spring problem. The results reveal that the proposed approach is performing better than other algorithms.

Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 165601, 12 pages.

Dates
First available in Project Euclid: 15 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1429105035

Digital Object Identifier
doi:10.1155/2015/165601

Mathematical Reviews number (MathSciNet)
MR3312761

Zentralblatt MATH identifier
07000917

Citation

Sabarinath, P.; Thansekhar, M. R.; Saravanan, R. Multiobjective Optimization Method Based on Adaptive Parameter Harmony Search Algorithm. J. Appl. Math. 2015 (2015), Article ID 165601, 12 pages. doi:10.1155/2015/165601. https://projecteuclid.org/euclid.jam/1429105035


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References

  • J. L. Marcelin, “Genetic optimisation of gears,” International Journal of Advanced Manufacturing Technology, vol. 17, no. 12, pp. 910–915, 2001.
  • K. Deb and S. Jain, “Multi-speed gearbox design using multi-objective evolutionary algorithms,” Journal of Mechanical Design, vol. 125, no. 3, pp. 609–619, 2003.
  • H. Hirani, K. Athre, and S. Biswas, “Comprehensive design methodology for an engine journal bearing,” Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, vol. 214, no. 4, pp. 401–412, 2000.
  • J. S. Rao and R. Tiwari, “Optimum design and analysis of thrust magnetic bearings using multi objective genetic algorithms,” International Journal for Computational Methods in Engineering Science and Mechanics, vol. 9, no. 4, pp. 223–245, 2008.
  • B. R. Rao and R. Tiwari, “Optimum design of rolling element bearings using genetic algorithms,” Mechanism and Machine Theory, vol. 42, no. 2, pp. 233–250, 2007.
  • D.-H. Choi and K.-C. Yoon, “A design method of an automotive wheel-bearing unit with discrete design variables using genetic algorithms,” Transactions of ASME, Journal of Tribology, vol. 123, no. 1, pp. 181–187, 2001.
  • J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, pp. 1942–1948, Perth, Australia, December 1995.
  • P. Sabarinath, M. R. Thansekhar, and R. Saravanan, “Performance evaluation of particle swarm optimization algorithm for optimal design of belt pulley system,” in Swarm, Evolutionary, and Memetic Computing, vol. 8297 of Lecture Notes in Computer Science, pp. 601–616, Springer, Cham, Switzerland, 2013.
  • X.-S. Yang, “Firefly algorithm, stochastic test functions and design optimization,” International Journal of Bio-Inspired Computation, vol. 2, no. 2, pp. 78–84, 2010.
  • X. S. Yang and S. Deb, “Cuckoo Search via Lévy flights,” in Proceedings of the World Congress on Nature & Biologically Inspired Computing (NaBIC '09), pp. 210–214, IEEE, Coimbatore, India, December 2009.
  • 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.
  • V. Kumar, J. K. Chhabra, and D. Kumar, “Parameter adaptive harmony search algorithm for unimodal and multimodal optimization problems,” Journal of Computational Science, vol. 5, no. 2, pp. 144–155, 2014.
  • K. Naidu, H. Mokhlis, and A. H. A. Bakar, “Multiobjective optimization using weighted sum Artificial Bee Colony algorithm for Load Frequency Control,” International Journal of Electrical Power & Energy Systems, vol. 55, pp. 657–667, 2014.
  • A. Kattan, R. Abdullah, and R. A. Salam, “Harmony search based supervised training of artificial neural networks,” in Proceedings of the International Conference on Intelligent Systems, Modelling and Simulation (ISMS '10), pp. 105–110, Liverpool, UK, January 2010.
  • E. Sandgren, “Nonlinear integer and discrete programming in mechnical design optimization,” ASME Transactions on Mechanical Design, vol. 112, no. 2, pp. 223–229, 1990.
  • J.-L. Chen and Y.-C. Tsao, “Optimal design of machine elements using genetic algorithms,” Journal of the Chinese Society of Mechanical Engineers, vol. 14, no. 2, pp. 193–199, 1993.
  • S.-J. Wu and P.-T. Chow, “Genetic algorithms for nonlinear mixed discrete-integer optimization problems via meta-genetic parameter optimization,” Engineering Optimization, vol. 24, no. 2, pp. 137–159, 1995.
  • C.-X. Guo, J.-S. Hu, B. Ye, and Y.-J. Cao, “Swarm intelligence for mixed-variable design optimization,” Journal of Zhejiang University Science, vol. 5, no. 7, pp. 851–860, 2004.
  • J. Lampinen and I. Zelinka, “Mixed integer-discrete-continuous optimization by differential evolution,” in Proceedings of the 5th International Conference on Soft Computing, pp. 71–76, Brno, Czech Republic, June 1999.
  • J. Kennedy and R. C. Eberhart, “A discrete binary version of the particle swarm algorithm,” in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, pp. 4104–4108, October 1997.
  • A. Osyczka and S. Kundu, “A modified distance method for multicriteria optimization, using genetic algorithms,” Computers and Industrial Engineering, vol. 30, no. 4, pp. 871–882, 1996.
  • T. Ray and K. M. Liew, “A swarm metaphor for multiobjective design optimization,” Engineering Optimization, vol. 34, no. 2, pp. 141–153, 2002.
  • A. R. Y\ild\iz, N. Öztürk, N. Kaya, and F. Öztürk, “Hybrid multi-objective shape design optimization using Taguchi's method and genetic algorithm,” Structural and Multidisciplinary Optimization, vol. 34, no. 4, pp. 317–332, 2007.
  • A. R. Y\ild\iz, “An effective hybrid immune-hill climbing optimization approach for solving design and manufacturing optimization problems in industry,” Journal of Materials Processing Technology, vol. 209, no. 6, pp. 2773–2780, 2009.
  • X.-S. Yang and S. Deb, “Multi objective cuckoo search for design optimization,” Computers and Operations Research, vol. 40, no. 6, pp. 1616–1624, 2013.
  • X.-S. Yang, “Multiobjective firefly algorithm for continuous optimization,” Engineering with Computers, vol. 29, no. 2, pp. 175–184, 2013.
  • X.-S. Yang, M. Karamanoglu, and X. Heb, “Multi-objective flower algorithm for optimization,” Procedia Computer Science, vol. 18, pp. 861–868, 2013.
  • G. Reynoso-Meza, X. Blasco, J. Sanchis, and J. M. Herrero, “Comparison of design concepts in multi-criteria decision-making using level diagrams,” Information Sciences, vol. 221, pp. 124–141, 2013.
  • K. Deb and M. Goyal, “Optimizing engineering designs using a combined genetic search,” in Proceedings of the 7th International Conference on Genetic Algorithms, I. T. Back, Ed., pp. 512–528, 1997.
  • D. Datta and J. R. Figueira, “A real-integer-discrete-coded particle swarm optimization for design problems,” Applied Soft Computing Journal, vol. 11, no. 4, pp. 3625–3633, 2011.
  • S. He, E. Prempain, and Q. H. Wu, “An improved particle swarm optimizer for mechanical design optimization problems,” Engineering Optimization, vol. 36, no. 5, pp. 585–605, 2004.
  • K. Deb, A. Pratap, and S. Moitra, “Mechanical component design for multiple objectives using elitist non-dominated sorting GA,” Technical Report No. 200002, Kanpur Genetic Algorithms Laboratory (KanGAL), Indian Institute of Technology, Kanpur, India, 2000.
  • Z. W. Geem, J.-H. Kim, and G. V. Loganathan, “Harmony search optimization: application to pipe network design,” International Journal of Modelling and Simulation, vol. 22, no. 2, pp. 125–133, 2002.
  • 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 the Korean Society of Civil Engineers, vol. 21, no. 2, pp. 119–128, 2001.
  • Z. W. Geem, “Optimal cost design of water distribution networks using harmony search,” Engineering Optimization, vol. 38, no. 3, pp. 259–277, 2006.
  • Z. Geem and H. Hwangbo, “Application of harmony search to multi-objective optimization for satellite heat pipe design,” in Proceedings of the Us-Korea Conference on Science, Technology and Entrepreneurship, pp. 1–3, Citeseer, Teaneck, NJ, USA, 2006.
  • S. O. Degertekin, “Optimum design of steel frames using harmony search algorithm,” Structural and Multidisciplinary Optimization, vol. 36, no. 4, pp. 393–401, 2008.
  • L. D. S. Coelho and V. C. Mariani, “An improved harmony search algorithm for power economic load dispatch,” Energy Conversion and Management, vol. 50, no. 10, pp. 2522–2526, 2009.
  • V. R. Pandi, B. K. Panigrahi, M. K. Mallick, A. Abraham, and S. Das, “Improved harmony search for economic power dispatch,” in Proceedings of the 9th International Conference on Hybrid Intelligent Systems (HIS '09), pp. 403–408, Shenyang, China, August 2009.
  • S. Sivasubramani and K. S. Swarup, “Multi-objective harmony search algorithm for optimal power flow problem,” International Journal of Electrical Power and Energy Systems, vol. 33, no. 3, pp. 745–752, 2011.
  • Z. W. Geem, K. S. Lee, and Y. Park, “Application of harmony search to vehicle routing,” American Journal of Applied Sciences, vol. 2, no. 12, pp. 1552–1557, 2005.
  • Z. W. Geem, C. Tseng, and Y. Park, “Harmony search for generalized orienteering problem: best touring in China,” in Advances in Natural Computation, vol. 3612 of Lecture Notes in Computer Science, pp. 741–750, Springer, Berlin, Germany, 2005.
  • H. Xu, X. Z. Gao, T. Wang, and K. Xue, “Harmony search optimization algorithm: application to a reconfigurable mobile robot prototype,” in Recent Advances in Harmony Search Algorithm, vol. 270 of Studies in Computational Intelligence, pp. 11–22, Springer, Berlin, Germany, 2010.
  • B. Amiri, L. Hossain, and S. E. Mosavi, “Applications of harmony search algorithm on clustering,” in Proceedings of the World Congress on Engineering and Computer Science, pp. 460–465, 2010.
  • M. Mahdavi, M. Fesanghary, and E. Damangir, “An improved harmony search algorithm for solving optimization problems,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1567–1579, 2007.
  • Z. Kong, L. Gao, L. Wang, Y. Ge, and S. Li, “On an adaptive harmony search algorithm,” International Journal of Innovative Computing, Information and Control, vol. 5, no. 9, pp. 2551–2560, 2009.
  • M. G. H. Omran and M. Mahdavi, “Global-best harmony search,” Applied Mathematics and Computation, vol. 198, no. 2, pp. 643–656, 2008.
  • S. Das, A. Mukhopadhyay, A. Roy, A. Abraham, and B. K. Panigrahi, “Exploratory power of the harmony search algorithm: analysis and improvements for global numerical optimization,” IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, vol. 41, no. 1, pp. 89–106, 2011.
  • O. M. Alia and R. Mandava, “The variants of the harmony search algorithm: an overview,” Artificial Intelligence Review, vol. 36, no. 1, pp. 49–68, 2011.
  • M. Mahdavi and H. Abolhassani, “Harmony $K$-means algorithm for document clustering,” Data Mining and Knowledge Discovery, vol. 18, no. 3, pp. 370–391, 2009.
  • C. Worasucheep, “A harmony search with adaptive pitch adjustment for continuous optimization,” International Journal of Hybrid Information Technology, vol. 4, no. 4, pp. 13–24, 2011.
  • X. S. Yang, “Harmony search as a metaheuristic algorithm,” in Music Inspired Harmony Search Algorithm, Theory and Applications, Z. W. Geem, Ed., pp. 1–14, Springer, Berlin, Germany, 2009.
  • N. Taherinejad, “Highly reliable harmony search algorithm,” in Proceedings of the European Conference on Circuit Theory and Design, pp. 818–822, August 2009.
  • P. Chakraborty, G. G. Roy, S. Das, D. Jain, and A. Abraham, “An improved harmony search algorithm with differential mutation operator,” Fundamenta Informaticae, vol. 95, no. 4, pp. 401–426, 2009.
  • C.-M. Wang and Y.-F. Huang, “Self-adaptive harmony search algorithm for optimization,” Expert Systems with Applications, vol. 37, no. 4, pp. 2826–2837, 2010.
  • R. T. Marler and J. S. Arora, “The weighted sum method for multi-objective optimization: new insights,” Structural and Multidisciplinary Optimization, vol. 41, no. 6, pp. 853–862, 2010.
  • S. Hemamalini and S. P. Simon, “Economic/emission load dispatch using artificial bee colony algorithm,” ACEEE International Journal on Electrical and Power Engineering, vol. 1, no. 2, pp. 27–33, 2010.
  • Y. K. Jain and S. K. Bhandare, “Min max normalization based data perturbation method for privacy protection,” International Journal of Computer & Communication Technology, vol. 2, 2011.
  • P. Sabarinath, R. Hariharasudhan, M. R. Thansekhar, and R. Saravanan, “Optimal design of disc brake using NSGA II algorithm,” International Journal of Innovative Research in Science, Engineering and Technology, vol. 3, no. 3, pp. 1400–1405, 2014. \endinput