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Multi-Objective Optimization and Cluster-Wise Regression Analysis to Establish Input–Output Relationships of a Process

  • Amit Kumar Das
  • Debasish Das
  • Dilip Kumar PratiharEmail author
Chapter

Abstract

Multi-objective evolutionary algorithm (MOEA) is an efficient tool for solving different problems in engineering and various other fields. This chapter deals with an approach used to establish input–output relationships of a process utilizing the concepts of multi-objective optimization and cluster-wise regression analysis. At first, an initial Pareto-front is obtained for a given process using a multi-objective optimization technique. Then, these Pareto-optimal solutions are applied to train a neuro-fuzzy system (NFS). The training of the NFS is implemented using a meta-heuristic optimization algorithm. Now, for generating a modified Pareto-front, the trained NFS is used in MOEA for evaluating the objective function values. In this way, a new set of trade-off solutions is formed. These modified Pareto-optimal solutions are then clustered using a clustering algorithm. Cluster-wise regression analysis is then carried out to determine input–output relationships of the process. These relationships are found to be superior in terms of precision to that of the equations obtained using conventional statistical regression analysis on the experimental data. To validate the performance of the developed method, an engineering problem, related to the electron beam welding (EBW) of SS 304, is selected and its input–output relationships have been established.

Keywords

Multi-objective optimization NSGA-II Input–output relationships Clustering Regression analysis Neuro-fuzzy system 

References

  1. M. Aghbashlo, S. Hosseinpour, M. Tabatabaei, H. Younesi, G. Najafpour, On the exergetic optimization of continuous photobiological hydrogen production using hybrid ANFIS–NSGA-II (adaptive neuro-fuzzy inference system–non-dominated sorting genetic algorithm-II). Energy 96, 507–520 (2016)CrossRefGoogle Scholar
  2. M.H. Ahmadi, M. Mehrpooya, Thermo-economic modeling and optimization of an irreversible solar-driven heat engine. Energy Convers. Manag. 103, 616–622 (2015)CrossRefGoogle Scholar
  3. M.H. Ahmadi, M.A. Ahmadi, S.A. Sadatsakkak, Thermodynamic analysis and performance optimization of irreversible Carnot refrigerator by using multi-objective evolutionary algorithms (MOEAs). Renew. Sustain. Energy Rev. 51, 1055–1070 (2015)CrossRefGoogle Scholar
  4. M.H. Ahmadi, M.A. Ahmadi, A. Mellit, F. Pourfayaz, M. Feidt, Thermodynamic analysis and multi objective optimization of performance of solar dish Stirling engine by the centrality of entransy and entropy generation. Int. J. Electr. Power Energy Syst. 78, 88–95 (2016)CrossRefGoogle Scholar
  5. M. Asadi-Eydivand, M. Solati-Hashjin, A. Fathi, M. Padashi, N.A.A. Osman, Optimal design of a 3D-printed scaffold using intelligent evolutionary algorithms. Appl. Soft Comput. 39, 36–47 (2016)CrossRefGoogle Scholar
  6. S.S. Askar, A. Tiwari, Multi-objective optimisation problems: a symbolic algorithm for performance measurement of evolutionary computing techniques. in Proceedings of EMO 2009 (Springer, 2009), pp. 169–182Google Scholar
  7. S. Askar, A. Tiwari, Finding innovative design principles for multiobjective optimization problems. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev 41(4), 554–559 (2011)Google Scholar
  8. S. Bandaru, C.C. Tutum, K. Deb, J.H. Hattel, Higher-level innovization: a case study from friction stir welding process optimization. Evol. Comput. (CEC) 2011, 2782–2789 (2011)Google Scholar
  9. S. Bandaru, T. Aslam, A.H. Ng, K. Deb, Generalized higher-level automated innovization with application to inventory management. Eur. J. Oper. Res. 243(2), 480–496 (2015)MathSciNetCrossRefGoogle Scholar
  10. J.C. Bezdek, Fuzzy mathematics in pattern classification. Ph.D. thesis, Applied Math. Center, Cornell University, 1973Google Scholar
  11. H.R. Berenji, P. Khedkar, Learning and tuning fuzzy logic controllers through reinforcements. IEEE Trans. Neural Netw. 3(5), 724–740 (1992)CrossRefGoogle Scholar
  12. A.E. Brownlee, J.A. Wright, Constrained, mixed-integer and multi-objective optimisation of building designs by NSGA-II with fitness approximation. Appl. Soft Comput. 33, 114–126 (2015)CrossRefGoogle Scholar
  13. D. Das, D.K. Pratihar, G.G. Roy, Electron beam melting of steel plates: temperature measurement using thermocouples and prediction through finite element analysis. CAD/CAM, Robotics and Factories of the Future (Springer, 2016), pp. 579–588Google Scholar
  14. D. Das, D.K. Pratihar, G.G. Roy, A.R. Pal, Phenomenological model-based study on electron beam welding process, an input-output modeling using neural networks trained by back-propagation algorithm, genetic algorithm, particle swarm optimization algorithm and bat algorithm. Appl. Intell. (2017).  https://doi.org/10.1007/s10489-017-1101-2CrossRefGoogle Scholar
  15. K. Deb, Unveiling innovative design principles by means of multiple conflicting objectives. Eng. Optim. 35(5), 445–470 (2003)CrossRefGoogle Scholar
  16. K. Deb, S. Jain, Multi-speed gearbox design using multi-objective evolutionary algorithms. Trans. Am. Soc. Mech. Eng. J. Mech. Des. 125(3), 609–619 (2003)Google Scholar
  17. K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  18. K. Deb, A. Srinivasan, Innovization: Discovery of innovative design principles through multiobjective evolutionary optimization. Multiobjective Problem Solving from Nature, pp. 243–262 (2008)Google Scholar
  19. K. Deb, S. Gupta, D. Daum, J. Branke, A.K. Mall, D. Padmanabhan, Reliability-based optimization using evolutionary algorithms. IEEE Trans. Evol. Comput. 13(5), 1054–1074 (2009)CrossRefGoogle Scholar
  20. K. Deb, K. Sindhya, Deciphering innovative principles for optimal electric brushless DC permanent magnet motor design. in IEEE World Congress on Computational Intelligence Evolutionary Computation 2008, pp. 2283–2290 (2008)Google Scholar
  21. K. Deb, S. Bandaru, D. Greiner, A. Gaspar-Cunha, C.C. Tutum, An integrated approach to automated innovization for discovering useful design principles: case studies from engineering. Appl. Soft Comput. 15, 42–56 (2014)CrossRefGoogle Scholar
  22. C. Dudas, M. Frantzén, A.H. Ng, A synergy of multi-objective optimization and data mining for the analysis of a flexible flow shop. Robot. Comput. Integr. Manuf. 27(4), 687–695 (2011)CrossRefGoogle Scholar
  23. M. Ester, H.-P. Kriegel, J. Sander, X. Xu, A density-based algorithm for discovering clusters in large spatial databases with noise. in Proceedings of KDD 1996, vol. 34, pp. 226–231 (1996)Google Scholar
  24. M.A. Gil, Fuzziness and loss of information in statistical problems. IEEE Trans. Syst. Man Cybern. 17(6), 1016–1025 (1987)CrossRefGoogle Scholar
  25. M.A. Gil, P. Gil, Fuzziness in the experimental outcomes: comparing experiments and removing the loss of information. J. Stat. Plan. Inference 31(1), 93–111 (1992)MathSciNetCrossRefGoogle Scholar
  26. D.E. Goldberg, The Design of Innovation: Lessons from and for Competent Genetic Algorithms, vol. 7 (Springer Science & Business Media, 2002)Google Scholar
  27. J. Horn, N. Nafpliotis, D.E. Goldberg, A niched Pareto genetic algorithm for multiobjective optimization. in IEEE World Congress on Computational Intelligence Evolutionary Computation 1994, pp. 82–87 (1994)Google Scholar
  28. H. Ishibuchi, H. Tanaka, H. Okada, Interpolation of fuzzy if-then rules by neural networks. Int. J. Approx. Reason. 10(1), 3–27 (1994)CrossRefGoogle Scholar
  29. J.-S. Jang, ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans. Syst. Man Cybern. 23(3), 665–685 (1993)CrossRefGoogle Scholar
  30. Y. Jarraya, S. Bouaziz, A.M. Alimi, A. Abraham, Evolutionary multi-objective optimization for evolving hierarchical fuzzy system. Evol. Comput. (CEC) 2015, 3163–3170 (2015)Google Scholar
  31. M. Jha, D.K. Pratihar, A. Bapat, V. Dey, M. Ali, A. Bagchi, Modeling of input-output relationships for electron beam butt welding of dissimilar materials using neural networks. Int. J. Comput. Intell. Appl. 13(03), 1450016 (2014)CrossRefGoogle Scholar
  32. J. Kar, S. Mahanty, S.K. Roy, G. Roy, Estimation of average spot diameter and bead penetration using process model during electron beam welding of AISI 304 stainless steel. Trans. Indian Inst. Met. 68(5), 935–941 (2015)CrossRefGoogle Scholar
  33. J.M. Keller, R.R. Yager, H. Tahani, Neural network implementation of fuzzy logic. Fuzzy Sets Syst. 45(1), 1–12 (1992)MathSciNetCrossRefGoogle Scholar
  34. F. Khoshbin, H. Bonakdari, S.H. Ashraf Talesh, I. Ebtehaj, A.H. Zaji, H. Azimi, Adaptive neuro-fuzzy inference system multi-objective optimization using the genetic algorithm/singular value decomposition method for modelling the discharge coefficient in rectangular sharp-crested side weirs. Eng. Optim. 48(6), 933–948 (2016)CrossRefGoogle Scholar
  35. J. Knowles, D. Corne, The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation. CEC 99, 98–105 (1999)Google Scholar
  36. K. Lwin, R. Qu, G. Kendall, A learning-guided multi-objective evolutionary algorithm for constrained portfolio optimization. Appl. Soft Comput. 24, 757–772 (2014)CrossRefGoogle Scholar
  37. E.H. Mamdani, S. Assilian, An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man Mach. Stud. 7(1), 1–13 (1975)CrossRefGoogle Scholar
  38. M. Marinaki, Y. Marinakis, G.E. Stavroulakis, Fuzzy control optimized by a multi-objective differential evolution algorithm for vibration suppression of smart structures. Comput. Struct. 147, 126–137 (2015)CrossRefGoogle Scholar
  39. K. Miettinen, Nonlinear Multiobjective Optimization, vol. 12 (Springer Science & Business Media, 1999)Google Scholar
  40. S. Mitra, S.K. Pal, Neuro-fuzzy expert systems: relevance, features and methodologies. IETE J. Res. 42(4–5), 335–347 (1996)CrossRefGoogle Scholar
  41. S. Obayashi, D. Sasaki, Visualization and data mining of Pareto solutions using self-organizing map. in Proceedings of EMO 2003 (Springer, 2003), pp. 796–809Google Scholar
  42. D.K. Pratihar, Soft Computing (Alpha Science International, Ltd, 2007)Google Scholar
  43. S.A. Sadatsakkak, M.H. Ahmadi, M.A. Ahmadi, Optimization performance and thermodynamic analysis of an irreversible nano scale Brayton cycle operating with Maxwell-Boltzmann gas. Energy Convers. Manag. 101, 592–605 (2015)CrossRefGoogle Scholar
  44. H.A. Taboada, D.W. Coit, Data mining techniques to facilitate the analysis of the Pareto-optimal set for multiple objective problems. in Proceedings 2006, Institute of Industrial and Systems Engineers (IISE) IIE Annual Conference, pp. 1–6 (2006)Google Scholar
  45. H. Takagi, I. Hayashi, NN-driven fuzzy reasoning. Int. J. Approx. Reason. 5(3), 191–212 (1991)CrossRefGoogle Scholar
  46. H. Takagi, N. Suzuki, T. Koda, Y. Kojima, Neural networks designed on approximate reasoning architecture and their applications. IEEE Trans. Neural Netw. 3(5), 752–760 (1992)CrossRefGoogle Scholar
  47. C. Wang, X. Li, X. Zhou, A. Wang, N. Nedjah, Soft computing in big data intelligent transportation systems. Appl. Soft Comput. 38, 1099–1108 (2016)CrossRefGoogle Scholar
  48. J. Yao, M. Dash, S. Tan, H. Liu, Entropy-based fuzzy clustering and fuzzy modeling. Fuzzy Sets Syst. 113(3), 381–388 (2000)CrossRefGoogle Scholar
  49. Z.-H. Zhan, J. Li, J. Cao, J. Zhang, H.S.-H. Chung, Y.-H. Shi, Multiple populations for multiple objectives: a coevolutionary technique for solving multiobjective optimization problems. IEEE Trans. Cybern. 43(2), 445–463 (2013)CrossRefGoogle Scholar
  50. Q. Zhang, H. Li, MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)CrossRefGoogle Scholar
  51. Y.-J. Zheng, S.-Y. Chen, H.-F. Ling, Evolutionary optimization for disaster relief operations: a survey. Appl. Soft Comput. 27, 553–566 (2015)CrossRefGoogle Scholar
  52. E. Zitzler, L. Thiele, An evolutionary algorithm for multiobjective optimization: the strength Pareto approach (1998)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Amit Kumar Das
    • 1
  • Debasish Das
    • 1
  • Dilip Kumar Pratihar
    • 1
    Email author
  1. 1.Indian Institute of Technology KharagpurKharagpurIndia

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