Comparison of NSGA-II and MODE performances by using MCDM methods for multi-response experimental data

Abstract

Multi-response experimental data, composed with more than one response variable, can be ex-amined in three stages: modeling, optimization and decision making. In this study, these three stages were considered sequentially. Model parameters were estimated through Seemingly Unrelated Regression (SUR) method due to linear correlation between responses during the modeling stage. In the optimization stage, simultaneous optimization of predicted multiple responses were considered as a multi-objective optimization (MOO) problem. For this purpose, Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Multi Objective Differential Evolution (MODE), were applied to obtain Pareto solution sets. In the decision making stage, compromise solution was chosen from the Pareto sets through various multi-criteria decision making (MCDM) methods. This study aims to compare performances of the NSGA-II and the MODE via various MCDM methods using three real data sets taken from different fields. The novelty of this paper is applying the MCDM methods to the Pareto solution set to choose a compromise solution by taking into account the Entropy weights of responses primarily. Afterwards, closeness of the compromise solution to the ideal solution using the mean absolute error (MAE) and the root mean square error (RMSE) metrics is calculated for decision making on the performance of the MOO methods. The results showed that compromise solution of the MODE is closer to the ideal solution than the NSGA-II according to the MAE and RMSE metrics. As a result, the MODE outperforms the NSGA-II.

Keywords

• Multi-response Experimental Data
• NSGA-II
• MODE
• MCDM

References

1. REFERENCES
2. [1] Zellner A. An efficient method of estimating seemingly unrelated regressions and tests of aggregation bias. J Am Stat Assoc 1962;57:348–368. [CrossRef]
3. [2] Liu A. Efficient estimation of two seemingly unrelated regression equations. J Multivar Anal 2002;82:445–456. [CrossRef]
4. [3] Bera S, Barman G, Mukherjee I. Effect of seemingly unrelated regression-based modeling approach on solution quality for correlated multiple response optimization problems. Proceedings of the 2011 IEEE IEEM. 2011. p. 1490–1494. [CrossRef]
5. [4] Costa N, Lourenço J, Pereira ZL. Responses modeling and optimization criteria impact on the optimization of multiple quaility characteristics. Comput Ind Eng 2012;62:927–935. [CrossRef]
6. [5] Rout SK, Hussein AK, Mohanti CP. Multi-objective optimization of a three-dimensional internally finned tube based on response surface methodology(RSM). Therm Eng 2015;1:131–145. [CrossRef]
7. [6] Shah HK, Montgomery DC, Carlyle WM. Response surface modeling and optimization in multiresponse experiments using seemingly unrelated regression. Qual Eng 2004;16:387–397. [CrossRef]
8. [7] Akçay H, Anagün AS. Multiresponse optimization application on a manufacturing factory. Math Comput Appl 2013;18:531–538. [CrossRef]

9. [8] Shivakoti I, Kalita K, Kibria G, Sharma A, Pradhan BB, Ghadai RK. Parametric analysis and multi response optimization of laser surface texturing of titanium super alloy. J Braz Soc Mech Sci Eng 2021;43:400. [CrossRef]
10. [9] Tunçel S. Çok yanıtlı deneysel verilerin görünüşte ilişkisiz regresyon analizi ile modellenmesi ve optimal değişken değerlerinin belirlenmesi (Yüksek lisans tezi). Ankara: Ankara Üniversitesi; 2022.
11. [10] Türkşen Ö. Optimization and decision making stages for multiple responses: an application of NSGA-II and FCM clustering algorithm. Gazi Univ J Sci 2015;28:321–330.
12. [11] Türkşen Ö, Vural N. Analyses of replicated spectophotometric data by using soft computing methods. J Iran Chem Soc 2020;17:2651–2661. [CrossRef]
13. [12] Yıldırım A, Güneş F, Belen MA. Differential evolution optimization applied to the performance analysis of a microwave transistor. Sigma J Eng Nat Sci 2017;8:135–144.
14. [13] Lu J, Feng X, Han Y, Xue C. Optimization of subcritical fluid extraction of carotenoids and chlorophyll a from Laminaria japonica aresh by response surface methodology. J Sci Food Agric 2014;94:139–145. [CrossRef]
15. [14] Deb K. Multi objective optimization using evolutionary algorithms. New York: John-Wiley and Sons; 2001. p. 497.
16. [15] Bektaş G, Niğdeli SM, Yücel M, Kayabekir AE. Yapay Zeka Optimizasyon Algoritmaları ve Mühendislik Uygulamaları. Ankara: Seçkin Yayıncılık; 2021. [Turkish]
17. [16] Karaboğa D. Yapay Zeka Optimizasyon Algoritmaları. Ankara: Nobel Yayınları; 2020. [Turkish]
18. [17] Esfe MH, Hajmohammad H, Moradi R, Arani AAA. Multi-objective optimization of cost and thermal performance of double walled carbon nanotubes/ water nanofluids by NSGA-II using response surface method. Appl Therm Eng 2017;112:1648–1657. [CrossRef]
19. [18] Joshi M, Ghadai RK, Madhu S, Kalita K, Gao X. Comparison of NSGA-II,MAOLA and MODA for multi-objective optimization of micro-machining processes. Materials (Basel) 2021;14:5109. [CrossRef]
20. [19] Ravichandran S, Kumudinidevi RP, Bharathidasan SG, Jeba E. Cordinated controller design of grid connected DFIG based wind turbine using response surface methodology and NSGA II. Sustain Energy Technol Assess 2014;8:120–130. [CrossRef]
21. [20] Thirumalai R, Seenivasan M, Panneerselvam K. Experimental investigation and multi response optimization of turning process parameters for inconel 718 using TOPSIS approach. Mater Today Proc 2021;45:467–472. [CrossRef]
22. [21] Torabi SHR, Alibabaei S, Bonab BBM, Sadeghi H, Faraji G. Design and optimization of turbine blade preform forging using RSM and NSGA II. J Intell Manuf 2017;28:1409–1419. [CrossRef]
23. [22] Babu B V, Anbarasu B. Multi-objective differential evolution (MODE): an evolutionary algorithm for multi-objective optimization problems (moops). Proceedings of International Symposium and 58th Annual Session of IIChE, 2005.
24. [23] Souza MN, Silva MA, Machado AR, Lobato FS. Treatment of multi-response surface applied to machinability of stainess steel using multi-objective optimization differential evolution. 21. Brazilian Congress of Mechanical Engineering, 2011.
25. [24] Basu M.: Economic environmental dispatch using multi-objective differential evolution. Appl Soft Comput 2011;11:2845–2853. [CrossRef]
26. [25] Gaitonde VN, Manjaiah M, Maradi S, Karnik SR, Petkar PM, Davim JP. Multiresponse optimization in wire electric discharge machining (WEDM) of HCHCR steel by integrating response surface methodology (RSM) with differential evolution(DE). Comput Methods Eng 2017;199–221. [CrossRef]
27. [26] Monsef H, Naghashzadegen M, Jamali A, Farmani R. Comparison of evolutionary multi objective optimization algorithms in optimum design of water distribution network. Ain Shams Eng 2019;10:103– 111. [CrossRef]
28. [27] Singh GK, Yadava V, Kumar R. Multiresponse optimization of electro-discharge diamond face grinding process using robust design of experiments. Mater Manuf Process 2013;25:851–856. [CrossRef]
29. [28] Zhao W, Ma A, Ji J, Chen X, Yao T. Multiobjective optimization of a double-side linear vernier PM motor using response surface method and differential evolution. IEEE Trans Ind 2020;67:80–90. [CrossRef]
30. [29] Reddy VV. Turning process parameters optimization of al7075 hybrid mmc’s composite using TOPSIS method. Sigma J Eng Nat Sci 2020;38:2043–2055.
31. [30] Yalçın N, Uncu N. Applying EDAS as an applicable mcdm method for industrial robot selection. Sigma J Eng Nat Sci 2019;37:779–796.
32. [31] Bölükbaş U, Güneri AF. A fuzzy multi-criteria decision approach for measuring technology competency performance of smes. Sigma J Eng Nat Sci 2017;8:31–40.
33. [32] Trung DD. A combination method for multi-criteria decision making problem in turning process. Manuf Rev. 2021;8:1–17. [CrossRef]
34. [33] Pandiyan GK, Prabaharan T, James DJD, Sivalingam V. Machinability Analysis and Optimization of Electrical Discharge Machining in AA6061- T6/15wt.% SiC Composite by the Multi-criteria Decision-Making Approach. J Mater Eng Perform 2022;31:3741–3752. [CrossRef]
35. [34] Khan MM, Dey A. Hybrid MCDM approach for examining the high-stress abrasive wear behaviour of in situ ZA-27/TiCp MMCs. Mater Chem Phys 2022;277:125319. [CrossRef]
36. [35] Patil SB, Patole TA, Jadhav RS, Suryawanshi SS, Raykar SJ. Complex proportional assessment (COPRAS) based multiple-criteria decision making (MCDM) paradigm for hard turning process parameters. Mater Today Proc 2022;59:835–840. [CrossRef]
37. [36] Rahman Z, Siddiquee AN, Khan AZ, Ahmad S. Multi-response optimization of FSP parameters on mechanical properties of surface composite, Mater Today Proc 2022;62:5–8. [CrossRef]
38. [37] Somasundaram M, Kumar JP. Multi response optimization of EDM process parameters for biodegradable AZ31 magnesium alloy using TOPSIS and grey relational analysis. Sādhanā 2022;47:136. [CrossRef]
39. [38] Divya C, Raju LS, Singaravel B. Application of mcdm methods for process parameter optimization in turning process-a review. Recent Trends in Mechanical Engineering. Singapore: Springer; 2021. p. 199–207. [CrossRef]
40. [39] Bagal DK, Giri A, Pattanaik AK, Jeet S, Barua A, Panda SN. MCDM optimization of characteristics in resistance spot welding for dissimilar meterials utilizing advanced hybrid taguchi method-coupled CoCoSo, EDAS and WASPAS method. Next Generation Meterials and Processing Technologies. Singapore: Springer; 2020. [CrossRef]
41. [40] Abhilash P, Chakradhar D. Multi-response optimization of wire EDM of inconel 718 using a hybrid entropy weighted GRA-TOPSIS method. Process Integr Optim Sustain 2022;6:61-72. [CrossRef]
42. [41] Singh A, Prapoorna Biligiri K, Venkatesh Sampath P. Development of framework for ranking pervious concrete pavement mixtures: application of multi-criteria decision-making methods. Int J Pavement Eng 2022;24:2021406. [CrossRef]
43. [42] Kuo Y, Yang T, Huang GW. The use of grey relational analysis in solving multiple attribute decision-making problems, Comput Ind Eng 2008;55:80–93. [CrossRef]
44. [43] Deb K, Pratab A, Agarwal S, Meyarivan T. Fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans Evol Comput 2002;6:182–197. [CrossRef]
45. [44] Storn R, Price K. Differential evolution- a simple and efficient adaptive scheme for global optimization over continuous spaces. J Glob Optim 1997;11:341– 359. [CrossRef]
46. [45] Shannon CE. A mathematical theory of communication. Bell Syst Tech J 1948;27:379–423. [CrossRef]
47. [46] Zavadskas EK, Podvezko V. Integrated determination of objective criteria weights in MCDM. Int J Inf Technol Decis Mak 2016;15:267–283. [CrossRef]
48. [47] Gül Ş, Fırat M. Determination of priority regions for rehabilitation in water networks by multiple criteria decision making methods. Sigma J Eng Nat Sci 2020;38:1481–1494.
49. [48] Hwang CL, Yoon K. Multiple Attribute Decision Making: Methods and Applications. New York: Springer- Verlag; 1981. [CrossRef]
50. [49] Chen C. Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst. 2000;114:1–9. [CrossRef]
51. [50] Opricovic S, Tzeng G. Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 2004;156:445–455. [CrossRef]
52. [51] Zavadskas EK, Kaklauskas A, Sarka V. The new method of multi-criteria Complex Proportional Assessment (COPRAS) of Projects. Technol Econ Dev Econ 1994;1:131-139.
53. [52] Chakraborty S, Zavadskas EK, Antucheviciene J. Applications of WASPAS method as a multi-criteria decision-making tool. Econ Comput Econ Cyber Studi Res 2015;49:5–22.
54. [53] Keshavarz-Ghorabaee M, Zavadskas EK, Olfat L, Turkis Z. Multi-criteria ınventory classification using a new method of evaluation based on distance from average solution (EDAS). Informatica 2015;26:435–451. [CrossRef]
55. [54] Keshavarz-Ghorabaee M, Zavadskas Turkis Z. Antucheviciene, J. A new combinative distance- based assessment (CODAS) method for multi-criteria decision-making. Econ Comp and Econ Cyb Stud Res 2016;50:25–44.
56. [55] Deng J. Control problems of grey systems. Syst Control Lett 1982;5:288-294. [CrossRef]
57. [56] Lin CL. Use of the Taguchi Method and grey relational analysis to optimize turning operations with multiple performance characteristics. Mater Manuf Process 2004;19:209–220. [CrossRef]
58. [57] Pamučar D, Ćirović G. The selection of transport and handling resources in logistics centers using Multi- Attributive Border Approximation area Comparison (MABAC). Expert Syst Appl 2015;42:3016–3028. [CrossRef]
59. [58] Khuri AI, Cornell JA. Response Surfaces: Designs and Analyses. New York: Marcel Dekker; 1996. p. 510.