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A robust multiobjective solution approach for mean-variance optimisation of correlated multiple quality characteristics

Abhinav Kumar Sharma (School of Business Management, Narsee Monjee Institute of Management Studies, Mumbai, India)
Indrajit Mukherjee (Shailesh J Mehta School of Management, Indian Institute of Technology Bombay, Mumbai, India)
Sasadhar Bera (Indian Institute of Management Ranchi, Ranchi, India)
Raghu Nandan Sengupta (Industrial and Management Engineering, Indian Institute of Technology Kanpur, Kanpur, India)

International Journal of Quality & Reliability Management

ISSN: 0265-671X

Article publication date: 24 September 2021

Issue publication date: 17 October 2022




The primary objective of this study is to propose a robust multiobjective solution search approach for a mean-variance multiple correlated quality characteristics optimisation problem, so-called “multiple response optimisation (MRO) problem”. The solution approach needs to consider response surface (RS) model parameter uncertainties, response uncertainties, process setting sensitivity and response correlation strength to derive the robust solutions iteratively.


This study adopts a new multiobjective solution search approach to determine robust solutions for a typical mean-variance MRO formulation. A fine-tuned, non-dominated sorting genetic algorithm-II (NSGA-II) is used to derive efficient multiobjective solutions for varied mean-variance MRO problems. The iterative search considers RS model uncertainties, process setting uncertainties and response correlation structure to derive efficient fronts. The final solutions are ranked based on two different multi-criteria decision-making (MCDM) techniques.


Five different mean-variance MRO cases are selected from the literature to verify the efficacy of the proposed solution approach. Results derived from the proposed solution approach are compared and contrasted with the best solution(s) derived from other approaches suggested in the literature. Comparative results indicate significant superiorities of the top-ranked predicted robust solutions in nondominated frequency, closeness-to-target and response variabilities.

Research limitations/implications

The solution approach depends on RS modelling and considers continuous search space.

Practical implications

In this study, promising robust solutions are expected to be more suitable for implementation than point estimate-based MOO solutions for a real-life MRO problem.


No evidence of earlier research demonstrates the superiority of a MOO-based iterative solution search approach for mean-variance MRO problems by simultaneously considering model uncertainties, response correlation and process setting sensitivity.



The authors would like to thank the anonymous reviewers for many insightful comments and suggestions which helped to improve the quality of the manuscript.


Sharma, A.K., Mukherjee, I., Bera, S. and Sengupta, R.N. (2022), "A robust multiobjective solution approach for mean-variance optimisation of correlated multiple quality characteristics", International Journal of Quality & Reliability Management, Vol. 39 No. 9, pp. 2205-2232.



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