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<p>Simultaneous optimisation of multiple design characteristics (or ‘responses’) derived from a process is critical to ensure product quality. Due to the correlations between these responses, multiple non-dominated Pareto trade-off solutions (or process-setting conditions) are inevitable. Such optimisation problems are categorised as ‘multiple response optimisation (MRO)’ problems. In the context of MRO, considering response predictive uncertainties and determining robust Pareto solutions is always challenging for decision-makers. Yet, there is little evidence of work that explores the potential of different Multi-Objective Optimisation (MOO) algorithms to derive robust solutions for complex real-life MRO problems, considering predictive response uncertainties. The efficiency of an MOO algorithm can define the quality of feasible and implementable near-optimal solutions. This study attempts to compare and contrast the performance and efficiency of different MOO algorithms, broadly classified based on sources of inspiration (viz. swarm intelligence, human behaviour, physics, evolutionary), applied to three different ‘<i>mean’</i> and four different <i>‘mean–variance’</i> continuous, and two different <i>‘mean–variance’</i> mixed-integer real-life MRO problems. In addition, a modified Non-dominated Sorting Genetic Algorithm III (NSGA-III), based on Tabu search (TS), is proposed to enhance the balance between search intensification and diversification strategy. The performance and efficiency of these algorithms are measured based on recommended metrics, viz., average hypervolume, worst-case weighted mean square error, worst-case Mahalanobis Distance, and signal-to-noise (S/N) ratio. Multi-criteria decision-making (MCDM) techniques are used to rank the MOO algorithms. The findings indicate consistent rank superiority of Speed-constrained Multi-objective Particle Swarm Optimisation (SMPSO), Multi-Objective Individualised-Instruction Teaching–Learning-Based Optimisation (INM-TLBO), and the modified NSGA-III algorithm for varied ‘<i>mean</i>’ and ‘<i>mean–variance</i>’ MRO problems.</p>

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A comparative study to enhance decision-making for multi-objective ‘mean’ and ‘mean–variance’ optimisation of multiple responses considering predictive uncertainties

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Abhinav Kumar Sharma,
  • Indrajit Mukherjee,
  • Felix T. S. Chan,
  • Raghu Nandan Sengupta

摘要

Simultaneous optimisation of multiple design characteristics (or ‘responses’) derived from a process is critical to ensure product quality. Due to the correlations between these responses, multiple non-dominated Pareto trade-off solutions (or process-setting conditions) are inevitable. Such optimisation problems are categorised as ‘multiple response optimisation (MRO)’ problems. In the context of MRO, considering response predictive uncertainties and determining robust Pareto solutions is always challenging for decision-makers. Yet, there is little evidence of work that explores the potential of different Multi-Objective Optimisation (MOO) algorithms to derive robust solutions for complex real-life MRO problems, considering predictive response uncertainties. The efficiency of an MOO algorithm can define the quality of feasible and implementable near-optimal solutions. This study attempts to compare and contrast the performance and efficiency of different MOO algorithms, broadly classified based on sources of inspiration (viz. swarm intelligence, human behaviour, physics, evolutionary), applied to three different ‘mean’ and four different ‘mean–variance’ continuous, and two different ‘mean–variance’ mixed-integer real-life MRO problems. In addition, a modified Non-dominated Sorting Genetic Algorithm III (NSGA-III), based on Tabu search (TS), is proposed to enhance the balance between search intensification and diversification strategy. The performance and efficiency of these algorithms are measured based on recommended metrics, viz., average hypervolume, worst-case weighted mean square error, worst-case Mahalanobis Distance, and signal-to-noise (S/N) ratio. Multi-criteria decision-making (MCDM) techniques are used to rank the MOO algorithms. The findings indicate consistent rank superiority of Speed-constrained Multi-objective Particle Swarm Optimisation (SMPSO), Multi-Objective Individualised-Instruction Teaching–Learning-Based Optimisation (INM-TLBO), and the modified NSGA-III algorithm for varied ‘mean’ and ‘mean–variance’ MRO problems.