<p>Multi-objective robust optimization is an effective approach to improve product quality in practice. However, uncertainties in experimental data, parameters, and models may lead to Pareto front variability, significantly affecting the robustness of the final optimal solutions. This paper proposes a novel active learning multi-objective optimization method that integrates Gaussian process (GP) modeling, posterior analysis, and Vorob’ev expectation and deviation (ED) techniques to address parameter optimization problems considering the Pareto front uncertainty. First, the active learning modeling approach is used to improve prediction accuracy for both local and global response surfaces. Second, the GP-based conditional simulation is adopted to quantify the response uncertainty. The posterior probability analysis and Vorob’ev ED techniques are adopted to quantify the Pareto front uncertainty and enhance the robustness of Pareto solutions. Finally, the solution with the minimum distance to the ideal solution is selected as the final optimal solution. Numerical and simulation experiments are used to illustrate the effectiveness of the proposed method. The comparison results show that the proposed method obtains more robust solutions with smaller prediction errors and quality loss than the other methods.</p>

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Multi-objective robust optimization using active learning Gaussian process model considering uncertainty on Pareto fronts

  • Zebiao Feng,
  • Jianjun Wang

摘要

Multi-objective robust optimization is an effective approach to improve product quality in practice. However, uncertainties in experimental data, parameters, and models may lead to Pareto front variability, significantly affecting the robustness of the final optimal solutions. This paper proposes a novel active learning multi-objective optimization method that integrates Gaussian process (GP) modeling, posterior analysis, and Vorob’ev expectation and deviation (ED) techniques to address parameter optimization problems considering the Pareto front uncertainty. First, the active learning modeling approach is used to improve prediction accuracy for both local and global response surfaces. Second, the GP-based conditional simulation is adopted to quantify the response uncertainty. The posterior probability analysis and Vorob’ev ED techniques are adopted to quantify the Pareto front uncertainty and enhance the robustness of Pareto solutions. Finally, the solution with the minimum distance to the ideal solution is selected as the final optimal solution. Numerical and simulation experiments are used to illustrate the effectiveness of the proposed method. The comparison results show that the proposed method obtains more robust solutions with smaller prediction errors and quality loss than the other methods.