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Toward a robust optimal point selection: a multiple-criteria decision-making process applied to multi-objective optimization using response surface methodology

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Abstract

During the multi-objective optimization process, numerous efficient solutions may be generated to form the Pareto frontier. Due to the complexity of formulating and solving mathematical problems, choosing the best point to be implemented becomes a non-trivial task. Thus, this paper introduces a weighting strategy named robust optimal point selection, based on ratio diversification/error, to choose the most preferred Pareto optimal point in multi-objective optimization problems using response surface methodology. Furthermore, this paper proposes to explore a theoretical gap—the prediction variance behavior related to the weighting. The ratios Shannon’s entropy/error and diversity/error and the unscaled prediction variance are experimentally modeled using mixture design and the optimal weights for the multi-objective optimization process are defined by the maximization of the proposed measures. The study could demonstrate that the weights used in the multi-objective optimization process influence the prediction variance. Furthermore, the use of diversification measures, such as entropy and diversity, associated with measures of error, such as mean absolute percent error, was determined to be useful in mapping regions of minimum variance within the Pareto optimal responses obtained in the optimization process.

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Acknowledgements

The authors would like to express their gratitude to CAPES, CNPq and FAPEMIG for their financial support and research incentive.

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Correspondence to Paulo Rotela Junior.

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Rocha, L.C.S., Rotela Junior, P., Aquila, G. et al. Toward a robust optimal point selection: a multiple-criteria decision-making process applied to multi-objective optimization using response surface methodology . Engineering with Computers (2020). https://doi.org/10.1007/s00366-020-00973-5

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Keywords

  • Multi-objective programming
  • Multi-criteria analysis
  • Robust optimal point selection (ROPS)
  • Diversification measures
  • Error measures