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A sequential surrogate-based multiobjective optimization method: effect of initial data set

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Abstract

Process optimization based on high-fidelity computer simulations or real experimentation is commonly expensive. Therefore, surrogate models are frequently used to reduce the computational or experimental cost. However, surrogate models need to achieve a maximum accuracy with a limited number of sampled points. Sequential sampling is a procedure in which sequentially surrogates are fitted and each surrogate defines the points that need to be sampled and used to fit the next model. For optimization purposes, points are sampled on regions of high potential for the optimal solutions. In this work, we first compared the effect of using different initial sets of points (experimental designs) in a sequential surrogate-based multiobjective optimization method. The optimization method is tested on five benchmark problems and the performance is quantified based on the total number of function evaluations and the quality of the final Pareto Front. Then an industrial applications on titanium welding is presented to show the use of the method. The case study is based on real experimental data.

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Acknowledgements

The authors gratefully acknowledge the financial support by the Mexican National Council for Science and Technology (CONACYT) through the PhD. Scholarship of J.D. Mosquera-Artamonov. The author also would like to thank Professor Mauricio Cabrera-Rios for early contributions on the development of the optimization method used here.

Author information

Authors and Affiliations

  1. Modeling Optimization and Computing Technology SAS de CV, Monterrey, NL, Mexico

    Maria Guadalupe Villarreal-Marroquin

  2. Posgrado en Ingenieria de Sistemas, Universidad Autonoma de Nuevo Leon, Monterrey, NL, Mexico

    Jose Daniel Mosquera-Artamonov

  3. Gerencia de Manufactura y Procesos Especiales, Centro de Ingenieria y Desarrollo Industrial, Estado de Mexico, Edomex, Mexico

    Celso E. Cruz

  4. Integrated Systems Engineering Department, The Ohio State University, Columbus, OH, USA

    Jose M. Castro

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  1. Maria Guadalupe Villarreal-Marroquin
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  2. Jose Daniel Mosquera-Artamonov
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  3. Celso E. Cruz
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Correspondence to Jose Daniel Mosquera-Artamonov.

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Appendix A

Appendix A

See the Figs. 7, 8, 9, 10, 11, 12, 13 and 14.

Fig. 7
figure 7

Comparison of final Pareto Sets for MOP1: a True (dark gray), b CCI (o), c LHD (+), d D-Opt (x), e Rand (\(*\)), f Sobol-Seq (\(\diamond\)). Different colors (light blue, blue, purple, orange, yellow, green) represent the different repeats (Color figure online)

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Fig. 8
figure 8

Comparison of final Pareto Fronts for MOP1: a True (dark gray), b CCI (o), c LHD (+), d D-Opt (x), e Rand (\(*\)), f Sobol-Seq (\(\diamond\)). Different colors (light blue, blue, purple, orange, yellow, green) represent the different repeats (Color figure online)

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Fig. 9
figure 9

Comparison of final Pareto Sets for MOP2: a True (dark gray), b CCI (o), c LHD (+), d D-Opt (x), e Rand (\(*\)), f Sobol-Seq (\(\diamond\)). Different colors (light blue, blue, purple, orange, yellow, olive) represent the different repeats (Color figure online)

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Fig. 10
figure 10

Comparison of final Pareto Fronts for MOP2: a True (dark gray), b CCI (o), c LHD (+), d D-Opt (x), e Rand (\(*\)), f Sobol-Seq (\(\diamond\)). Different colors (light blue, blue, purple, orange, yellow, olive) represent the different repeats (Color figure online)

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Fig. 11
figure 11

Comparison of final Pareto Sets for MOP3: a True (dark gray), b CCI (o), c LHD (+), d D-Opt (x), e Rand (\(*\)), f Sobol-Seq (\(\diamond\)). Different colors (light blue, blue, purple, orange, yellow, olive) represent the different repeats (Color figure online)

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Fig. 12
figure 12

Comparison of final Pareto Fronts for MOP3: a True (dark gray), b CCI (o), c LHD (+), d D-Opt (x), e Rand (\(*\)), f Sobol-Seq (\(\diamond\)). Different colors (light blue, blue, purple, orange, yellow, olive) represent the different repeats (Color figure online)

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Fig. 13
figure 13

Comparison of final Pareto Sets for MOP4: a True (dark gray (\(x_3=0.5\))), b CCI (o), c LHD (+), d D-Opt (x), e Rand (\(*\)), f Sobol-Seq (\(\diamond\)). Different colors (light blue, blue, purple, magenta, scarlet, orange, yellow, olive, green) represent different repeats (Color figure online)

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Fig. 14
figure 14

Comparison of final Pareto Fronts for MOP4: a True (dark gray), b CCI (o), c LHD (+), d D-Opt (x), e Rand (\(*\)), f Sobol-Seq (\(\diamond\)). Different colors (light blue, blue, purple, magenta, scarlet, orange, yellow, olive, green) represent different repeats (Color figure online)

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Villarreal-Marroquin, M.G., Mosquera-Artamonov, J.D., Cruz, C.E. et al. A sequential surrogate-based multiobjective optimization method: effect of initial data set. Wireless Netw 26, 5727–5750 (2020). https://doi.org/10.1007/s11276-019-02212-2

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