Uniform mixture design via evolutionary multi-objective optimization
Por:
Menchaca-Mendez, Adriana, Zapotecas-Martinez, Saul, García-Velázquez L.M., Coello Coello, Carlos A.
Publicada:
1 feb 2022
Resumen:
Design of experiments is a branch of statistics that has been employed
in different areas of knowledge. A particular case of experimental
designs is uniform mixture design. A uniform mixture design method aims
to spread points (mixtures) uniformly distributed in the experimental
region. Each mixture should meet the constraint that the sum of its
components must be equal to one. In this paper, we propose a new method
to approximate uniform mixture designs via evolutionary multi-objective
optimization. For this task, we formulate three M-objective optimization
problems whose Pareto optimal fronts correspond to a mixture design of M
components (or dimensions). In order to obtain a uniform mixture design,
we consider six well-known algorithms used in the area of evolutionary
multi-objective optimization to solve M-objective optimization problems.
Thus, a set of solutions approximates the entire Pareto front of each
M-objective problem, while it implicitly approximates a uniform mixture
design. We evaluate our proposed methodology by generating mixture
designs in two, three, and up to eight dimensions, and we compare the
results obtained concerning those produced by different methods
available in the specialized literature. Our results indicate that the
proposed strategy is a promising alternative to approximate uniform
mixture designs. Unlike most of the existing approaches, it obtains
mixture designs for an arbitrary number of points. Moreover, the
generated design points are properly distributed in the experimental
region.& nbsp;
Filiaciones:
Menchaca-Mendez, Adriana:
Technologies for Information in Science, ENES, Campus Morelia, UNAM, Morelia, Michoacán, Mexico
UNAM, Unidad Morelia, ENES, Technol Informat Sci, Morelia, Michoacan, Mexico
Zapotecas-Martinez, Saul:
Departamento de Matemáticas Aplicadas y Sistemas UAM, Unidad CuajimalpaCiudad de México, Mexico
Dept Matemat Aplicadas & Sistemas UAM, Unidad Cuajimalpa, Ciudad De Mexico, Mexico
García-Velázquez L.M.:
Technologies for Information in Science, ENES, Campus Morelia, UNAM, Morelia, Michoacán, Mexico
Coello Coello, Carlos A.:
Evolutionary Computation Group, CINVESTAV, IPN, Ciudad de México, Mexico
IPN, Evolutionary Computat Grp, CINVESTAV, Ciudad De Mexico, Mexico
Bronze, All Open Access; Bronze
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