Resumo:
Several factors affect the performance of the Normal Border Intersection Method (NBI)
when employed in the optimization of multiple response surfaces. Such factors cause discontinuities
in the Pareto-optimal solution set, instability in the detection of solutions
in continuous space and the inversion of the original sense of relationship between the
various objective functions. After an extensive research period, three fundamental causes
for these inconsistencies were detected: (a) the presence of correlation between objective
functions as well as their neglect, (b) the definition of anchor points, utopia and Nadir
outside the regions. of confidence associated with the experimental data caused by the
individual optimization step and (c) the nature of the initialization points of the gradient
algorithm used to find the solutions of the multiobjective problem in each desired weight
vector. To minimize the influence of these factors, the original method was modified to
allow for the inclusion of elliptic constraints based on multivariate quadratic distance, and
to replace the original objective functions with other independent functions - obtained by
response surfaces of rotating factor scores with angles of diversified rotation. To improve
the stability in finding and finding viable solutions for each weight of interest, we used
a diffuse initialization process in which a matrix of viable initial solutions were tested a
priori. For all tests, the quality of the obtained solutions was evaluated by calculating the
Mahalanobis distance for the various solution vectors. This proposal was tested with twoand
multi-dimensional assemblies associated with the H13 hardened steel turning process
and the results were extremely satisfactory. During simulations with the experimental
models obtained, it was identified that the emergence of correlation structures between
stochastic objective functions is due, in large part, to a relationship between the amplitudes
attributed to the decision variables within the experimental arrangements. Such
simulations emphasize that natural correlations can become stronger depending on the
amplitudes chosen for the input variable levels.
