Método de interseção normal à fronteira por escores rotacionados em espaço elíptico de solução

Abstract

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.