Modeling and Optimization: Theory and Applications by Luis F. Zuluaga & Tamás Terlaky

Author:Luis F. Zuluaga & Tamás Terlaky
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

4.4 Results of Underdetermined Simplex Gradient Descent

Table 2 shows the results of applying the USGD initialization procedure and the two other alternatives (SS and DS) on the 200-D test problems. Table 3 shows the results of applying USGD-Fast and the other methods on the 1000-D problems. Note that the simple modification provided by DS already yields large improvements on the best objective function value over SS. However, USGD and USGD-Fast yield even better improvements over DS on 15 of the 16 problems (all except the Keane problem). Moreover, on the Keane problem, DS is only slightly better than USGD or USGD-Fast. These results suggest that moving in the direction that makes an acute angle with the negative simplex gradient during the initialization phase for a surrogate-based optimization method results in significant improvement on the objective function value on high-dimensional problems.Table 2Mean and standard error of the best objective function values in 30 trials for three initialization strategies for surrogate-based optimization methods on GWB72 and on the 200-D problems

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