PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES

Abstract

This paper focuses on exploring effect of the step length, used in the line search, computation techniques on the performance of steepest descent (SD) method in the geometry fitting of the 2D measured profiles. To this end, the three step length computation techniques or line search conditions accommodating Weak Wolfe (WWC), Strong Wolfe (SWC) and the exact minimizer finder have been implemented during the fitting process. To test the line search conditions performances, the 2D primitive geometry test set consisting of five different geometries such as circle, square, triangle, ellipse and rectangle have been employed. The 2D profiles of those geometries have been extracted using coordinate measuring machine (CMM) with high precision. For performance assessments, the total number of function evaluations when the SD method-line search condition combination satisfies the required converge tolerance have been used. By means of those data, the performance profiles have been created to conduct reliable and efficient assessments on the line search conditions. The results have shown that the step length computation technique plays a crucial role for the SD method performance. Based on the performance profiles, it has been determined that the fastest line search condition is the WWC. Besides that, it has been revealed that the optimum technique is the exact minimizer finder for the geometry fitting process in the study.