Performance Evaluation of Non-Linear Optimization Methods Via Pairwise Comparison and Fuzzy Numbers

摘要

In this paper the author extends the deterministic performance evaluation of non-linear optimization methods. A pairwise comparison is done using fuzzy estimates of the performance ratios to obtain fuzzy final scores of the methods under consideration. The key instrument is the concept of fuzzy numbers with triangular membership functions. The algebraic operations on them are simple extensions of the operations on real numbers; they are exact in the parameters (lower, modal, and upper values), not necessarily exact in the shape of the membership function. The fuzzy performance evaluation is illustrated by the ranking and rating of well-known non-linear optimization methods, using the results of some recent test batteries.