Performance Evaluation of Non-Linear Optimization Methods via Multi-Criteria Decision Analysis and via Linear Model Analysis

摘要

This report shows how Saaty's priority theory for pairwise comparison can be used to evaluate the performance of non-linear optimization methods. First, priorities are assigned to the predominant performance criteria: generality, robustness, efficiency, capacity, simplicity of use, and program organization. Thereafter, the comparative studies of non-linear optimization codes are used to assign weights to the methods under each of the performance criteria separately. Here, Saaty's eigenvector method is modified, and logarithmic regression is employed in order to deal with incomplete and multiple pairwise comparisons. The procedure outlines what performance evaluation can do and what it cannot do: it demonstrates how multi-criteria decision analysis can be used for an integrated assessment of optimization methods, taking into account both the performance criteria of decision makers and the results of comparative studies. Finally, it is shown that efficiency weights can be obtained from these studies by the analysis of variance.