Fuzzy Performance Evaluation of Nonlinear Optimization Methods, with Sensitivity Analysis of the Final Scores

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Abstract
We employ pairwise-comparison methods in the two-level decision problem of weighing five nonlinear optimization algorithms (geometric programming and four general methods) under conflicting performance criteria. First, we show that the stimuli in a single-level problem have a scale-independent rank order if the judgemental statements are put on ratio scales with geometric progression. We use the leading comparative studies in nonlinear optimization to obtain preference ratios (robustness ratios, efficiency ratios,…), and we calculate final scores for the five alternatives on various scales to demonstrate that the scale sensitivity is low. Next, we describe a fuzzy pairwise-comparison method. The key instrument is the concept of fuzzy numbers with triangular membership functions. Under the assumption that the preference ratios have a uniform degree of fuzziness, we find a simple, analytical expression for the fuzzy final scores of the alternatives, and we develop a scale-independent measure to test whether the superiority of the leading alternative (the algorithm with quadratic approximations) is significant.