Abstract
In this paper we extend the deterministic performance evaluation of nonlinear optimization methods: we carry out a pairwise comparison 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. We illustrate the fuzzy performance evaluation by the ranking and rating of five methods (geometric programming and four general methods) for solving geometric-programming problems, using the results of recent computational studies. Some general methods appear to be leading, an outcome which is not only due to their performance under subjective criteria like domain of applications and conceptual simplicity of use; they also score higher under more objective criteria like robustness and efficiency.
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Lootsma, F.A. Performance evaluation of nonlinear optimization methods via pairwise comparison and fuzzy numbers. Mathematical Programming 33, 93–114 (1985). https://doi.org/10.1007/BF01582014
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DOI: https://doi.org/10.1007/BF01582014