Dynamic Parameter Adaptation for Meta-Heuristic Optimization Algorithms Through Type-2 Fuzzy Logic by Frumen Olivas Fevrier Valdez Oscar Castillo & Patricia Melin

Author:Frumen Olivas, Fevrier Valdez, Oscar Castillo & Patricia Melin
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Original GSA

FGSA with parameter adaptation

Best

1.5346

9.5827e−8

Worst

4.1710

4.1371e−7

Average

2.7181

2.1254e−7

Standard deviation

0.7513

5.6615e−8

From Table 5.14, FGSA, which has the proposed methodology for parameter adaptation, can obtain better results than the original GSA method and obtain the best controller of all; also, the worst controller is better than the best controller of the original GSA method and obtains the best average of 30 experiments and the lower standard deviation.

This benchmark problem of the optimization of a fuzzy controller has been studied by Cervantes et al. [9], where they use a hierarchical genetic algorithm (HGA) and its best experiment was of 9.6e−5, which is a good result but compared with our best experiment which is 9.5827e−8, even our worst experiment is better that the proposed in [9].

The best fuzzy system, which represents the best experiment from Table 5.14, is the fuzzy system illustrated in Fig. 5.4, and its error is 9.5827e−8, this is with the use of the proposed methodology for parameter adaptation GSA can optimize the membership functions from the fuzzy system illustrated in Fig. 3.​8 which error is 2.7758.

Fig. 5.4Best fuzzy system used for control the temperature in a shower

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