General type-2 fuzzy logic in dynamic parameter adaptation for the harmony search algorithm (Q1989250)

The publication offers a concise exposure to a useful synergy of one of the metaheuristics such as harmony search (HS) and the technology of fuzzy sets. The design of the HS algorithm involves three hyperparameters such as harmony memory ($r_{\textit{accept}}$), pitch adjustment rate ($p_{\text{Arate}}$) and randomization whose values impact the performance of the method. The crux of the proposed approach is to endow the HS with fuzzy sets by forming a sound strategy of adjustments of the values of the hyperparameters. The strategy is expressed through a collection of rules whose conditions concern the current environment of the search and conclusions deal with the hyperparameters of the optimization method, for instance ``if iteration is \textit{low} then harmony memory acceptance is \textit{low}'' (where iteration=current\(_-\)iteration/ maximum\(_-\)iteration) and the terms \textit{low} and \textit{high} are quantified in the form of fuzzy sets. Both Mamdani and Takagi-Sugeno rule-based models are investigated and type-1 and type-2 fuzzy sets are studied. The material of the publication is self-contained. Its organization is coherent and provides a thorough top-down exposure of the topics. Chapter 1 presents a brief introduction to optimization strategies. Chapter 2 focuses on the description of the HR algorithm. The augmented fuzzy HR is covered in Chapter 3. Various simulation studies are presented in Chapter 4 while conclusions are presented in Chapter 5. The reported experiments (Chapter 4) fall under the two categories: they show the use of the augmented HR optimization to determine minima of nonlinear functions coming from the benchmark studies CEC 2015 and CEC 2017 and present the realization of control strategies for commonly studied nonlinear control benchmarks including ball and beam and inverted pendulum. The comparative analysis is also covered including pertinent statistical testing demonstrating the advantages of the fuzzy set augmentation of the HS over the generic HS method. Overall, the material could be of interest to readers looking for enhancements of existing metaheuristics, especially when being applied to challenging optimization problems.