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Metaheuristics are commonly employed as a means of solving many distinct kinds of optimization problems. Several natural-process-inspired metaheuristic optimizers have been introduced in the recent years. The convergence, computational burden and statistical relevance of metaheuristics should be studied and compared for their potential use in future algorithm design and implementation. In this paper, eight different variants of dragonfly algorithm, i.e. classical dragonfly algorithm (DA), hybrid memory-based dragonfly algorithm with differential evolution (DADE), quantum-behaved and Gaussian mutational dragonfly algorithm (QGDA), memory-based hybrid dragonfly algorithm (MHDA), chaotic dragonfly algorithm (CDA), biogeography-based Mexican hat wavelet dragonfly algorithm (BMDA), hybrid Nelder-Mead algorithm and dragonfly algorithm (INMDA), and hybridization of dragonfly algorithm and artificial bee colony (HDA) are applied to solve four industrial chemical process optimization problems. A fuzzy multi-criteria decision making tool in the form of fuzzy-measurement alternatives and ranking according to compromise solution (MARCOS) is adopted to ascertain the relative rankings of the DA variants with respect to computational time, Friedman's rank based on optimal solutions and convergence rate. Based on the comprehensive testing of the algorithms, it is revealed that DADE, QGDA and classical DA are the top three DA variants in solving the industrial chemical process optimization problems under consideration. [ABSTRACT FROM AUTHOR]

In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete (Diagonalization complete) and H-complete (Hypercomputation complete) classes. In the paper, in the spirit of Cook/Levin/Karp, we started the population process of these new classes assigning several undecidable problems to them. We justify that some super-Turing models of computation, i.e., models going beyond Turing machines, are tremendously expressive and they allow to accept arbitrary languages over a given alphabet including those undecidable ones. We prove also that one of such super-Turing models of computation - the $-Calculus, designed as a tool for automatic problem solving and automatic programming, has also such tremendous expressiveness. We investigate also completeness of cost metrics and meta-search algorithms in $-calculus. [ABSTRACT FROM AUTHOR]