Theoretical foundations of evolutionary computation
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In recent decades, evolutionary algorithms have been used successfully to solve a wide range of optimization problems. However, a review of the literature suggests that the theoretical works on evolutionary algorithms are still lagging behind their applications. This special issue features three of the latest theoretical contributions, each representing a different theoretical aspect of evolutionary algorithms. These three papers were initially selected from SEAL’06 and further extended from the authors’ original works. The extended papers were again rigorously reviewed in two rounds by at least three anonymous reviewers. In the first paper, Mitavskiy, Rowe, Wright and Schmitt present a study of the properties of Markov chains modelling evolutionary algorithms, by using a quotient construction method. This innovative Markov chains quotient construction method provides a simpler way for deduction of known and new results than existing methods. In the second paper, Zhou, Heckendorn and Sun describe a mathematic model of epistatic discovery, which extends from early works on binary parameter space to parameters of higher cardinality. The authors also extend Walsh transform techniques to general discrete Fourier transform methods, and are able to derive new properties about these Fourier transforms for higher cardinality models. This study shows that understanding the epistatic structure of the parameter space of a problem plays an important role in designing suitable and competent evolutionary algorithms. In the third paper, from the perspective of population genetics, Whigham and Dick describe a general model of selection via the Moran process (where spatial structure is defined by a graph). Using this model they examine several parent selection methods and their effects on fixation probabilities, which have significant relevance to fine-grained spatially-structured evolutionary algorithms.