Based on a geometric theory of evolutionary algorithms, it was shown that all evolutionary algorithms equipped with a geometric crossover and no mutation operator do the same kind of convex search across representations, and that they are well-matched with generalised forms of concave fitness landscapes for which they provably find the optimum in polynomial time [13]. Analysing the landscape structure is essential to understand the relationship between problems and evolutionary algorithms. This paper continues such investigations by considering the following challenge: develop an analytical method to recognise that the fitness landscape for a given problem provably belongs to a class of concave fitness landscapes. Elementary landscapes theory provides analytic algebraic means to study the landscape structure [15]. This work begins linking both theories to better understand how such method could be devised using elementary landscapes. Examples on the well known One Max, Leading Ones, Not-All-Equal Satisfiability and Weight Partition problems illustrate the fundamental concepts supporting this approach.
CITATION STYLE
García, M. D., & Moraglio, A. (2018). Bridging elementary landscapes and a geometric theory of evolutionary algorithms: First steps. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11102 LNCS, pp. 194–206). Springer Verlag. https://doi.org/10.1007/978-3-319-99259-4_16
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