A Unifying View on Recombination Spaces and Abstract Convex Evolutionary Search [chapter]

Marcos Diez García, Alberto Moraglio
2019 Lecture Notes in Computer Science  
Previous work proposed to unify an algebraic theory of fitness landscapes and a geometric framework of evolutionary algorithms (EAs). One of the main goals behind this unification is to develop an analytical method that verifies if a problem s landscape belongs to certain abstract convex landscape classes, where certain recombination-based EAs (without mutation) have polynomial runtime performance. This paper advances such unification by showing that: (a) crossovers can be formally classified
more » ... cording to geometric or algebraic axiomatic properties; and (b) the population behaviour induced by certain crossovers in recombination-based EAs can be formalised in the geometric and algebraic theories. These results make a significant contribution to the basis of an integrated geometric-algebraic framework with which analyse recombination spaces and recombination based EAs. Keywords: Abstract convex landscape · Abstract convex search · Convex hull closure · Geometric crossover · Recombination P-structure
doi:10.1007/978-3-030-16711-0_12 fatcat:bscffzyxijc7baa46wgarkqu4a