Bridging Elementary Landscapes and a Geometric Theory of Evolutionary Algorithms: First Steps
Diez García, Marcos; Moraglio, Alberto
Date: 21 August 2018
Conference paper
Publisher
Springer
Publisher DOI
Abstract
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 ...
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. 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 landscapes structure. This work begins linking both theories to better understand how such method could be devised using elementary landscapes. Examples on well known One Max, Leading Ones, Not-All-Equal Satisfiability and Weight Partitioning problems illustrate the fundamental concepts supporting this approach.
Computer Science
Faculty of Environment, Science and Economy
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