An analysis of the XOR dynamic problem generator based on the dynamical system

This is the post-print version of the article - Copyright @ 2010 Springer-VerlagIn this paper, we use the exact model (or dynamical system approach) to describe the standard evolutionary algorithm (EA) as a discrete dynamical system for dynamic optimization problems (DOPs). Based on this dynamical system model, we analyse the properties of the XOR DOP Generator, which has been widely used by researchers to create DOPs from any binary encoded problem. DOPs generated by this generator are described as DOPs with permutation, where the fitness vector is changed according to a permutation matrix. Some properties of DOPs with permutation are analyzed, which allows explaining some behaviors observed in experimental results. The analysis of the properties of problems created by the XOR DOP Generator is important to understand the results obtained in experiments with this generator and to analyze the similarity of such problems to real world DOPs.This work was supported by Brazil FAPESP under Grant 04/04289-6 and by UK EPSRC under Grant EP/E060722/2

On the Incommensurate Phase of Pure and Doped Spin-Peierls System CuGeO_3

Phases and phase transitions in pure and doped spin-Peierls system CuGeO_3 are considered on the basis of a Landau-theory. In particular we discuss the critical behaviour, the soliton width and the low temperature specific heat of the incommensurate phase. We show, that dilution leads always to the destruction of long range order in this phase, which is replaced by an algebraic decay of correlations if the disorder is weak.Comment: 4 pages revtex, no figure