Differential EvolutionSchoolofComputer ScienceandIT,RMiTUniversityMelbourne,AustraliaMarch2015
Differential Evolution School of Computer Science and IT, RMIT University Melbourne, Australia March 2015
OutlineBackgroundBasicsaboutDEDE variantsPerturbationContour matchingRotation invarianceDE parametersNofreelunchtheoremExample questions after reading20/09/2026
20/09/2026 Outline ◼ Background ◼ Basics about DE ◼ DE variants ◼ Perturbation ◼ Contour matching ◼ Rotation invariance ◼ DE parameters ◼ No free lunch theorem ◼ Example questions after reading
BackgroundProposed by Kenneth Price and Rainer Stornin 1995. It has become increasingly popularin the optimization field. A population-based stochastic method forglobal optimization.One key feature is the use of the differentialbetween two randomly chosen vectorsMany DE variants have been developed20/09/2026
Background ◼ Proposed by Kenneth Price and Rainer Storn in 1995. It has become increasingly popular in the optimization field. ◼ A population-based stochastic method for global optimization. ◼ One key feature is the use of the differential between two randomly chosen vectors. ◼ Many DE variants have been developed. 20/09/2026
DE basicsD)ThepopulationPx.g = (xi.si=0,1,,Np-1, g=0,...8max(1)Xi.g =xji,g), j=0,],.,D-1.where Np denotes the number of population vectors,g defines the generation counterandD thedimensionality,i.e.thenumber of parameters.2)Theinitialization of thepopulationviaX ji,. = rand,[0,1) (bj,u-bj,)+ bj,L(2)The D-dimensional initialization vectors, b and bu indicate the lower and upperbounds of the parameter vectors Xij.The random number generator, rand;[o,1), returnsa uniformly distributed random number from within the range [0,1), i.e., O ≤ rand[o,1)< 1.The subscript, j, indicates that a new random value is generated for eachparameter.20/09/2026
DE basics 20/09/2026
DE basics3)Theperturbationof abasevectoryi.byusinga differencevectorbasedmutationVi.g = Yi.g + F (xrl.g -X,2.8(3)to generate a mutation vector vi,g. The difference vector indices, rl and r2, arerandomly selected once per base vector. Setting yi,g = xrO,g defines what is oftencalled classic DE where the basevector is also a randomly chosen population vector.4)DiversityenhancementThe classic variant of diversity enhancement is crossover [l,2.3,4,5, 6.71whichmixes parameters of the mutation vector Vi.g and the so-called target vector Xi.g inorderto generatethe trial vectoruigThemost commonformof crossoveris uniformandisdefinedasif (rand,[0,1) ≤ Cr(4)1otherwise.20/09/2026
DE basics 20/09/2026