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204 Blas Pelegrín, Pascual Fernández, Juani L. Redondo, Pilar M. Ortigosa, and I. GarcíaFor every member dogenerate random pointsP1Acheck middle pointsC1r1C1r1P1BM1ABC2r2P1CM1ACC2r2P1DM....P1ECnrnP2ACn rnInitial species-listat level iP2BP2CM2ABM2ACP1A riP1B riFinal species-listlevel iatadded onlevel ixxC3x xxxC1xP1BP1A M1ABxxxxC4xxxxx xxC2xPAMABPBif middle point is worse, then separate PA & PBnew speciesFigure 1.Generation and crossoverAs a result of this procedure the subp − list will eventually contain several subpopulationswith different levels (hence different radii). The motivation behind this methodis to create subpopulations that are on different ’hills’ so ensuring that there is a valleybetween the new species.Selection: This procedure has two mechanisms, the first tries to fuse subpopulations thatare too close and the second selects the subpopulations that will be maintained in thesubp − list.Fuse species: If the centers of any pair of subpopulations from the subp − list are closerto each other than the given radius, the two subpopulations are fused. The center of thenew subpopulation will be the one with the better function value while the level will bethe minimum of the levels of the fused subpopulations (so the radius will be the largestone).Select species: It deletes subpopulations to reduce the list length to the given value.Higher level subpopulations are deleted first; therefore subpopulations with larger radiiare always kept. For this reason one subpopulation at level 1 whose radius is equal tothe diameter of the search domain always exists, making it possible to escape from localoptima.Mutation: It applies consecutive mutations to every center of every subpopulation. A mutationmeans an interchange of one facility, so one gene of the center is changed from 0 to1 and other gene is changed from 1 to 0, according to our problem encoding.If when mutating an individual, its function value is better than the value of the center,then this new individual will replace the center. At level i, the maximum number ofconsecutive mutations applied to each center is n i /max subp num.Note that the fact that gasub may terminate simply because it has executed all its levels.The final number of function evaluations thus depends on the complexity of the ob-