splitting for optimization minimizing function ( ) is closely related to drawing random sample from level set of the form { ( gsuppose has minimum value gattained at xas long as gthis level set contains the minimizer moreoverif is close to gthe volume of this level set will be small soa randomly selected point from this set is expected to be close to xthusby gradually decreasing the level parameter gthe level sets will gradually shrink towards the set {xindeedthe ce method was developed with exactly this connection in mindseee [ note that the ce method employs parametric sampling distribution to obtain samples from the level sets (the elite samplesin [ non-parametric sampling mechanism is introduced that uses an evolving collection of particles the resulting optimization algorithmcalled splitting for continuous optimization (sco)provides fast and accurate way to optimize complicated continuous functions the details of sco are given in algorithm algorithm splitting for continuous optimization (scoinputobjective function sample size nrarity parameter %scale factor wbounded region that is known to contain global minimizerand maximum number of attempts maxtry outputfinal iteration number and sequence (xbest, )(xbest, bt of best solutions and function values at each iteration elite simulate { uniformly on set and dn% while stopping condition is not satisfied do determine the elite smallest valuess ( ( elite of { ( ) yt }and store the corresponding vectorsx( ( elite in xt+ set bt+ ( and xbest, + ( pn elite bi mod elite draw bi bernoulli ) elite with = elite for to do ri nnelite bi /random splitting factor (iy for to ri do draw { elite {iuniformly and let si | (ix( simulate uniform permutation ( pn of ( for to do for try to maxtry do (pk (pk si (pk )zz ( if ( (ythen and break add to yt+ - + return {(xbest, bk ) tat iteration the algorithm starts with population of particles { that are uniformly generated on some bounded region bwhich is large enough to contain global minimizer the function values of all particles in are sortedand the best level set splitting for continuous optimization