Seite - 123 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 50 Figure7.Branch-and-boundoptimizationresult. Figure8.Gradientalgorithmoptimizationresult. Resultsofanalysisgivesusunderstandingthat foramodestdimensionalityschedulingproblem bothconsideredapproachesareapplicable.However,as thenumberofoperations inmanufacturing proceduregrowsand thenumber of orders increases,wewill experience an enormousgrowthof algorithmiterations forenumeration(branch-and-bound) techniqueandthegradient-alikealgorithm willobviouslydetect localoptimumasthebestachievablesolution(whichmeans theoptimization resultswilldiffermoreandmorecompared to thedigits inTable1). Risingdifferencebetween the results is showninTable2. Expanding thepreviousproblemforaprocedureof500operations in2orderswewillget the resultspresented inTable3. 123