Page - 298 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 997 1x 2x 1x 2x 1x 2x Figure16.Divisionandselectionofpotentialoptimalhyper-rectangle inDIRECTalgorithm. It is supposed thatω1=min(5,8)= 5, andω2=min(6,2)= 2. First, thehypercube is cut in thedirectionperpendicular to x2. Then, thehypercube is cut in thedirectionperpendicular to x1. Themethodofcuttingthe longestsideof thehypercubecanensuredecreasingthe lengthof the longest side. InDIRECTalgorithm, theside lengthof thehypercube isatmost twovaluesaftereachdivision. Thehypercube,withafunctionvalueat thecenterpointequal to2 inFigure16, is thepotentialoptimal hyper-rectangleafter twodivisions. Basedontheaboveresult,Figure17canbeobtainedbysettingthefunctionvalueat thecenter pointasy-axis, andthedistancebetweenthecenterpointandvertexasx-axis. In thefigure, (1)–(3)are thepotentialoptimalhyper-rectangle fromthefirst to third iteration, respectively. In thefirst iteration, there isonlyone list of selectablepoints. Thehypercube,witha functionvalueat the centerpoint equal to2, is thepotentialoptimalhyper-rectangle.Weneedtodivide thecubefurther. Similarly, in theseconditeration,wecanget twohyper-cubeswith thesmallestvalue, tobedividedinthe third iteration. Theprocesscontinuesuntil it satisfies thestoppingcondition. 298