Optimized Solution

Mlt-bjctv ptmztn r Prt ptmztn (ls knwn s mlt-bjctv prgrmmng, vctr ptmztn, mltcrtr ptmztn, r mltttrbt ptmztn) s n r f mltpl-crtr dcsn mkng tht s cncrnd wth mthmtcl ptmztn prblms nvlvng mr thn n bjctv fnctn t b ptmzd smltnsly. Mlt-bjctv s typ f vctr ptmztn tht hs bn ppld n mny flds f scnc, ncldng ngnrng, cnmcs nd lgstcs whr ptml dcsns nd t b tkn n th prsnc f trd-ffs btwn tw r mr cnflctng bjctvs. Mnmzng cst whl mxmzng cmfrt whl byng cr, nd mxmzng prfrmnc whlst mnmzng fl cnsmptn nd mssn f plltnts f vhcl r xmpls f mlt-bjctv ptmztn prblms nvlvng tw nd thr bjctvs, rspctvly. n prctcl prblms, thr cn b mr thn thr bjctvs. Fr mlt-bjctv ptmztn prblm, t s nt grntd tht sngl sltn smltnsly ptmzs ch bjctv. Th bjctv fnctns r sd t b cnflctng. sltn s clld nndmntd, Prt ptml, Prt ffcnt r nnnfrr, f nn f th bjctv fnctns cn b mprvd n vl wtht dgrdng sm f th thr bjctv vls. Wtht ddtnl sbjctv prfrnc nfrmtn, thr my xst (pssbly nfnt) nmbr f Prt ptml sltns, ll f whch r cnsdrd qlly gd. Rsrchrs stdy mlt-bjctv ptmztn prblms frm dffrnt vwpnts nd, ths, thr xst dffrnt sltn phlsphs nd gls whn sttng nd slvng thm. Th gl my b t fnd rprsnttv st f Prt ptml sltns, nd/r qntfy th trd-ffs n stsfyng th dffrnt bjctvs, nd/r fndng sngl sltn tht stsfs th sbjctv prfrncs f hmn dcsn mkr (DM). Bcrtr ptmztn dnts th spcl cs n whch thr r tw bjctv fnctns. Thr s drct rltnshp btwn mlttsk ptmztn nd mlt-bjctv ptmztn.