Indlela Gomory. Ngesisombululo iingxaki iinkqubo elipheleleyo

iingxaki ubunzima kwezoqoqosho, ucwangciso kunye nemiba evela kwamanye amacandelo iingxaki zobomi bomntu ezinxulumene variables ezinxulumene integers. Ngenxa yokuba uhlalutyo labo kunye ukukhangela iindlela ifanelekileyo yokushukuxa ingcamango mngeni kakhulu. iimpawu zayo elizayo ngasentla kuthatha inxenye yexabiso lenani elipheleleyo, kwaye umsebenzi ngokwalo kuthathwa nemaathematika njengezona elipheleleyo lokuprograma.

Ukusebenzisa ezingundoqo iingxaki variable, inani, lo kahle. A indlela esisebenzisa elipheleleyo yomgama lwenkqubo, ekwabizwa ngokuba indlela cut-off.

indlela Gomory yathiywa emva sezibalo, ephuhliswe kuqala ngo-1957-1958 algorithm nangoku ngokubanzi ukusombulula elipheleleyo iingxaki linear lokuprograma. Ifom ezakha le ngxaki elipheleleyo kweenkqubo ivumela lula kwaye abhengeze ngokupheleleyo iingenelo kwale ndlela.

Gomori indlela olusetyenziswa iinkqubo yomgama nzima kakhulu umsebenzi lokufumana amaxabiso kangangoko. Emva integrality yimfuneko esisiseko, ngakumbi zonke parameters le ngxaki. Kukho iimeko xa ngxaki ngokuba (integer) izicwangciso esebenzayo, ubukho kwi umsebenzi injongo kwezithintelo kwi iseti ukuchophela, isigqibo uza ekuphumezeni eliphezulu. Oku kungenxa yokusilela nto izisombululo ibalulekileyo. Ngaphandle kweemeko ezifanayo, njengoko umthetho, ngokohlobo a isigqibo kumda wesangqa ezifanelekileyo.

Zokuzigwebela ubuchule lwamanani ngokuba zokusombulula iingxaki kukho imfuneko ukwenza superimposition olongezelelweyo iimeko ezahlukeneyo.

Ukusebenzisa indlela Gomory, ngokuqhelekileyo ingqalelo izicwangciso ezininzi ekuthiwa ingxaki izisombululo emacala elilinganiselweyo. Ngenxa yesi sizathu, i-isethi yonke isicwangciso nengxam unalo ixabiso ezisikelwe lo msebenzi.

Kwakhona, ngokuba iwaranti umsebenzi elipheleleyo bacinga ukuba amaxabiso okuza nazo integers. Nangona ubungqongqo kwezi meko, ukuba buthathaka baziphetheyo ezimbalwa.

indlela Gomory kubandakanywe izithintelo zokwakha, eso basinqumla izisombululo ezingekho nonintegral. Kulo mzekelo, akukho cut-off akukho izisombululo elipheleleyo sicwangciso.

I algorithm ukusombulula ingxaki kubandakanya ukufumana iindlela ezifanelekileyo indlela enegumbi elinye, ngaphandle kokuthatha ingqalelo iimeko integrality. Ukuba onke amacandelo esi sicwangciso eliphezulu iqulethe izigqibo ezinxulumene integers, oko kuthathwa ukuba injongo elipheleleyo kweenkqubo kuyaphunyezwa. Mhlawumbi efumaneka insolubility ingxaki, ngoko ke babe nobungqina bokuba le ngxaki elipheleleyo kweenkqubo akukho sisombululo.

Uhlobo, xa amacandelo yezisombululo eliphezulu iqulethe inani non-elipheleleyo. Kulo mzekelo, isithintelo elitsha longezwa zonke lwemiqobo emalunga ngxaki. Izithintelo ezintsha waphawulwa ngezinto eziliqela iipropati. Okokuqala, kufanele ukuba sibe yomgama, kufuneka wonqanyulwa, angabikho kwisethi abafunyanwa non-elipheleleyo isicwangciso kangangoko. Nam solution elipheleleyo akufuneki ilahleke, kunqunyulwa.

Xa imiqathango ukwakha kufuneka kukhethwe wengxenye kwesicwangciso ngokupheleleyo kunye iqhezu aphezulu. Yiyo lo umda ziya kongezelelwa kwetafile simplex okhoyo.

Sifumana isisombululo kwezi ngxaki onesiphumo ngokusebenzisa inguqu simplex oluqhelekileyo. Thina khangela isisombululo ingxaki kubukho isicwangciso kangangoko inani elipheleleyo, ukuba imeko uyaneliswa, ngoko ke ingxaki iyatyhilwa. Ukuba isiphumo ifunyenwe kwakhona kunye nobukho kwezisombululo non-elipheleleyo, ngoko singenise ngxaki ezongezelelweyo, uze uphinde inkqubo ukubala.

Bamthwalela phandle inani anesiphelo bophindo, siya ukuphumeza inkqubo ngokupheleleyo le ngxaki ebuziweyo phambi lwenkqubo elipheleleyo, okanye zingqina insolubility le ngxaki.