Indlela Gomory. Isixazululo ezinkingeni izinhlelo inamba

izinkinga Isisindo kwezomnotho, ukuhlela ngisho nezindaba ezivela kwezinye imikhakha nezinkinga zokuphila komuntu ezihambisana eziguquguqukayo ezihlobene integers. Ngenxa yalokho sokuhlaziya yabo kanye search for yezindlela ezingcono kakhulu ukubhekana inkolelo yokungafi nezinselelo kakhulu. Timphawu yinkulumo ezingenhla kudinga inani inamba, futhi umsebenzi uqobo uthathwa wezibalo njengoba inamba izinhlelo.

Ukusetshenziswa main zezinkinga variable, inenombolo, iyona nokwenza. Indlela osebenzisa inenombolo komugqa izinhlelo, ebizwa nangokuthi i-asikiwe indlela.

indlela Gomory yethiwa sezibalo, kuqala ithuthukiswe 1957-1958 algorithm namanje kabanzi ukuxazulula inamba izinkinga komugqa izinhlelo. Ifomu ezakha inkinga inamba izinhlelo ivumela kufinyeleleke futhi ngokugcwele liveze obala yezinzuzo zale nqubo.

Gomori indlela ozofakwa izinhlelo lwento inkimbinkimbi kakhulu umsebenzi wokuthola amagugu elilungile. Ngemva integrality kuyimfuneko eyisisekelo, eminye yonke nemingcele yenkinga. Kukhona amacala uma inkinga ngokuba evumelekile (inamba) izinhlelo, khona e umsebenzi umgomo kwezithibelo isethi zivumelekile, isinqumo kuziwa ekufinyeleleni esiphezulu. Lokhu kungenxa yokungabi kuba izixazululo ebalulekile. Ngaphandle kwezimo ezifanayo, njengoba umthetho, ngesimo isinqumo Vector ezifanele.

Ukuze baqiniseke ukuthi ubuchule zezinombolo ukuxazulula izinkinga kukhona isidingo afeze superimposition ezengeziwe kwezimiso ezehlukene.

Ukusebenzisa indlela Gomory, ngokuvamile ucabangele amacebo amaningi inkinga lokho okubizwa ngomlobokazi elinganiselwe polyhedron izixazululo. Kulesi sisekelo, isethi wonke umklamo ebalulekile inenani ezilinganiselwe ngomberego.

Futhi, i-iwaranti umsebenzi ebalulekile ucabange ukuthi abakuzuzile okuza nazo integers. Naphezu kobukhulu mibandela, ubuthakathaka abayiphethe ambalwa.

Gomory indlela ngokuyisisekelo kuhilela imingcele yokwakha, okuyinto usike izixazululo ukuthi akuzona nonintegral. Kulokhu, akukho asikiwe kungekho uhlelo inamba izixazululo.

I-algorithm ukuxazulula inkinga ehilela ukuthola ongakhetha efanelekayo indlela simplex, ngaphandle kucatshangelwa nemibandela integrality. Uma zonke izingxenye plan elilungile iqukethe izinqumo ezihlobene integers, kungaba bazitshela ukuthi umgomo inamba izinhlelo abayifunayo. Mhlawumbe ukuthi kutholakala insolubility yenkinga, ngakho kufanele ubufakazi bokuthi le nkinga inamba izinhlelo ayinakho isixazululo.

I okufana, lapho izingxenye ikhambi elilungile iqukethe inombolo-non-inamba. Kulokhu, kwezithibelo entsha yengezwe zonke izingqinamba yenkinga. Imingcele entsha zinezikhathi eziningi izakhiwo. Okokuqala, kuzomele kube yomugqa, kufanele nginqume isethi ezitholakele ze-non-inamba uhlelo elilungile. Ngiphakathi isixazululo inamba akufanele elahlekile, unqunyiwe.

Lapho imingcele yokwakha ingakhetfwa ingxenye uhlelo elilungile kanye ingxenyenamba eliphakeme. Kuyinto lo mkhawulo niyozenezelelwa etafuleni ekhona simplex.

Sithola isixazululo yenkinga umphumela usebenzisa ezivamile simplex ukuguqulwa. Sibheka ikhambi yenkinga ngokuba khona inenombolo uhlelo elilungile, uma isimo uyaneliswa ke inkinga isixazululekile. Uma umphumela etholwe futhi nokuba khona-non-inamba izixazululo ke thina ukwethula uhlelo umkhawulo eyengeziwe, bese uphinda inqubo yokubala.

Njengoba eyenziwa inombolo ezilinganiselwe iterations, sifeze uhlelo kahle inkinga owaphakanyiswa phambi izinhlelo inamba, noma afakazele insolubility yenkinga.