Gomory nzira. Kugadzirisa kwakaita integer zvirongwa matambudziko

Weight zvinetso zvemari, kuronga uye kunyange nyaya nevamwe mabhora zvoupenyu matambudziko evanhu chokuita variables chokuita integers. Somugumisiro Ongororo yavo uye kutsvaka nzira yakanakisisa yokutaura pfungwa matambudziko akanyanyisa. mamiriro ayo ari pamusoro chikabviswa anotora ane integer kukosha, uye basa pacharo anoonekwa masvomhu sezvo integer zvirongwa.

Kushandiswa chikuru nezvinetso shanduka, ane integer, ndiye Optimization. A nzira kuti anoshandisa integer Linear zvirongwa, kunonziwo chekawo-kure nzira.

Gomory nzira ainzi mushure yemasvomhu, kutanga yakatanga muna 1957-1958 algorithm richiri kushandiswa nevakawanda kugadzirisa integer Linear zvirongwa matambudziko. The dzakafuridzirwa chimiro dambudziko integer zvirongwa achibvumira inosvikirika buritsa zvakazara zvakanakira nzira iyi.

Gomori Nzira raireva Linear zvirongwa zvinoomesa zvikuru basa kuwana Zvakanyanya Kunaka Panguva Yepamuviri tsika. Pashure integrality chinhu chinokosha, mberi zvose parameters dambudziko. Pane zviitiko apo dambudziko nokuita kushanda (integer) urongwa, kuvapo muna chinangwa kushanda basa iri tambirika yakatarwa, chisarudzo anouya kuwana kunonyanyisa. Izvi imhaka kuishaya ibasa mhinduro. Pasina chete ezvinhu, sezvo mutemo, muchimiro chisarudzo kwakakodzera vector.

Kuti kupembedza kusanganiswa algorithms kuti matambudziko panodikanwa kuita mamwe superimposition mamiriro ezvinhu akasiyana.

Achishandisa nzira Gomory, kazhinji funga kuronga vakawanda vanonzi dambudziko yoruzivo polyhedron mhinduro. On hwaro ichi, yakatarwa zvose chakakosha urongwa ane finite ukoshi nokuda basa.

Uyewo, nokuti garandi chinokosha basa zvokufungidzira kuti tsika yacho coefficients ndeyakewo integers. Pasinei kwokuomerwa izvi zvinhu, asi kurukutika vanokwanisa mashoma.

Gomory nzira chezvematongerwe kunosanganisira chivakwa kurambidzwa, izvo akacheka zvingaitwa kuti havasi nonintegral. Muchiitiko chino, hapana chekawo-kure kusina integer mhinduro urongwa.

The algorithm nokuti kugadzirisa dambudziko kunosanganisira zvokuwana mikana simplex nzira, pasina kufungisisa zvinhu zviri integrality. Kana zvinoriumba dzose Zvakanyanya Kunaka Panguva Yepamuviri urongwa rine sarudzo chokuita integers, zvinganzi vaifungidzira kuti integer zvirongwa chinangwa kunokwanisika. Zvichida yakawanikwa insolubility dambudziko, saka tine uchapupu kuti dambudziko integer zvirongwa asina mhinduro.

The musiyano, kana zvinoumba ari Zvakanyanya Kunaka Panguva Yepamuviri mhinduro rine non-integer nhamba. Muchiitiko chino, mumwe mutemo itsva akawedzera vose constraints dambudziko. Basa itsva dziri dzinoratidzwa anoverengeka zvivako. Chokutanga, unofanira kuva Linear, vanofanira kubviswa kubva akawana seti vasiri integer Zvakanyanya Kunaka Panguva Yepamuviri urongwa. Kana integer mhinduro hakufaniri kurasika, kubviswa.

Kana kuvaka kurambidzwa zvinofanira kusarudzwa chezvinonhuwira ane Zvakanyanya Kunaka Panguva Yepamuviri zano pamwe chemhando hacho. Hazvina kukamurwa uku zvichawedzerwa aivapo tafura simplex.

Tinowana mhinduro yacho zvichizoita dambudziko vachishandisa kwakajairika simplex kushanduka. We tarisa mhinduro dambudziko iri nokuvapo ane integer Zvakanyanya Kunaka Panguva Yepamuviri plan, kana mamiriro nokuguta, ipapo dambudziko riri kugadziriswa. Kana mugumisiro rwaiwanikwa zvakare pamwe kuvapo asiri integer zvinogadzirisa, ipapo isu suma wokuwedzera nekurovererwa uye kudzokorora kuverenga kwacho.

Zvaakanga vakatakura munhu finite nhamba iterations Tinowana chinhu Zvakanyanya Kunaka Panguva Yepamuviri purogiramu dambudziko yakurukurwa pamberi integer zvirongwa, kana kuratidza insolubility dambudziko.