 sankshiptha bullett list ‌ loo travelling sales ‌ human samasya charithra emti ?
 travelling sales ‌ human samasya yokka moolaalu aspashtamgaa unnayi . 1832  nundi travelling sales ‌ men choose ooka handed ‌ boq samasyanu prastaavistundi mariyu geramny mariyu switzerlaand dwara udaaharanha paryatanalanu kaligi Pali ,  conei ganita chikithsanu kaligi undadhu .


 viliam rovan haamilton 
TSP  ganitasaastraparamgaa  19 va sataabdamloo irish ganita saastrajnudu viliam rovan haamilton mariyu british ganita saastrajnudu thomas kirk ‌ man chetha ruupomdimchabadimdi .  haamilton yokka icocian game hamiltonian cykil ‌ nu kanugonadampai aadhaarapadina vinoda puzzle . TSP  yokka sadarana roopam  1930 lalo viyannaalo mariyu haarvaard ‌ loo ganita saastrajnulachae modhatisaarigaa adhyayanam cheyabadinatlu kanipistundhi ,  mukhyamgaa kaarl mengar ,  samasyanu nirvachimchi ,  spastamaina broot - fores algaritham ‌ nu pariganaloki teeskunnadu mariyu sameepamloni naane - optemalityni gamaninchaadu .  porugu heuristic :

 meemu messenger samasya dwara suuchistaamu  ( aacharanalo yea prasnanu prathi poest ‌ human parishkarinchaali ,  yemainappatiki chaaala mandhi prayaanikulu kudaa )  kanugonavalasina pania ,  jatha vaipu dhooraalu telisina chaaala paayimtla choose ,  paayintlanu kalipa athi takuva margam .  vaasthavaaniki ,  yea samasya chaaala trails dwara parishkarinchabadutundi .  ichina paayimtla prastaaranala sanka kante trails sankhyanu dhiguvaku nette niyamaalu teliyavu .  ooka vyakti modhata praarambha sthaanam nundi sameepa binduvuku ,  taruvaata deeniki daggaraka unna binduvuku ,  modalaina vatiki vellaalane niyamam saadharanamga chinnadaina maargaanni andinchadu .

 paatasaala baasu ruting samasyanu parishkarinchaalani choosthunna merril  M.  flud dheenini  1930 lalo ganitasaastraparamgaa modhatisaarigaa pariganinchaaru .  prince ‌ tun universitylo haslar whitney yea samasyapai aasaktini kaliginchaadu ,  dhaanini athanu  "48  stetes samasya "  ani pilichadu . " travelling sales ‌ human samasya "  aney padabandhaanni upayoginchina mottamodati pracurana juliaa rabinson dwara  1949 RAND  corparetion nivedika , " aan dhi hamiltonian game  ( ooka travelling sales ‌ human samasya )."

1950 lu mariyu  1960 lalo ,  santa monikaloni  RAND  corparetion samasyanu parishkarinche caryalaku bahumatulu amdimchina tarwata samasya urope mariyu uunited stetes ‌ loni shaastreeya vargaallo bagaa praacuryam pondindi . RAND  corparetion nundi gorge dant ‌ zig ,  delbert Rae fulkerson mariyu selmer  M.  johnson ‌ lu gurthinchadagina sahakaaraanni andichaaru ,  varu samasyanu puurnaamka sarala prograamme ‌ gaaa vyakteekarinchaaru mariyu dani parishkaaram choose katting plain addhatini abhivruddhi chesar .  varu yea vishayampai seminal paiper ‌ gaaa pariganinchabadedaanni vraasaaru ,  yea kothha paddhathulatho varu  49  nagaraalato ooka tourer ‌ nu nirminchadam dwara anukuulatanu sadhincharu mariyu marea itara paryatana thakkuvaga undadani niroopinchaaru .  ayithe ,  dant ‌ zig ,  fulkerson mariyu johnson ,  sameepa saraina parishkaaraanni andinchinatlayithe ,  meemu takuva sankhyalo adanapu asamaanatalanu  ( kotalu )  jodinchadam dwara anukuulatanu kanugonagalamu ledha anukuulatanu niroopinchukogalamani oohinchaaru .  yestring modal ‌ ni upayoginchi vaari praarambha  49  nagara samasyanu parishkarinchadaaniki varu yea aalochananu upayoginchaaru .  vaari  49  nagara samasya parishkaaraaniki  26  kotalu Bara avasaramani varu kanugonnaru .  yea kaagitam  TSP  samasyalaku algarithmic vidhanaanni andinchanappatikii , TSP  choose khachitamaina parishkaara paddhatulanu roopondhinchadaaniki danilo unna aalochanlu chaaala avsaram ,  ayithe yea kothalanu roopondhinchadamloo algarithmic vidhanaanni kanugonadaniki  15  samvastaralu paduthundi .  plain paddhatulanu kattirinchadamtopaatu ,  dant ‌ zig ,  fulkerson mariyu johnson modhatisaarigaa branch mariyu bound algaritham ‌ lanu upayoginchaaru .

1959 loo ,  jilian baird ‌ wood , J.H.  halton mariyu jeanne hamersley cambridge philosophically sociiety journal ‌ loo  " dhi shortest path throu manee points "  aney sheershikathoo ooka kathanaanni prachurincharu .  baird ‌ wood - halton - hamersley siddhaantam travelling sales ‌ human samasyaku aacharanaatmaka parishkaaraanni andistundi .  illu ledha kaaryalayamlo praarambhinchi ,  prarambhaniki tirigi vachey mundhu nirneetha sankhyalo sdhaanaalanu sandarsinche sales ‌ human choose athi takuva margam yokka podavunu nirnayinchadaniki rachayitalu assimtotic faarmulaanu roopondinchaaru .

 tharuvaathi dasaabdaalaloo ,  yea samasyanu ganitham ,  computers science ,  chemistri ,  fysics mariyu itara saastraala nundi chaaala mandhi parisodhakulu adhyayanam chesar .  ayithe , 1960 va dasakamlo ,  ooka kothha vidhaanam srushtinchabadindi ,  saraina parishkaaralanu vetakadaaniki badhuluga ooka parishkaaraanni utpatthi chesthundu ,  deeni podavu saraina podavu yokka gunakaaramto niroopinchabadutundi mariyu ola cheeyadam valana samasyaku takuva haddulu erpadatayi ;  yea dhiguva haddulu branch mariyu bound vidhaanaalatoo upayoginchabadataayi .  graph yokka kanista vistiirnham gala chettunu srushtinchadam mariyu dani anchulannintinii rettinpu cheeyadam ila cheyadamlo ooka paddathi ,  idi saraina paryatana yokka podavu kanishtamgaa vistarimchi unna chettu kante remdu retlu ekuva baruvu kaligi umtumdi .

1976 loo , Christofides  mariyu  Serdyukov  swatantramgaa okarikokaru yea disaloo peddha purogathini sadhincharu : Christofides-Serdyukov  algoritham ooka parishkaaraanni andistundi ,  chethha sandarbhamlo ,  saraina parishkaaram kante garishtamgaa  1.5  retlu ekuva .  algoritham saralamainadi mariyu sheeghramainadi kabaadi ,  idi sameepa saraina parishkaara paddhatiki dhaari teestundani chaaala mandhi aashinchaaru .  ayithe ,  abhivruddhi choose yea aasha Merta kaaryaroopam dalchaledu mariyu christophides - serducov  2011  varku  " graphikal " TSP l upasamiti choose  ( chaaala )  koddhiga merugaina ujjayimpu algaritham abhivruddhi cheyabadinappudu ,  utthama chethha drushtaantamlo paddhatiga konasaagindi . 2020 loo yea chinna merugudhala porthi  ( metrik ) TSP ki vistarinchabadindi .

 richaard  M.  corp  1972 loo hamiltonian cykil samasya  NP- porthi ani choopinchaadu ,  idi  TSP  yokka  NP- kaatinyaanni suchisthundi .  idi saraina paryatanalanu kanugonadamlo spastamaina ganana kashtaniki ganita vivarananu andinchindi .

1970 l chivaraloo mariyu  1980 loo goppa purogati saadhinchabadindi ,  grot ‌ shale ,  pyaad ‌ berg ,  rinaldi mariyu Bundi  2,392  nagarala varku kating plain ‌ lu mariyu branch ‌ lanu upayoginchi udantaalanu sariggaa parishkarinchagaligaaru .

1990 lalo , Applegate, Bixby, Chvátal,  mariyu  Cook  anek itivali rikard solutions ‌ loo upayoginchabadina concord prograamme ‌ nu abhivruddhi chesar .  gerhard reinelt  1991 loo  TSPLIB ni prachurincharu ,  idi vividha takala kashtalaku sambamdhinchina bench ‌ marque udaaharanala samaharam ,  idi phalithaalanu polchadaaniki anek parisoedhanaa samuuhaalachae upayoginchabadindi . 2006 loo ,  cook mariyu Bundi microchip leout samasya dwara andimchabadina  85,900- nagara udaaharanha dwara saraina paryatananu ganinchaaru ,  prasthutham idi athipedda parishkaaramaina  TSPLIB  udaaharanha .  millionla koddi nagaraalato unna anek itara sandarbhaallo ,  saraina paryatanaloo  2-3%  lopala vundela haamii ivvabade parishkaaralanu kanugonavacchu .
* 19 va sathabdam  -  irish ganita saastrajnudu viliam rovan haamilton mariyu british ganita saastrajnudu thomas kirk ‌ man modhatisaarigaa ganitasaastraparamgaa roopondinchaaru 
* 1930 lu  -  viennaa mariyu haarvaard ‌ loo ganita shaasthrajnulu modhata adhyayanam chesaru ,  mukhyamgaa kaarl mengar mariyu merril  M.  flud paatasaala baasu ruting samasyanu parishkarinchaalani chustunnaaru .
* 1959 -  jilian baird ‌ wood , J.H.  halton mariyu jeanne hamersley cambridge philosophically sociiety journal ‌ loo  " dhi shortest path throu manee points "  aney sheershikathoo ooka kathanaanni prachurincharu ,  idi modati aacharanaatmaka parishkaaraanni andinchindi .
* 1960 lu  -  kothha vidhaanam srushtinchabadindi ,  idi ooka parishkaaraanni utpatthi chesthundu ,  deeni podavu saraina podavu yokka gunakaaramto niruupinchabadindi .
* 1972 -  hamiltonian cykil samasya  NP- porthi ani richaard  M.  corp choopinchaadu ,  idi travelling sales ‌ human samasya yokka  NP- kaatinyaanni suchisthundi .
* 1976 -  christophides mariyu serducov swatantramgaa kothha algaritham ‌ nu kanugonnaru ,  idi chethha sandarbhamlo saraina parishkaaram kante  1.5  retlu ekuva umdae parishkaaraanni andistundi .
* 1990 lu  - Applegate, Bixby, Chvátal,  mariyu  Cook  anek itivali rikard solutions ‌ loo upayoginchabadina concord prograamme ‌ nu abhivruddhi chesar .
* 1991 -  gerhard reinelt  TSPLIB ni prachurinchaadu ,  idi vividha kastala yokka bench ‌ marque udaaharanala samaharam ,  idi phalithaalanu polchadaaniki anek parisoedhana samuuhaalachae upayoginchabadindi .
* 2006 -  microchip leout samasya dwara andimchabadina  85,900- nagara udaaharanha dwara cook mariyu Bundi saraina paryatananu ganinchaaru ,  prasthutham idi athipedda parishkaaramaina  TSPLIB  udaaharanha .
* 2011 - " graphikal "  travelling sales ‌ human samasya yokka upasamiti choose komchem merugaina ujjayimpu algaritham abhivruddhi cheyabadindhi .
* 2020 - " graphikal "  yokka upasamiti choose abhivruddhi cheyabadina komchem merugaina ujjayimpu algaritham porthi travelling sales ‌ human samasyanu cover cheyadanki vistarinchabadindi .