CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="120"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'non-interactive',cRay: '91356d3aeccc407a',cH: 'HD5qtgv_kLdjCjB_xsyKeJuhn4wuf7LZvQmDaAy02fo-1739791630-1.2.1.1-euzVroYQ63XAZoCoynuYnLRKM_oRyf2iehzS5TpnuxSamsBNjwI41nBDl1O1YcP8',cUPMDTk: "\/abstracts\/search?q=traveling%20salesman%20problem&__cf_chl_tk=oZoQaO_vhhNVmsxoEFstMTrZraP7z9E3ma9x4IgSctc-1739791630-1.0.1.1-cO8z7L4Fcn871kgCyIlprfzywNNEhIVbC_oyIbJOY5E",cFPWv: 'b',cITimeS: '1739791630',cTTimeMs: '1000',cMTimeMs: '120000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/abstracts\/search?q=traveling%20salesman%20problem&__cf_chl_f_tk=oZoQaO_vhhNVmsxoEFstMTrZraP7z9E3ma9x4IgSctc-1739791630-1.0.1.1-cO8z7L4Fcn871kgCyIlprfzywNNEhIVbC_oyIbJOY5E",md: "l2rPkr5A6Me9tAFJmY7IoshXe6ytcObQotPhousQFso-1739791630-1.2.1.1-UJvMetq8h4d_Qds5ZlPOlRaYL7eCmVirMlYcUGaepNQTFhO6ifTp26.IDI9GsPSDFSuDVhfp3XBLqqP7CAqbYYdifK3Z2XDi0ZDEje9y1VgkhmNNrv8.CsfG.BP7._VZEhf8Pq_isnguYgSUo2L2XxX0eGlnUratiuUmZ3kd8uhoLtbNKPXuT_GsQluZtObxDx.bVf11.5FeSWNRnEyMAGtEkxIueCIp5y7DFTewFs3uIuOPEA.3K2hd0JrdVHTg8UwKdiX2K9yJtkYIN3QAVwEOgiAWtMooMqdpa0DWnx3AcSI2OVjm5mxYiUW9n05Sl16fovk3YiLL6YClACe_yo7h0g3n86S6qvI1nKkdH.28CnX0cyQaCCzc6PsEPYCuWrK1sZ0MnpS2piBaq8oGAJvFpZhk2Xnu97f12Eo05pXs2ST0ATxYpw9j_cJdicPrlOjqLbOI6ya5fDbI4QDxwW0ByZePPbKWTocVO3MnjLgfy4dlBx155olRKNpYUIWlmrJwsOq2Sx2G31nlUI76veZSzaGoFZ3SPF3fdeMF4BfNhKluxKV6TMBn_60Hz_r1J0aQuGcYLii5v0tvsvbqAU3jd5yMpJjdlg9vOfq4GITtOgb0MWHNdc80OL3ieg6QxS6hD9C4I3CD9ItV9iLr5ufhmETaeEvi7e0uxekFsN6UmiFkQGkjw91Qz3udETq3uawpzbYdyuwN_fuHWpbel4vPyYo6gD7ZMvptvRO5JyGy70gL2LF6zNWmpFjFEguhU4tqBqhFI2vUGOzlC0bQi7czQFUKd7C67mxoDDJN5_nfEHVjJ0gV39RG2oGErq.S.ctc36EskEQjKlh9G20JJdPEpn3Bbdq__J_IkxM9OUyk_UHthSPJAAjG6jO_7VxIzo4gqnLXEaITySk6L_RtapBckX5IELJOP7uRjIhVtNbMUllrLfuFnzWldk6grtk4eGgsN7wCjvRa6r6PzkTSN6RPdfcw8jwO9hVW9YNfjJ5W5.O.8JE81ckQ6_OF5tN4w.KFFs_3LwZPHV0dZsd9SaRRwPnf7cWjLMCxS9_ZFIb1dX1i9aLVkgD1rLisThfy76fTfpyPtS5C9JRXGKxTIgeHiqZaY5Et4lqX_o462hcPUA5J.vTevDRjGeR0WkD2JOKOelMM8iM_mlQ5t9MCYeyRUkQAcVHlFQDgvL9LWhS_htS_eAMNts.AU0pgd_m0MUzuSv25EpuERhhRh8_4NSDo4ftQ0LXADWYgOcD31.4pD0iVu.5tigrc2YZdhOYyqb86p8d9JJQf.5CDGJJaiI6gd1.T32MpCHihfdtv85tja5Deb464cpcBu3V4VwAHD2Ja4dYYOpQVVA8mX_.2B12gFH58PArCBxvOLVm2aZcpOAl0vyFOMJKVJ0Xsy9CxPr6cOpvYeLLd.W4tGLq7GN0iIgb7hZqNmYFcU5TQ7N2mWsVI9hiIk3jafb69btmVeDaDzoCoDvy9Cq5CPG1YF1lFVwuh4yfOZoIFVtCTBbSRw52k31Wq6V4pT0J5XM0FMZlFBCRE1tNPP.3BUk2oNnfepvVbiqT9lWZyLC5v1JP3LiDOIJ4jbl2jjALteva2zQPU.gmqEUQB2NNd19aO_fgKtvhyq6oGxN3STKlU.AaIRpkaD1XV80keUeRyN01dUdFvGWDJvke_zeQ.KopYkgUQI.FrZLk9dsOiOFr2k7vXsoelGP_I.XjfgMOQEMI1ULX7WB1ENfon3WkKLZLPdhZK.75EVL6GpaZ2WRrGzLNypeqcfcb_JoVdJ07k.KU0LnRTvJ.AtK1jrepAM2Zg5jtwx0olgXAh7NvWnUy85ds8AcbCG7ajdppgjlSdVrEemz900mXo86nLITj2blJD.iHBwWNA05TLPE_lYhzLeUVyYww7kaYnt0w7Ua_L9k6BjuizN0zmWtzQl53O7dUfv1WfPjZB2uS3bWMScp9gVP39ugNdq9CnZuVuZtFuSIhdDN8fvTRGD00RkiZ1v2AI_A",mdrd: "hjXFeEMsveABNaY8yL9YG9UGU4lOOAmK_aIdB_.R2Hk-1739791630-1.2.1.1-3xnzNwOJ8sp7CIKzqFaQi5928MzxqL3w.CK1_o2p0bxII9UW40Eb_76KoemAM6IYJo0dalYfL4HHNIc30xJArOwTvo7j0PFkCt26rXqHkvOT5VHc_qZmOifV03iEkFLeUSpY2dJoFa_X6ARZ4_bC3pEyKQnZa8gDBstKlBNVYVLjgDWBeIImYdcBvSaUzqcw_MYDbKYmlYwFDi9omX3fnChilUYlvQzefUU2Wv00Ji81YPtVe72FWNBVI0DeWIEgjMmOsGHhhVekVZfVZtfwSpM9EOZGJvKLamKdhhcpTBEJ5FeD0B4Q8dRr0pXA8lkz0gD3yOiPpnpac5huYm7vCGwUDvCzzwR5fgKMlgJIi8owwgX6nEeI2267ZRasq72qDtEtKvqA7BqBTRxY7CyYqznpB.j4KHIT19bmVcy3RfnBq84bHEv5uJhNM.FRDrh7vMosEuhDGtvAqzltbxU.iCEXfxdylibYiXOph5.paZBnZRAZtOc0wyhNBtrRnMcI7F80Q9PHCDSG7H.IACPEzO6ocKXKsqX_zKUTC9WKozf6cImoK7Ti5wOSWp8lnlGPgjnEFb_bfVp8ZB4yq1Vrn4pj7a4sTVCh5VBs_te04ZcGM.Qxujwao5l5Z_UJtWwp1NVr6jVyggdkLpkMOED_4D31cKNzd6Eek3Z0yO3hFZE5sxADzOUvKcZ85nojKnoJEu.TbgtoAv9GLhB4oR1j9G9T8fN4Ob6TxllJQDM7_EU0FP8GiPZP3o.4yA4ceoFh6QiQE.62rrW4RJbMOi.5BOD2NLD6ph4b9ESodQSAM0hGT4KheYsoqSEU0253rjOZCemjf.8wBYSBqw1eoF8jkLltP7E0n7nqfgWYrYWWtKSxdBDuzHZws1qB1KWnoyk6_TKxyywjDywZD_K4HMDxbi_ENxT2Av3NkR_eVuMASTS2X6jn4n7dHeshUkKKGuXy.HvLFJcb8HItKhh1_bdE7ZJrLWaizlGoOVl5Guvw0aCAE7_jWaDrJZzeGzcV2iMrIcR.yqClAgBLSTyoLE7NXTiDniiZearxMyBsVKxCnvFon9D9RIolOyOdCPq2fnkGXq6SH84oBUvrxekEH8z9XXci51J7XaespNDQJV_C7Y9p_qbCwb1gHxqaTLqR5IEh5JpAmwGuTZyUAolT1m85OCEPN5cwc4VjYS7FHSsQUvVZd0erLJF2p3hv6XAmgauvfYs6Qz1MRd8DJ20195aUOyPZvSa3UwK2iKU1yFXGynxGbaLbXLNQyU0XD5BWnLSJblNqsMBg.1rQxZHA1rBMtGyE4MNPmwgFFG.6rZ26MHbXolXNl8pQJY74oplmFdizyZ6TyAM4V5WIt4BNLDgGDj_4u_uI08j.._DoNOur83swP0SlQhcNHViV8Sbp1834YfbPB8LhvGmAHOfsfaHcQIKQZsdZsjrRbJ_LZIwUVWT6A._5zNnaQrCA891gDCepWg6GRMoxDC4ZZFfNreu5vlkSyH1BMWEDTlInsaJvvPuFLqtw5aJWMpmYDIWgYkthDLQTbdpuFmDsi2zqPbiAqxbIkx.Zo.xabZZXwq6JjorKWOELPV8ul3gvsluSozYIZV.Q7KWVV6Nerh7PXoJjd2YfBAWuf7QoulRR0p5YdvTadVYP9xvyOhC.ivHYyau5oMs6jYPV7dTFznDIMgh.EFe0DBkYUGFTWBpIjc52bkIVuhTgSXbSIciXQ6g.DtSBcL2whIqmUg8uZf3vYciWGEcKsXEio.ZWnefuLIxuzXQx_xwPaXG1Po3Z9nkeT8T4sRCuIrV6zg4TKoatfYUOoozCQlo7oVf0gRuN6Wtr4vaGQh4pNnwg2L7p9AW7m9QBsYKqEfbLvYWssX_yA7OTySiZRuCAR2qoHjbFv1gBqDjnr6QTSIzk55UiKassvGIpaiWxuk.7n2.wkgj9WPOIOAtXkY.u9uhMHVgCq1mUnMhSmVxpnOSK6Md04zmeaa2zKL1K0ZvrFDEIHDkmZAoPtA"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/b/orchestrate/chl_page/v1?ray=91356d3aeccc407a';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/abstracts\/search?q=traveling%20salesman%20problem&__cf_chl_rt_tk=oZoQaO_vhhNVmsxoEFstMTrZraP7z9E3ma9x4IgSctc-1739791630-1.0.1.1-cO8z7L4Fcn871kgCyIlprfzywNNEhIVbC_oyIbJOY5E" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>