{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T17:24:50Z","timestamp":1773681890388,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T00:00:00Z","timestamp":1643328000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T00:00:00Z","timestamp":1643328000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100002790","name":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["CRDPJ 479316-15"],"award-info":[{"award-number":["CRDPJ 479316-15"]}],"id":[{"id":"10.13039\/501100002790","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2022,4]]},"DOI":"10.1007\/s10589-021-00347-7","type":"journal-article","created":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T04:36:43Z","timestamp":1643344603000},"page":"741-767","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A successive relaxation algorithm to solve a MILP involving piecewise linear functions with application to road design"],"prefix":"10.1007","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5482-6831","authenticated-orcid":false,"given":"Dominique","family":"Monnet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Warren","family":"Hare","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yves","family":"Lucet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,1,28]]},"reference":[{"key":"347_CR1","first-page":"210","volume":"3","author":"MS Aljohani","year":"2003","unstructured":"Aljohani, M.S., Moreb, A.A.: Roadway profile modeled by polynomials to minimize earthwork cost. WSEAS Trans. Math. 3, 210\u2013213 (2003)","journal-title":"WSEAS Trans. Math."},{"key":"347_CR2","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/s10310-004-0136-5","volume":"10","author":"K Aruga","year":"2005","unstructured":"Aruga, K.: Tabu search optimization of horizontal and vertical alignments of forest roads. J. For. Res. 10, 275\u2013284 (2005)","journal-title":"J. For. Res."},{"key":"347_CR3","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.asoc.2017.12.015","volume":"64","author":"R Babapour","year":"2018","unstructured":"Babapour, R., Naghdi, R., Ghajar, I., Mortazavi, Z.: Forest road profile optimization using meta-heuristic techniques. Appl. Soft Comput. 64, 126\u2013137 (2018)","journal-title":"Appl. Soft Comput."},{"issue":"10","key":"347_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/0305215X.2016.1271880","volume":"49","author":"V Beiranvand","year":"2017","unstructured":"Beiranvand, V., Hare, W., Lucet, Y., Hossain, S.: Multi-haul quasi network flow model for vertical alignment optimization. Eng. Optim. 49(10), 1\u201319 (2017)","journal-title":"Eng. Optim."},{"key":"347_CR5","first-page":"63","volume":"31","author":"G Bosurgi","year":"2013","unstructured":"Bosurgi, G., Pellegrino, O., Sollazzo, G.: A PSO highway alignment optimization algorithm considering environmental constraints. Adv. Transp. Studies 31, 63\u201380 (2013)","journal-title":"Adv. Transp. Studies"},{"key":"347_CR6","doi-asserted-by":"crossref","unstructured":"Dantzig, G.\u00a0B.: On the significance of solving linear programming problems with some integer variables. Econom. J. Econom. Soc. 30\u201344, (1960)","DOI":"10.2307\/1905292"},{"issue":"2","key":"347_CR7","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91(2), 201\u2013213 (2002)","journal-title":"Math. Program."},{"key":"347_CR8","first-page":"1","volume":"1239","author":"TF Fwa","year":"1989","unstructured":"Fwa, T.F.: Highway vertical alignment analysis by dynamic programming. Transp. Res. Rec. 1239, 1\u20139 (1989)","journal-title":"Transp. Res. Rec."},{"key":"347_CR9","first-page":"105","volume":"33","author":"AB Goktepe","year":"2009","unstructured":"Goktepe, A.B., Altun, S., Ahmedzade, P.: Optimization of vertical alignment of highways utilizing discrete dynamic programming and weighted ground line. Turk. J. Eng. Environ. Sci. 33, 105\u2013116 (2009)","journal-title":"Turk. J. Eng. Environ. Sci."},{"key":"347_CR10","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/j.cor.2013.11.005","volume":"44","author":"W Hare","year":"2014","unstructured":"Hare, W., Hossain, S., Lucet, Y., Rhaman, F.: Models and strategies for efficiently determining an optimal vertical alignment of roads. Comput. Op. Res. 44, 161\u2013173 (2014)","journal-title":"Comput. Op. Res."},{"issue":"2","key":"347_CR11","doi-asserted-by":"publisher","first-page":"470","DOI":"10.1016\/j.ejor.2011.06.011","volume":"215","author":"W Hare","year":"2011","unstructured":"Hare, W., Koch, V.R., Lucet, Y.: Models and algorithms to improve earthwork operations in road design using mixed integer linear programming. Eur. J. Oper. Res. 215(2), 470\u2013480 (2011)","journal-title":"Eur. J. Oper. Res."},{"issue":"3","key":"347_CR12","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1016\/j.ejor.2014.08.035","volume":"241","author":"W Hare","year":"2015","unstructured":"Hare, W., Lucet, Y., Rahman, F.: A mixed-integer linear programming model to optimize the vertical alignment considering blocks and side-slopes in road construction. Eur. J. Oper. Res. 241(3), 631\u2013641 (2015)","journal-title":"Eur. J. Oper. Res."},{"key":"347_CR13","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.trc.2016.01.016","volume":"65","author":"D Hirpa","year":"2016","unstructured":"Hirpa, D., Hare, Y., Lucet, W., Pushak, Y., Tesfamariam, S.: A bi-objective optimization framework for three-dimensional road alignment design. Transp. Res. Part C: Emerg. Technol. 65, 61\u201378 (2016)","journal-title":"Transp. Res. Part C: Emerg. Technol."},{"issue":"HW1","key":"347_CR14","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1061\/JHCEA2.0000266","volume":"94","author":"Z Howard","year":"1968","unstructured":"Howard, Z., Bramnick, B.E., Shaw, J.F.B.: Optimum curvature principle in highway routing. J. Highw. Div. 94(HW1), 61\u201382 (1968)","journal-title":"J. Highw. Div."},{"issue":"5","key":"347_CR15","doi-asserted-by":"publisher","first-page":"847","DOI":"10.1287\/opre.1060.0277","volume":"54","author":"AB Keha","year":"2006","unstructured":"Keha, A.B., de Farias Jr, I.R., Nemhauser, G.L.: A branch-and-cut algorithm without binary variables for nonconvex piecewise linear optimization. Oper. Res. 54(5), 847\u2013858 (2006)","journal-title":"Oper. Res."},{"issue":"2","key":"347_CR16","doi-asserted-by":"crossref","first-page":"393","DOI":"10.3934\/jimo.2010.6.393","volume":"6","author":"VR Koch","year":"2010","unstructured":"Koch, V.R., Lucet, Y.: A note on: Spline technique for modeling roadway profile to minimize earthwork cost. J. Ind. Manag. Optim. 6(2), 393\u2013400 (2010)","journal-title":"J. Ind. Manag. Optim."},{"issue":"8","key":"347_CR17","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1111\/mice.12280","volume":"32","author":"W Li","year":"2017","unstructured":"Li, W., Pu, H., Schonfeld, P., Yang, J., Zhang, H., Wang, L., Xiong, J.: Mountain railway alignment optimization with bidirectional distance transform and genetic algorithm. Comput.-Aided Civil Infrastruct. Eng. 32(8), 691\u2013709 (2017)","journal-title":"Comput.-Aided Civil Infrastruct. Eng."},{"issue":"11","key":"347_CR18","first-page":"2967","volume":"8","author":"W Li","year":"2013","unstructured":"Li, W., Pu, H., Zhao, H., Liu, W.: Approach for optimizing 3D highway alignments based on two-stage dynamic programming. J. Softw. 8(11), 2967\u201373 (2013)","journal-title":"J. Softw."},{"key":"347_CR19","doi-asserted-by":"crossref","unstructured":"Markowitz, H.\u00a0M., Manne, A.\u00a0S.: On the solution of discrete programming problems. Econom.: J. Econom. Soc. 84\u2013110, (1957)","DOI":"10.2307\/1907744"},{"key":"347_CR20","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/j.cor.2015.05.018","volume":"64","author":"S Mondal","year":"2015","unstructured":"Mondal, S., Lucet, Y., Hare, W.: Optimizing horizontal alignment of roads in a specified corridor. Comput. Op. Res. 64, 130\u2013138 (2015)","journal-title":"Comput. Op. Res."},{"issue":"2","key":"347_CR21","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/s10589-019-00160-3","volume":"75","author":"D Monnet","year":"2020","unstructured":"Monnet, D., Hare, W., Lucet, Y.: Fast feasibility check of the multi-material vertical alignment problem in road design. Comput. Optim. Appl. 75(2), 515\u2013536 (2020)","journal-title":"Comput. Optim. Appl."},{"issue":"1","key":"347_CR22","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1016\/0377-2217(95)00095-X","volume":"93","author":"AA Moreb","year":"1996","unstructured":"Moreb, A.A.: Linear programming model for finding optimal roadway grades that minimize earthwork cost. Eur. J. Oper. Res. 93(1), 148\u2013154 (1996)","journal-title":"Eur. J. Oper. Res."},{"issue":"2","key":"347_CR23","doi-asserted-by":"crossref","first-page":"275","DOI":"10.3934\/jimo.2009.5.275","volume":"5","author":"AA Moreb","year":"2009","unstructured":"Moreb, A.A.: Spline technique for modeling roadway profile to minimize earthwork cost. J. Ind. Manag. Optim. 5(2), 275\u2013283 (2009)","journal-title":"J. Ind. Manag. Optim."},{"key":"347_CR24","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.asoc.2019.01.051","volume":"78","author":"H Pu","year":"2019","unstructured":"Pu, H., Song, T., Schonfeld, P., Li, W., Zhang, H., Hu, J., Peng, X., Wang, J.: Mountain railway alignment optimization using stepwise & hybrid particle swarm optimization incorporating genetic operators. Appl. Soft Comput. 78, 41\u201357 (2019)","journal-title":"Appl. Soft Comput."},{"key":"347_CR25","doi-asserted-by":"publisher","first-page":"972","DOI":"10.1111\/mice.12475","volume":"34","author":"H Pu","year":"2019","unstructured":"Pu, H., Song, P., Schonfeld, T., Li, W., Zhang, H., Wang, J., Hu, J., Peng, X.: A three-dimensional distance transform for optimizing constrained mountain railway alignments. Comput.-Aided Civil Infrastruct. Eng. 34, 972\u2013990 (2019)","journal-title":"Comput.-Aided Civil Infrastruct. Eng."},{"key":"347_CR26","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/S0304-0208(08)73476-5","volume":"11","author":"JA Tomlin","year":"1981","unstructured":"Tomlin, J.A.: A suggested extension of special ordered sets to non-separable nonconvex programming problems. Stud. Graphs Discrete Program. 11, 359\u2013370 (1981)","journal-title":"Stud. Graphs Discrete Program."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-021-00347-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-021-00347-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-021-00347-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T00:59:57Z","timestamp":1674608397000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-021-00347-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,28]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["347"],"URL":"https:\/\/doi.org\/10.1007\/s10589-021-00347-7","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,28]]},"assertion":[{"value":"4 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 December 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 January 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}