{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T19:12:45Z","timestamp":1787857965197,"version":"build-2784847793"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1998,8]]},"abstract":"<jats:p>This paper proposes an alternate method for finding several Pareto optimal points for a general nonlinear multicriteria optimization problem. Such points collectively capture the trade-off among the various conflicting objectives. It is proved that this method is independent of the relative scales of the functions and is successful in producing an evenly distributed set of points in the Pareto set given an evenly distributed set of parameters, a property which the popular method of minimizing weighted combinations of objective functions lacks. Further, this method can handle more than two objectives while retaining the computational efficiency of continuation-type algorithms. This is an improvement over continuation techniques for tracing the trade-off curve since continuation strategies cannot easily be extended to handle more than two objectives.<\/jats:p>","DOI":"10.1137\/s1052623496307510","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"631-657","source":"Crossref","is-referenced-by-count":2300,"title":["Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems"],"prefix":"10.1137","volume":"8","author":[{"given":"Indraneel","family":"Das","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. E.","family":"Dennis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","unstructured":"I. Das,\n                      Nonlinear Multicriteria Optimization and Robust Optimality\n                      , Ph.D. Thesis, Dept. of Computational and Applied Mathematics, Rice University, Houston, TX, 1997."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01197559"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"H. Eschenauer, J. Koski, and A. Osyczka,\n                      Multicriteria Design Optimization\n                      , Springer\u2010Verlag, Berlin, 1990.","DOI":"10.1007\/978-3-642-48697-5"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3734-6"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"JiguanLin, Three methods for dertemining Pareto\u2010optimal solutions of multiple\u2010objective problems, Plenum, New York, 1976, 117\u201313856:9420","DOI":"10.1007\/978-1-4684-2259-7_9"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0956-0521(91)90049-B"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"J. R. Rao and P. Y. Papalambros,\n                      A non\u2010linear programming continuation strategy for one parameter design optimization problems\n                      , in Proceedings of ASME Design Automation Conference, Montreal, Quebec, Canada, Sept. 17\u201320, 1989, pp. 77\u201389.","DOI":"10.1115\/DETC1989-0077"},{"key":"R8","unstructured":"B. N. 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Giesy,\n                      Multiobjective Insensitive Design of Airplane Control Systems with Uncertain Parameters\n                      , in Proc. of the AIAA Guidance and Control Conference, Albuquerque, NM, Aug. 19\u201321, 1981.","DOI":"10.2514\/6.1981-1818"},{"key":"R12","unstructured":"A. A. Schy, D. P. Giesy, and K. J. Johnson,\n                      Pareto\u2010optimal multi\u2010objective design of airplane control systems\n                      , in Proceedings of the 1980 Joint Automatic Control Conference, American Automatic Control Council, ASME, Vol. 1, New York, 1980."},{"key":"R13","doi-asserted-by":"crossref","unstructured":"AlbertSchy, DanielGiesy, Multicriteria optimization methods for design of aircraft control systems, Math. Concepts Methods Sci. Engrg., Vol. 37, Plenum, New York, 1988, 225\u2013262941594","DOI":"10.1007\/978-1-4899-3734-6_8"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"JuhaniKoski, Multicriteria truss optimization, Math. Concepts Methods Sci. Engrg., Vol. 37, Plenum, New York, 1988, 263\u2013307941595","DOI":"10.1007\/978-1-4899-3734-6_9"},{"key":"R15","unstructured":"Y. Haimes, W. Hall, and H. Freedman,\n                      Multiobjective Optimization in Water Resources Systems\n                      , Elsevier Scientific Publishing Co., Amsterdam, 1975."},{"key":"R16","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1109\/TAC.1976.1101338","volume":"21","author":"Lin Jiguan","year":"1976","journal-title":"IEEE Trans. Automatic Control"},{"key":"R17","unstructured":"G.Katopis, J.Lin, Non\u2010inferiority of controls under double performance objectives: minimal time and minimal energy, Western Periodicals, North Hollywood, Calif., 1974, 129\u201313156:4973"},{"key":"R18","unstructured":"J. G. Lin,\n                      Circuit design under multiple performance objectives\n                      , in Proceedings of the 1974 IEEE Int. Symp. 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