{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T03:34:30Z","timestamp":1761708870165,"version":"3.40.4"},"publisher-location":"Berlin, Heidelberg","reference-count":28,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642371394"},{"type":"electronic","value":"9783642371400"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-37140-0_15","type":"book-chapter","created":{"date-parts":[[2013,3,12]],"date-time":"2013-03-12T15:18:19Z","timestamp":1363101499000},"page":"156-170","source":"Crossref","is-referenced-by-count":12,"title":["Theory and Algorithms for Finding Knees"],"prefix":"10.1007","author":[{"given":"Pradyumn Kumar","family":"Shukla","sequence":"first","affiliation":[]},{"given":"Marlon Alexander","family":"Braun","sequence":"additional","affiliation":[]},{"given":"Hartmut","family":"Schmeck","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"15_CR1","volume-title":"Cours d\u2019Economie Politique","author":"V. Pareto","year":"1896","unstructured":"Pareto, V.: Cours d\u2019Economie Politique. Droz, Gen\u00e8ve (1896)"},{"key":"15_CR2","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1525\/9780520411586-036","volume-title":"Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability","author":"H.W. Kuhn","year":"1951","unstructured":"Kuhn, H.W., Tucker, A.W.: Nonlinear programming. In: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481\u2013492. University of California Press, Berkeley (1951)"},{"issue":"1","key":"15_CR3","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1023\/A:1021775112119","volume":"101","author":"E.K. Makarov","year":"1999","unstructured":"Makarov, E.K., Rachkovski, N.N.: Unified representation of proper efficiency by means of dilating cones. J. Optim. Theory Appl.\u00a0101(1), 141\u2013165 (1999)","journal-title":"J. Optim. Theory Appl."},{"key":"15_CR4","doi-asserted-by":"publisher","first-page":"618","DOI":"10.1016\/0022-247X(68)90201-1","volume":"22","author":"A.M. Geoffrion","year":"1968","unstructured":"Geoffrion, A.M.: Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and Applications\u00a022, 618\u2013630 (1968)","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"2","key":"15_CR5","doi-asserted-by":"publisher","first-page":"1630","DOI":"10.1016\/j.ejor.2006.08.002","volume":"181","author":"P.K. Shukla","year":"2007","unstructured":"Shukla, P.K., Deb, K.: On finding multiple pareto-optimal solutions using classical and evolutionary generating methods. European J. Oper. Res.\u00a0181(2), 1630\u20131652 (2007)","journal-title":"European J. Oper. Res."},{"key":"15_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/978-3-642-15871-1_14","volume-title":"Parallel Problem Solving from Nature, PPSN XI","author":"P.K. Shukla","year":"2010","unstructured":"Shukla, P.K., Hirsch, C., Schmeck, H.: A Framework for Incorporating Trade-Off Information Using Multi-Objective Evolutionary Algorithms. In: Schaefer, R., Cotta, C., Ko\u0142odziej, J., Rudolph, G. (eds.) PPSN XI, Part II. LNCS, vol.\u00a06239, pp. 131\u2013140. Springer, Heidelberg (2010)"},{"issue":"2","key":"15_CR7","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1109\/TPAS.1983.317716","volume":"102","author":"H. Merrill","year":"1983","unstructured":"Merrill, H.: Cogeneration - a strategic evaluation. IEEE Transactions on Power Apparatus and Systems\u00a0102(2), 463\u2013471 (1983)","journal-title":"IEEE Transactions on Power Apparatus and Systems"},{"issue":"3","key":"15_CR8","doi-asserted-by":"publisher","first-page":"1284","DOI":"10.1109\/59.14593","volume":"3","author":"W. Burke","year":"1988","unstructured":"Burke, W., Merrill, H., Schweppe, F., Lovell, B., McCoy, M., Monohon, S.: Trade off methods in system planning. IEEE Transactions on Power Systems\u00a03(3), 1284\u20131290 (1988)","journal-title":"IEEE Transactions on Power Systems"},{"issue":"11","key":"15_CR9","doi-asserted-by":"publisher","first-page":"1175","DOI":"10.1080\/0305215X.2010.548863","volume":"43","author":"K. Deb","year":"2011","unstructured":"Deb, K., Gupta, S.: Understanding knee points in bicriteria problems and their implications as preferred solution principles. Engineering Optimization\u00a043(11), 1175\u20131204 (2011)","journal-title":"Engineering Optimization"},{"issue":"6","key":"15_CR10","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1080\/0305215042000274942","volume":"36","author":"C.A. Mattson","year":"2004","unstructured":"Mattson, C.A., Mullur, A.A., Messac, A.: Smart pareto filter: obtaining a minimal representation of multiobjective design space. Engineering Optimization\u00a036(6), 721\u2013740 (2004)","journal-title":"Engineering Optimization"},{"issue":"4","key":"15_CR11","doi-asserted-by":"publisher","first-page":"810","DOI":"10.1109\/TEVC.2009.2017515","volume":"13","author":"L. Rachmawati","year":"2009","unstructured":"Rachmawati, L., Srinivasan, D.: Multiobjective evolutionary algorithm with controllable focus on the knees of the pareto front. IEEE Transactions on Evolutionary Computation\u00a013(4), 810\u2013824 (2009)","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"15_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"722","DOI":"10.1007\/978-3-540-30217-9_73","volume-title":"Parallel Problem Solving from Nature - PPSN VIII","author":"J. Branke","year":"2004","unstructured":"Branke, J., Deb, K., Dierolf, H., Osswald, M.: Finding Knees in Multi-objective Optimization. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guerv\u00f3s, J.J., Bullinaria, J.A., Rowe, J.E., Ti\u0148o, P., Kab\u00e1n, A., Schwefel, H.-P. (eds.) PPSN VIII. LNCS, vol.\u00a03242, pp. 722\u2013731. Springer, Heidelberg (2004)"},{"issue":"2-3","key":"15_CR13","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/BF01195985","volume":"18","author":"I. Das","year":"1999","unstructured":"Das, I.: On characterizing the \u201cknee\u201d of the Pareto curve based on Normal-Boundary Intersection. Structural Optimization\u00a018(2-3), 107\u2013115 (1999)","journal-title":"Structural Optimization"},{"key":"15_CR14","volume-title":"Nonlinear Multiobjective Optimization","author":"K. Miettinen","year":"1999","unstructured":"Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer, Boston (1999)"},{"key":"15_CR15","doi-asserted-by":"publisher","first-page":"1118","DOI":"10.1145\/1774088.1774325","volume-title":"Proceedings of the 2010 ACM Symposium on Applied Computing, SAC 2010","author":"S. Bechikh","year":"2010","unstructured":"Bechikh, S., Ben Said, L., Gh\u00e9dira, K.: Searching for knee regions in multi-objective optimization using mobile reference points. In: Proceedings of the 2010 ACM Symposium on Applied Computing, SAC 2010, pp. 1118\u20131125. ACM, New York (2010)"},{"issue":"3","key":"15_CR16","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1137\/S1052623496307510","volume":"8","author":"I. Das","year":"1998","unstructured":"Das, I., Dennis, J.: Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal of Optimization\u00a08(3), 631\u2013657 (1998)","journal-title":"SIAM Journal of Optimization"},{"issue":"6","key":"15_CR17","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1109\/TAC.1975.1101105","volume":"20","author":"F. Gembicki","year":"1975","unstructured":"Gembicki, F., Haimes, Y.: Approach to performance and sensitivity multiobjective optimization: The goal attainment method. IEEE Transactions on Automatic Control\u00a020(6), 769\u2013771 (1975)","journal-title":"IEEE Transactions on Automatic Control"},{"key":"15_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1007\/978-3-540-87700-4_79","volume-title":"Parallel Problem Solving from Nature \u2013 PPSN X","author":"O. Sch\u00fctze","year":"2008","unstructured":"Sch\u00fctze, O., Laumanns, M., Coello Coello, C.: Approximating the Knee of an MOP with Stochastic Search Algorithms. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN X. LNCS, vol.\u00a05199, pp. 795\u2013804. Springer, Heidelberg (2008)"},{"key":"15_CR19","doi-asserted-by":"crossref","unstructured":"Kaliszewski, I.: Quantitative Pareto analysis by cone separation technique. Kluwer Academic Publishers (1994)","DOI":"10.1007\/978-1-4615-2772-5"},{"key":"15_CR20","unstructured":"Kaliszewski, I.: Soft computing for complex multiple criteria decision making. Springer, New York (2006)"},{"key":"15_CR21","doi-asserted-by":"crossref","unstructured":"Conway, J.B.: Functions of one complex variable, 2nd edn. Graduate Texts in Mathematics, vol.\u00a011. Springer (1978)","DOI":"10.1007\/978-1-4612-6313-5"},{"key":"15_CR22","series-title":"Classics in Applied Mathematics","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971309","volume-title":"Optimization and nonsmooth analysis","author":"F.H. Clarke","year":"1990","unstructured":"Clarke, F.H.: Optimization and nonsmooth analysis, 2nd edn. Classics in Applied Mathematics, vol.\u00a05. SIAM, Philadelphia (1990)","edition":"2"},{"issue":"2","key":"15_CR23","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1109\/4235.996017","volume":"6","author":"K. Deb","year":"2002","unstructured":"Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation\u00a06(2), 182\u2013197 (2002)","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"15_CR24","unstructured":"Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley (2001)"},{"key":"15_CR25","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/1-84628-137-7_6","volume-title":"Evolutionary Multiobjective Optimization","author":"K. Deb","year":"2005","unstructured":"Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. In: Abraham, A., et al. (eds.) Evolutionary Multiobjective Optimization, pp. 105\u2013145. Springer, London (2005)"},{"issue":"10","key":"15_CR26","doi-asserted-by":"publisher","first-page":"760","DOI":"10.1016\/j.advengsoft.2011.05.014","volume":"42","author":"J.J. Durillo","year":"2011","unstructured":"Durillo, J.J., Nebro, A.J.: jmetal: A java framework for multi-objective optimization. Advances in Engineering Software\u00a042(10), 760\u2013771 (2011)","journal-title":"Advances in Engineering Software"},{"issue":"4","key":"15_CR27","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1162\/evco.2006.14.4.463","volume":"14","author":"K. Deb","year":"2006","unstructured":"Deb, K., Gupta, H.: Introducing robustness in multi-objective optimization. Evol. Comput.\u00a014(4), 463\u2013494 (2006)","journal-title":"Evol. Comput."},{"issue":"4","key":"15_CR28","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1145\/321906.321910","volume":"22","author":"H.T. Kung","year":"1975","unstructured":"Kung, H.T., Luccio, F., Preparata, F.P.: On finding the maxima of a set of vectors. Journal of the Association for Computing Machinery\u00a022(4), 469\u2013476 (1975)","journal-title":"Journal of the Association for Computing Machinery"}],"container-title":["Lecture Notes in Computer Science","Evolutionary Multi-Criterion Optimization"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-37140-0_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T00:19:41Z","timestamp":1745972381000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-37140-0_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642371394","9783642371400"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-37140-0_15","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}