{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T05:16:58Z","timestamp":1780636618545,"version":"3.54.1"},"publisher-location":"Cham","reference-count":37,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030125974","type":"print"},{"value":"9783030125981","type":"electronic"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-12598-1_36","type":"book-chapter","created":{"date-parts":[[2019,2,2]],"date-time":"2019-02-02T14:41:50Z","timestamp":1549118510000},"page":"451-462","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Pareto Optimal Set Approximation by Models: A Linear Case"],"prefix":"10.1007","author":[{"given":"Aimin","family":"Zhou","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haoying","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guixu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,2,3]]},"reference":[{"key":"36_CR1","volume-title":"Nonlinear Multiobjective Optimization","author":"K Miettinen","year":"1999","unstructured":"Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer, Dordrecht (1999)"},{"key":"36_CR2","volume-title":"Multi-objective Optimization using Evolutionary Algorithms","author":"K Deb","year":"2001","unstructured":"Deb, K.: Multi-objective Optimization using Evolutionary Algorithms. Wiley, Hoboken (2001)"},{"issue":"1","key":"36_CR3","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.swevo.2011.03.001","volume":"1","author":"A Zhou","year":"2011","unstructured":"Zhou, A., Qu, B.-Y., Li, H., Zhao, S.-Z., Suganthan, P.N., Zhang, Q.: Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evol. Comput. 1(1), 32\u201349 (2011)","journal-title":"Swarm Evol. Comput."},{"key":"36_CR4","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.asoc.2013.10.011","volume":"15","author":"K Deb","year":"2014","unstructured":"Deb, K., Bandaru, S., Greinerc, D., Gaspar-Cunhad, A., Tutum, C.C.: An integrated approach to automated innovization for discovering useful design principles: case studies from engineering. Appl. Soft Comput. 15, 42\u201356 (2014)","journal-title":"Appl. Soft Comput."},{"issue":"4","key":"36_CR5","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s40747-018-0080-1","volume":"4","author":"R Cheng","year":"2018","unstructured":"Cheng, R., He, C., Jin, Y., Yao, X.: Model-based evolutionary algorithms: a short survey. Complex Intell. Syst. 4(4), 283\u2013292 (2018)","journal-title":"Complex Intell. Syst."},{"issue":"5","key":"36_CR6","doi-asserted-by":"publisher","first-page":"1167","DOI":"10.1109\/TEVC.2009.2021467","volume":"13","author":"A Zhou","year":"2009","unstructured":"Zhou, A., Zhang, Q., Jin, Y.: Approximating the set of pareto-optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm. IEEE Trans. Evol. Comput. 13(5), 1167\u20131189 (2009)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"36_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"398","DOI":"10.1007\/978-3-642-37140-0_31","volume-title":"Evolutionary Multi-Criterion Optimization","author":"A Zhou","year":"2013","unstructured":"Zhou, A., Zhang, Q., Zhang, G.: Approximation model guided selection for evolutionary multiobjective optimization. In: Purshouse, R.C., Fleming, P.J., Fonseca, C.M., Greco, S., Shaw, J. (eds.) EMO 2013. LNCS, vol. 7811, pp. 398\u2013412. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-37140-0_31"},{"issue":"4","key":"36_CR8","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1109\/TEVC.2013.2281535","volume":"18","author":"K Deb","year":"2014","unstructured":"Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, Part I: solving problems with box constraints. IEEE Trans. Evol. Comput. 18(4), 577\u2013601 (2014)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"3","key":"36_CR9","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1109\/TEVC.2009.2033671","volume":"14","author":"Q Zhang","year":"2010","unstructured":"Zhang, Q., Liu, W., Tsang, E., Virginas, B.: Expensive multiobjective optimization by MOEA\/D with Gaussian process model. IEEE Trans. Evol. Comput. 14(3), 456\u2013474 (2010)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"36_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1007\/978-3-319-54157-0_12","volume-title":"Evolutionary Multi-Criterion Optimization","author":"K Deb","year":"2017","unstructured":"Deb, K., Hussein, R., Roy, P., Toscano, G.: Classifying metamodeling methods for evolutionary multi-objective optimization: first results. In: Trautmann, H., et al. (eds.) EMO 2017. LNCS, vol. 10173, pp. 160\u2013175. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-54157-0_12"},{"key":"36_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1007\/978-3-319-54157-0_43","volume-title":"Evolutionary Multi-Criterion Optimization","author":"V Volz","year":"2017","unstructured":"Volz, V., Rudolph, G., Naujoks, B.: Surrogate-assisted partial order-based evolutionary optimisation. In: Trautmann, H., et al. (eds.) EMO 2017. LNCS, vol. 10173, pp. 639\u2013653. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-54157-0_43"},{"key":"36_CR12","series-title":"Studies in Computational Intelligence","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/978-3-540-34954-9_10","volume-title":"Scalable Optimization via Probabilistic Modeling","author":"M Pelikan","year":"2006","unstructured":"Pelikan, M., Sastry, K., Goldberg, D.E.: Multiobjective estimation of distribution algorithms. In: Pelikan, M., Sastry, K., Cant\u00faPaz, E. (eds.) Scalable Optimization via Probabilistic Modeling. Studies in Computational Intelligence, vol. 33, pp. 223\u2013248. Springer, Berlin, Heidelberg (2006). https:\/\/doi.org\/10.1007\/978-3-540-34954-9_10"},{"issue":"3","key":"36_CR13","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/S0888-613X(02)00090-7","volume":"31","author":"PA Bosman","year":"2002","unstructured":"Bosman, P.A., Thierens, D.: Multi-objective optimization with diversity preserving mixture-based iterated density estimation evolutionary algorithms. Int. J. Approx. Reason. 31(3), 259\u2013289 (2002)","journal-title":"Int. J. Approx. Reason."},{"key":"36_CR14","doi-asserted-by":"crossref","unstructured":"Zapotecas-Mart\u00ednez, S., Derbel, B., Liefooghe, A., Brockhoff, D., Aguirre, H.E., Tanaka, K.: Injecting CMA-ES into MOEA\/D. In: Proceedings of the Annual Conference on Genetic and Evolutionary Computation (GECCO), pp. 783\u2013790. ACM (2015)","DOI":"10.1145\/2739480.2754754"},{"key":"36_CR15","doi-asserted-by":"crossref","unstructured":"Wang, T.-C., Liaw, R.-T., Ting, C.-K.: MOEA\/D using covariance matrix adaptation evolution strategy for complex multi-objective optimization problems. In: IEEE Congress on Evolutionary Computation (CEC), pp. 983\u2013990 (2016)","DOI":"10.1109\/CEC.2016.7743896"},{"issue":"1","key":"36_CR16","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1109\/TCYB.2015.2507366","volume":"47","author":"H Li","year":"2017","unstructured":"Li, H., Zhang, Q., Deng, J.: Biased multiobjective optimization and decomposition algorithm. IEEE Trans. Cybern. 47(1), 52\u201366 (2017)","journal-title":"IEEE Trans. Cybern."},{"key":"36_CR17","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/j.ins.2013.06.037","volume":"248","author":"VA Shim","year":"2013","unstructured":"Shim, V.A., Tan, K.C., Cheong, C.Y., Chia, J.Y.: Enhancing the scalability of multi-objective optimization via restricted Boltzmann machine-based estimation of distribution algorithm. Inf. Sci. 248, 191\u2013213 (2013)","journal-title":"Inf. Sci."},{"issue":"7","key":"36_CR18","doi-asserted-by":"publisher","first-page":"912","DOI":"10.1080\/0305215X.2013.812727","volume":"46","author":"P Bhardwaj","year":"2014","unstructured":"Bhardwaj, P., Dasgupta, B., Deb, K.: Modelling the pareto-optimal set using B-spline basis functions for continuous multi-objective optimization problems. Eng. Optim. 46(7), 912\u2013938 (2014)","journal-title":"Eng. Optim."},{"key":"36_CR19","doi-asserted-by":"crossref","unstructured":"Ahn, C.W., Ramakrishna, R.S.: Multiobjective real-coded Bayesian optimization algorithm revisited: diversity preservation. In: Proceedings of the Annual Conference on Genetic and Evolutionary Computation (GECCO), pp. 593\u2013600 (2007)","DOI":"10.1145\/1276958.1277079"},{"issue":"4","key":"36_CR20","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s10472-012-9303-0","volume":"68","author":"L Mart\u00ed","year":"2013","unstructured":"Mart\u00ed, L., Garc\u00eda, J., Berlanga, A., Molina, J.M.: Multi-objective optimization with an adaptive resonance theory-based estimation of distribution algorithm. Ann. Math. Artif. Intell. 68(4), 247\u2013273 (2013)","journal-title":"Ann. Math. Artif. Intell."},{"issue":"6","key":"36_CR21","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1109\/TEVC.2015.2395073","volume":"19","author":"R Cheng","year":"2015","unstructured":"Cheng, R., Jin, Y., Narukawa, K., Sendhoff, B.: A multiobjective evolutionary algorithm using Gaussian process-based inverse modeling. IEEE Trans. Evol. Comput. 19(6), 838\u2013856 (2015)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"36_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8280-4","volume-title":"Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach","author":"C Hillermeier","year":"2001","unstructured":"Hillermeier, C.: Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach. Birkhauser, Basel (2001)"},{"issue":"1","key":"36_CR23","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1109\/TEVC.2007.894202","volume":"12","author":"Q Zhang","year":"2008","unstructured":"Zhang, Q., Zhou, A., Jin, Y.: RM-MEDA: a regularity model-based multiobjective estimation of distribution algorithm. IEEE Trans. Evol. Comput. 12(1), 41\u201363 (2008)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"36_CR24","unstructured":"Dai, G., Wang, J., Zhu, J.: A hybrid multi-objective algorithm using genetic and estimation of distribution based on design of experiments. In: IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS), vol. 1, pp. 284\u2013288 (2009)"},{"issue":"9","key":"36_CR25","doi-asserted-by":"publisher","first-page":"2555","DOI":"10.1016\/j.camwa.2011.02.048","volume":"31","author":"Y Liu","year":"2011","unstructured":"Liu, Y., Xiao, B., Dai, G.: Hybrid multi-objective algorithm based on probabilistic model. J. Comput. Appl. 31(9), 2555\u20132558 (2011)","journal-title":"J. Comput. Appl."},{"key":"36_CR26","unstructured":"Yang, D., Jiao, L., Gong, M., Feng, H.: Hybrid multiobjective estimation of distribution algorithm by local linear embedding and an immune inspired algorithm. In: IEEE Congress on Evolutionary Computation (CEC), pp. 463\u2013470 (2009)"},{"issue":"8","key":"36_CR27","doi-asserted-by":"publisher","first-page":"2654","DOI":"10.1016\/j.asoc.2012.04.005","volume":"12","author":"Y Qi","year":"2012","unstructured":"Qi, Y., Liu, F., Liu, M., Gong, M., Jiao, L.: Multi-objective immune algorithm with Baldwinian learning. Appl. Soft Comput. 12(8), 2654\u20132674 (2012)","journal-title":"Appl. Soft Comput."},{"issue":"7","key":"36_CR28","doi-asserted-by":"publisher","first-page":"1383","DOI":"10.1007\/s00500-013-1151-2","volume":"18","author":"Y Li","year":"2014","unstructured":"Li, Y., Xu, X., Li, P., Jiao, L.: Improved RM-MEDA with local learning. Soft Comput. 18(7), 1383\u2013397 (2014)","journal-title":"Soft Comput."},{"issue":"1","key":"36_CR29","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1162\/EVCO_a_00122","volume":"18","author":"H Wang","year":"2015","unstructured":"Wang, H., Jiao, L., Shang, R., He, S., Liu, F.: A memetic optimization strategy based on dimension reduction in decision space. Evol. Comput. 18(1), 69\u2013100 (2015)","journal-title":"Evol. Comput."},{"key":"36_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/978-3-642-16493-4_24","volume-title":"Advances in Computation and Intelligence","author":"L Mo","year":"2010","unstructured":"Mo, L., Dai, G., Zhu, J.: The RM-MEDA Based on elitist strategy. In: Cai, Z., Hu, C., Kang, Z., Liu, Y. (eds.) ISICA 2010. LNCS, vol. 6382, pp. 229\u2013239. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-16493-4_24"},{"issue":"11","key":"36_CR31","doi-asserted-by":"publisher","first-page":"3526","DOI":"10.1016\/j.asoc.2012.06.008","volume":"12","author":"Y Wang","year":"2012","unstructured":"Wang, Y., Xiang, J., Cai, Z.: A regularity model-based multiobjective estimation of distribution algorithm with reducing redundant cluster operator. Appl. Soft Comput. 12(11), 3526\u20133538 (2012)","journal-title":"Appl. Soft Comput."},{"issue":"6","key":"36_CR32","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1109\/TEVC.2007.892759","volume":"11","author":"Q Zhang","year":"2007","unstructured":"Zhang, Q., Li, H.: MOEA\/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712\u2013731 (2007)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"2","key":"36_CR33","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1109\/TEVC.2008.925798","volume":"13","author":"H Li","year":"2009","unstructured":"Li, H., Zhang, Q.: Multiobjective optimization problems with complicated Pareto sets, MOEA\/D and NSGA-II. IEEE Trans. Evol. Comput. 13(2), 284\u2013302 (2009)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"36_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-79159-1","volume-title":"Adaptive Scalarization Methods in Multiobjective Optimization","author":"G Eichfelder","year":"2008","unstructured":"Eichfelder, G.: Adaptive Scalarization Methods in Multiobjective Optimization. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-79159-1"},{"issue":"3","key":"36_CR35","first-page":"440","volume":"21","author":"A Trivedi","year":"2017","unstructured":"Trivedi, A., Srinivasan, D., Sanyal, K., Ghosh, A.: A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans. Evol. Comput. 21(3), 440\u2013462 (2017)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"36_CR36","unstructured":"Zhou, A., Zhang, Q., Jin, Y., Tsang, E.P.K., Okabe, T.: A model-based evolutionary algorithm for bi-objective optimization. In: IEEE Congress on Evolutionary Computation (CEC), pp. 2568\u20132575 (2005)"},{"issue":"2","key":"36_CR37","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1109\/TEVC.2003.810758","volume":"7","author":"E Zitzler","year":"2003","unstructured":"Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117\u2013132 (2003)","journal-title":"IEEE Trans. Evol. Comput."}],"container-title":["Lecture Notes in Computer Science","Evolutionary Multi-Criterion Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-12598-1_36","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T17:25:10Z","timestamp":1710264310000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-12598-1_36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030125974","9783030125981"],"references-count":37,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-12598-1_36","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"3 February 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"EMO","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Evolutionary Multi-Criterion Optimization","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"East Lansing, MI","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 March 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13 March 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"emo2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.emo2019.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"76","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"59","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"78% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.6","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"4.1","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}