{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T22:21:39Z","timestamp":1787437299431,"version":"build-2736575974"},"publisher-location":"Cham","reference-count":14,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032362223","type":"print"},{"value":"9783032362230","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T00:00:00Z","timestamp":1787443200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T00:00:00Z","timestamp":1787443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2027]]},"DOI":"10.1007\/978-3-032-36223-0_1","type":"book-chapter","created":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T21:44:21Z","timestamp":1787435061000},"page":"3-18","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Permutation-Based Reformulation for\u00a0Approximating Weitzman Diversity for\u00a0Benchmarking in\u00a0Multi-objective Optimization"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-7637-7635","authenticated-orcid":false,"given":"Mahboubeh","family":"Nezhadmoghaddam","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-7615-4201","authenticated-orcid":false,"given":"Adri\u00e1n Isa\u00ed","family":"Morales-Paredes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8748-3807","authenticated-orcid":false,"given":"Julio","family":"Ju\u00e1rez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1131-098X","authenticated-orcid":false,"given":"Jes\u00fas Guillermo","family":"Falc\u00f3n-Cardona","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1099-8148","authenticated-orcid":false,"given":"V\u00edctor Adri\u00e1n Sosa","family":"Hern\u00e1ndez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,8,23]]},"reference":[{"key":"1_CR1","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1162\/106365600568202","volume":"8","author":"E Zitzler","year":"2000","unstructured":"Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8, 173\u2013195 (2000)","journal-title":"Evol. Comput."},{"key":"1_CR2","doi-asserted-by":"crossref","unstructured":"Li, M., Yao, X.: Quality evaluation of solution sets in multiobjective optimisation: a survey. ACM Comput. Surv. 52, 26:1\u201326:38 (2019)","DOI":"10.1145\/3300148"},{"key":"1_CR3","unstructured":"Schott, J.R.: Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. Master\u2019s thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts (1995)"},{"issue":"3","key":"1_CR4","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1109\/MCI.2019.2919398","volume":"14","author":"Y Tian","year":"2019","unstructured":"Tian, Y., Cheng, R., Zhang, X., Li, M., Jin, Y.: Diversity assessment of multi-objective evolutionary algorithms: performance metric and benchmark problems [research frontier]. IEEE Comput. Intell. Mag. 14(3), 61\u201374 (2019)","journal-title":"IEEE Comput. Intell. Mag."},{"key":"1_CR5","first-page":"1","volume":"29","author":"J Falc\u00f3n-Cardona","year":"2024","unstructured":"Falc\u00f3n-Cardona, J., Uribe, L., Rosas, P.: Riesz $$s$$-energy as a diversity indicator in evolutionary multi-objective optimization. IEEE Trans. Evol. Comput. 29, 1\u201315 (2024)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"6","key":"1_CR6","doi-asserted-by":"publisher","first-page":"1510","DOI":"10.1109\/TCYB.2016.2550502","volume":"47","author":"H Wang","year":"2017","unstructured":"Wang, H., Jin, Y., Yao, X.: Diversity assessment in many-objective optimization. IEEE Trans. Cybern. 47(6), 1510\u20131522 (2017)","journal-title":"IEEE Trans. Cybern."},{"issue":"2","key":"1_CR7","doi-asserted-by":"publisher","first-page":"363","DOI":"10.2307\/2118476","volume":"107","author":"ML Weitzman","year":"1992","unstructured":"Weitzman, M.L.: On diversity$$^*$$. Quart. J. Econ. 107(2), 363\u2013405 (1992)","journal-title":"Quart. J. Econ."},{"key":"1_CR8","doi-asserted-by":"publisher","unstructured":"Emmerich, M.T., Deutz, A.H., Kruisselbrink, J.W.: On quality indicators for black-box level set approximation. In:\u00a0Tantar, E., et al. (eds.) EVOLVE\u2014A Bridge Between Probability, Set Oriented Numerics and Evolutionary Computation. Studies in Computational Intelligence, vol.\u00a0447, ch.\u00a04, pp.\u00a0157\u2013185. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-32726-1_4","DOI":"10.1007\/978-3-642-32726-1_4"},{"key":"1_CR9","doi-asserted-by":"crossref","unstructured":"Falc\u00f3n-Cardona, J.G.,\u00a0Nezhadmoghaddam, M.,\u00a0Bernal-Zubieta, E.: An analysis of the preferences of distribution indicators in evolutionary multi-objective optimization. In: 2024 IEEE Congress on Evolutionary Computation (CEC), Yokohama, Japan, pp.\u00a01\u20138 (2024)","DOI":"10.1109\/CEC60901.2024.10611924"},{"key":"1_CR10","volume-title":"The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization","author":"EL Lawler","year":"1985","unstructured":"Lawler, E.L., Lenstra, J.K., Kan, A.H.G.R., Shmoys, D.B.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. John Wiley & Sons, Chichester (1985)"},{"key":"1_CR11","unstructured":"Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical Report (1976)"},{"key":"1_CR12","unstructured":"Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT press, Cambridge (2022)"},{"issue":"3","key":"1_CR13","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1137\/S1052623496307510","volume":"8","author":"I Das","year":"1998","unstructured":"Das, I., Dennis, J.E.: Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM J. Optim. 8(3), 631\u2013657 (1998)","journal-title":"SIAM J. Optim."},{"key":"1_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2026.123470","volume":"747","author":"M Nezhadmoghaddam","year":"2026","unstructured":"Nezhadmoghaddam, M., Ju\u00e1rez, J., Falc\u00f3n-Cardona, J.G., Emmerich, M.T., Deutz, A.: Approximating optimal $$\\mu $$-point distributions over a generalized sphere for Riesz s-energy using a gradient descent algorithm. Inf. Sci. 747, 123470 (2026)","journal-title":"Inf. Sci."}],"container-title":["Lecture Notes in Computer Science","Parallel Problem Solving from Nature \u2013 PPSN XIX"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-36223-0_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T21:44:22Z","timestamp":1787435062000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-36223-0_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,23]]},"ISBN":["9783032362223","9783032362230"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-36223-0_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,23]]},"assertion":[{"value":"23 August 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"PPSN","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Parallel Problem Solving from Nature","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Trento","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 August 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2 September 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ppsn2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}