{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T03:25:05Z","timestamp":1769916305122,"version":"3.49.0"},"publisher-location":"Cham","reference-count":34,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319554525","type":"print"},{"value":"9783319554532","type":"electronic"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-55453-2_16","type":"book-chapter","created":{"date-parts":[[2017,3,8]],"date-time":"2017-03-08T05:12:42Z","timestamp":1488949962000},"page":"233-248","source":"Crossref","is-referenced-by-count":42,"title":["Understanding Phase Transitions with Local Optima Networks: Number Partitioning as a Case Study"],"prefix":"10.1007","author":[{"given":"Gabriela","family":"Ochoa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nadarajen","family":"Veerapen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fabio","family":"Daolio","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Tomassini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,3,9]]},"reference":[{"key":"16_CR1","volume-title":"Computers and Intractability","author":"MR Garey","year":"1979","unstructured":"Garey, M.R., Johnson, D.S.: Computers and Intractability. Freeman, San Francisco (1979)"},{"key":"16_CR2","volume-title":"Combinatorial Optimization: Algorithms and Complexity","author":"CH Papadimitriou","year":"1982","unstructured":"Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Englewood Cliffs (1982)"},{"key":"16_CR3","unstructured":"Gent, I.P., Walsh, T.: The SAT phase transition. In: Proceedings of ECAI 1996, vol. 94, pp. 105\u2013109. PITMAN (1994)"},{"issue":"1","key":"16_CR4","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S0304-3975(01)00164-5","volume":"265","author":"J Culberson","year":"2001","unstructured":"Culberson, J., Gent, I.P.: Frozen development in graph coloring. Theor. Comput. Sci. 265(1), 227\u2013264 (2001)","journal-title":"Theor. Comput. Sci."},{"key":"16_CR5","unstructured":"Gent, I.P., Walsh, T.: Phase transitions and annealed theories: number partitioning as a case study. In: Proceedings of ECAI 1996, pp. 170\u2013174. PITMAN (1996)"},{"key":"16_CR6","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/S1574-6526(06)80022-2","volume-title":"Handbook of Constraint Programming","author":"C Gomes","year":"2006","unstructured":"Gomes, C., Walsh, T.: Randomness and structure. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, vol. 2, pp. 639\u2013664. Elsevier, New York (2006)"},{"key":"16_CR7","doi-asserted-by":"crossref","unstructured":"Kambhampati, S.C., Liu, T.: Phase transition and network structure in realistic SAT problems. In: Proceedings of the Twenty-Seventh AAAI Conference on Artificial Intelligence, AAAI 2013, pp. 1619\u20131620. AAAI Press (2013)","DOI":"10.1609\/aaai.v27i1.8529"},{"issue":"1","key":"16_CR8","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0304-3975(01)00149-9","volume":"265","author":"OC Martin","year":"2001","unstructured":"Martin, O.C., Monasson, R., Zecchina, R.: Statistical mechanics methods and phase transitions in optimization problems. Theor. Comput. Sci. 265(1), 3\u201367 (2001)","journal-title":"Theor. Comput. Sci."},{"issue":"6","key":"16_CR9","doi-asserted-by":"crossref","first-page":"066114","DOI":"10.1103\/PhysRevE.78.066114","volume":"78","author":"M Tomassini","year":"2008","unstructured":"Tomassini, M., V\u00e9rel, S., Ochoa, G.: Complex-network analysis of combinatorial spaces: the NK landscape case. Phys. Rev. E 78(6), 066114 (2008)","journal-title":"Phys. Rev. E"},{"issue":"6","key":"16_CR10","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1109\/TEVC.2010.2046175","volume":"15","author":"S Verel","year":"2011","unstructured":"Verel, S., Ochoa, G., Tomassini, M.: Local optima networks of NK landscapes with neutrality. IEEE Trans. Evol. Comput. 15(6), 783\u2013797 (2011)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"14","key":"16_CR11","doi-asserted-by":"crossref","first-page":"6896","DOI":"10.1063\/1.478595","volume":"110","author":"JPK Doye","year":"1999","unstructured":"Doye, J.P.K., Miller, M.A., Wales, D.J.: The double-funnel energy landscape of the 38-atom Lennard-Jones cluster. J. Chem. Phys. 110(14), 6896\u20136906 (1999)","journal-title":"J. Chem. Phys."},{"key":"16_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1007\/978-3-540-87700-4_50","volume-title":"Parallel Problem Solving from Nature \u2013 PPSN X","author":"M Lunacek","year":"2008","unstructured":"Lunacek, M., Whitley, D., Sutton, A.: The impact of global structure on search. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 498\u2013507. Springer, Heidelberg (2008). doi: 10.1007\/978-3-540-87700-4_50"},{"key":"16_CR13","doi-asserted-by":"crossref","unstructured":"Kerschke, P., Preuss, M., Wessing, S., Trautmann, H.: Detecting funnel structures by means of exploratory landscape analysis. In: Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, GECCO 2015, pp. 265\u2013272. ACM, New York (2015)","DOI":"10.1145\/2739480.2754642"},{"key":"16_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1007\/978-3-319-30698-8_5","volume-title":"Evolutionary Computation in Combinatorial Optimization","author":"G Ochoa","year":"2016","unstructured":"Ochoa, G., Veerapen, N.: Deconstructing the big valley search space hypothesis. In: Chicano, F., Hu, B., Garc\u00eda-S\u00e1nchez, P. (eds.) EvoCOP 2016. LNCS, vol. 9595, pp. 58\u201373. Springer, Heidelberg (2016). doi: 10.1007\/978-3-319-30698-8_5"},{"key":"16_CR15","doi-asserted-by":"crossref","unstructured":"Ochoa, G., Veerapen, N.: Additional dimensions to the study of funnels in combinatorial landscapes. In: Proceedings of the Genetic and Evolutionary Computation Conference 2016, GECCO 2016, pp. 373\u2013380. ACM, New York (2016)","DOI":"10.1145\/2908812.2908820"},{"key":"16_CR16","doi-asserted-by":"crossref","unstructured":"Herrmann, S., Ochoa, G., Rothlauf, F.: Communities of local optima as funnels in fitness landscapes. In: Proceedings of the Genetic and Evolutionary Computation Conference 2016, GECCO 2016, pp. 325\u2013331. ACM, New York (2016)","DOI":"10.1145\/2908812.2908818"},{"issue":"15","key":"16_CR17","doi-asserted-by":"crossref","first-page":"3417","DOI":"10.1088\/0305-4470\/31\/15\/007","volume":"31","author":"FF Ferreira","year":"1998","unstructured":"Ferreira, F.F., Fontanari, J.F.: Probabilistic analysis of the number partitioning problem. J. Phys. A: Math. Gen. 31(15), 3417 (1998)","journal-title":"J. Phys. A: Math. Gen."},{"issue":"20","key":"16_CR18","doi-asserted-by":"crossref","first-page":"4281","DOI":"10.1103\/PhysRevLett.81.4281","volume":"81","author":"S Mertens","year":"1998","unstructured":"Mertens, S.: Phase transition in the number partitioning problem. Phys. Rev. Lett. 81(20), 4281\u20134284 (1998)","journal-title":"Phys. Rev. Lett."},{"issue":"5","key":"16_CR19","doi-asserted-by":"crossref","first-page":"056701","DOI":"10.1103\/PhysRevE.67.056701","volume":"67","author":"PF Stadler","year":"2003","unstructured":"Stadler, P.F., Hordijk, W., Fontanari, J.F.: Phase transition and landscape statistics of the number partitioning problem. Phys. Rev. E 67(5), 056701 (2003)","journal-title":"Phys. Rev. E"},{"issue":"2\/2002","key":"16_CR20","first-page":"155","volume":"216","author":"C Flamm","year":"2002","unstructured":"Flamm, C., Hofacker, I.L., Stadler, P.F., Wolfinger, M.T.: Barrier trees of degenerate landscapes. Z. Phys. Chem. (Int. J. Res. Phys. Chem. Chem. Phy.) 216(2\/2002), 155\u2013173 (2002)","journal-title":"Z. Phys. Chem. (Int. J. Res. Phys. Chem. Chem. Phy.)"},{"key":"16_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1007\/978-3-662-44320-0_18","volume-title":"Evolutionary Computation in Combinatorial Optimisation","author":"K Alyahya","year":"2014","unstructured":"Alyahya, K., Rowe, J.E.: Phase transition and landscape properties of the number partitioning problem. In: Blum, C., Ochoa, G. (eds.) EvoCOP 2014. LNCS, vol. 8600, pp. 206\u2013217. Springer, Heidelberg (2014). doi: 10.1007\/978-3-662-44320-0_18"},{"issue":"2","key":"16_CR22","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/0167-6377(94)90065-5","volume":"16","author":"KD Boese","year":"1994","unstructured":"Boese, K.D., Kahng, A.B., Muddu, S.: A new adaptive multi-start technique for combinatorial global optimizations. Oper. Res. Lett. 16(2), 101\u2013113 (1994)","journal-title":"Oper. Res. Lett."},{"issue":"2","key":"16_CR23","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1057\/jors.2010.116","volume":"62","author":"DR Hains","year":"2011","unstructured":"Hains, D.R., Whitley, L.D., Howe, A.E.: Revisiting the big valley search space structure in the TSP. J. Oper. Res. Soc. 62(2), 305\u2013312 (2011)","journal-title":"J. Oper. Res. Soc."},{"key":"16_CR24","doi-asserted-by":"crossref","first-page":"3951","DOI":"10.1103\/PhysRevLett.74.3951","volume":"74","author":"RS Berry","year":"1995","unstructured":"Berry, R.S., Kunz, R.E.: Topography and dynamics of multidimensional interatomic potential surfaces. Phys. Rev. Lett. 74, 3951\u20133954 (1995)","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"16_CR25","doi-asserted-by":"crossref","first-page":"S86","DOI":"10.1088\/1478-3975\/2\/4\/S02","volume":"2","author":"DJ Wales","year":"2005","unstructured":"Wales, D.J.: Energy landscapes and properties of biomolecules. Phys. Biol. 2(4), S86\u2013S93 (2005)","journal-title":"Phys. Biol."},{"issue":"4","key":"16_CR26","doi-asserted-by":"crossref","first-page":"1495","DOI":"10.1063\/1.473299","volume":"106","author":"OM Becker","year":"1997","unstructured":"Becker, O.M., Karplus, M.: The topology of multidimensional potential energy surfaces: theory and application to peptide structure and kinetics. J. Chem. Phys. 106(4), 1495 (1997)","journal-title":"J. Chem. Phys."},{"key":"16_CR27","doi-asserted-by":"crossref","first-page":"197205","DOI":"10.1103\/PhysRevLett.94.197205","volume":"94","author":"M M\u00e9zard","year":"2005","unstructured":"M\u00e9zard, M., Mora, T., Zecchina, R.: Clustering of solutions in the random satisfiability problem. Phys. Rev. Lett. 94, 197205 (2005)","journal-title":"Phys. Rev. Lett."},{"key":"16_CR28","first-page":"187","volume":"117","author":"PF Stadler","year":"2002","unstructured":"Stadler, P.F.: Fitness landscapes. Appl. Math. Comput. 117, 187\u2013207 (2002)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"16_CR29","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1073\/pnas.93.1.397","volume":"93","author":"MA Huynen","year":"1996","unstructured":"Huynen, M.A., Stadler, P.F., Fontana, W.: Smoothness within ruggedness: the role of neutrality in adaptation. Proc. Nat. Acad. Sci. U.S.A. 93(1), 397\u2013401 (1996)","journal-title":"Proc. Nat. Acad. Sci. U.S.A."},{"key":"16_CR30","first-page":"18","volume-title":"Proceedings of the Sixth International Conference on Artificial Life, ALIFE VI","author":"L Barnett","year":"1998","unstructured":"Barnett, L.: Ruggedness and neutrality - the NKp family of fitness landscapes. In: Adami, C., Belew, R.K., Kitano, H., Taylor, C. (eds.) Proceedings of the Sixth International Conference on Artificial Life, ALIFE VI, pp. 18\u201327. The MIT Press, Cambridge (1998)"},{"key":"16_CR31","doi-asserted-by":"crossref","unstructured":"Daolio, F., Verel, S., Ochoa, G., Tomassini, M.: Local optima networks of the quadratic assignment problem. In: 2010 IEEE Congress on Evolutionary Computation (CEC), pp. 1\u20138 (2010)","DOI":"10.1109\/CEC.2010.5586481"},{"issue":"9","key":"16_CR32","doi-asserted-by":"crossref","first-page":"1684","DOI":"10.1016\/j.physa.2011.01.005","volume":"390","author":"F Daolio","year":"2011","unstructured":"Daolio, F., Tomassini, M., V\u00e9rel, S., Ochoa, G.: Communities of minima in local optima networks of combinatorial spaces. Phys. A: Stat. Mech. Appl. 390(9), 1684\u20131694 (2011)","journal-title":"Phys. A: Stat. Mech. Appl."},{"key":"16_CR33","doi-asserted-by":"crossref","unstructured":"Auger, A., Hansen, N.: Performance evaluation of an advanced local search evolutionary algorithm. In: The 2005 IEEE Congress on Evolutionary Computation, vol. 2, pp. 1777\u20131784. IEEE (2005)","DOI":"10.1109\/CEC.2005.1554903"},{"key":"16_CR34","series-title":"The Santa Fe Institute Studies in the Sciences of Complexity","first-page":"125","volume-title":"Computational Complexity and Statistical Physics","author":"S Mertens","year":"2006","unstructured":"Mertens, S.: The easiest hard problem: number partitioning. In: Percus, A., Istrate, G., Moore, C. (eds.) Computational Complexity and Statistical Physics. The Santa Fe Institute Studies in the Sciences of Complexity, vol. 125, pp. 125\u2013139. Oxford University Press, New York (2006)"}],"container-title":["Lecture Notes in Computer Science","Evolutionary Computation in Combinatorial Optimization"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-55453-2_16","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T11:36:27Z","timestamp":1658748987000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-55453-2_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319554525","9783319554532"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-55453-2_16","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]}}}