{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T03:02:05Z","timestamp":1778554925024,"version":"3.51.4"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T00:00:00Z","timestamp":1687478400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T00:00:00Z","timestamp":1687478400000},"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":["Optim Lett"],"published-print":{"date-parts":[[2024,1]]},"DOI":"10.1007\/s11590-023-02029-1","type":"journal-article","created":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T20:30:50Z","timestamp":1687552250000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The set partitioning problem in a quantum context"],"prefix":"10.1007","volume":"18","author":[{"given":"Rafael","family":"Cacao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lucas R. C. T.","family":"Cortez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jackson","family":"Forner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hamidreza","family":"Validi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ismael R. de","family":"Farias","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Illya V.","family":"Hicks","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,23]]},"reference":[{"issue":"2","key":"2029_CR1","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1016\/j.ejor.2006.12.068","volume":"186","author":"B Alidaee","year":"2008","unstructured":"Alidaee, B., Kochenberger, G., Lewis, K., Lewis, M., Wang, H.: A new approach for modeling and solving set packing problems. Eur. J. Oper. Res. 186(2), 504\u2013512 (2008)","journal-title":"Eur. J. Oper. Res."},{"issue":"2","key":"2029_CR2","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1287\/opre.12.2.300","volume":"12","author":"ML Balinski","year":"1964","unstructured":"Balinski, M.L., Quandt, R.E.: On an integer program for a delivery problem. Oper. Res. 12(2), 300\u2013304 (1964)","journal-title":"Oper. Res."},{"issue":"5516","key":"2029_CR3","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1126\/science.1057726","volume":"292","author":"E Farhi","year":"2001","unstructured":"Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., Preda, D.: A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292(5516), 472\u2013475 (2001)","journal-title":"Science"},{"issue":"2","key":"2029_CR4","doi-asserted-by":"publisher","first-page":"915","DOI":"10.1103\/PhysRevA.58.915","volume":"58","author":"E Farhi","year":"1998","unstructured":"Farhi, E., Gutmann, S.: Quantum computation and decision trees. Phys. Rev. A 58(2), 915 (1998)","journal-title":"Phys. Rev. A"},{"key":"2029_CR5","unstructured":"Garey, M.R., Johnson, D.S.: Computers and intractability, vol. 174. Freeman San Francisco (1979)"},{"issue":"5","key":"2029_CR6","doi-asserted-by":"publisher","first-page":"848","DOI":"10.1287\/opre.17.5.848","volume":"17","author":"RS Garfinkel","year":"1969","unstructured":"Garfinkel, R.S., Nemhauser, G.L.: The set-partitioning problem: set covering with equality constraints. Oper. Res. 17(5), 848\u2013856 (1969)","journal-title":"Oper. Res."},{"key":"2029_CR7","doi-asserted-by":"crossref","unstructured":"Glover, F., Kochenberger, G., Hennig, R., Du, Y.: Quantum bridge analytics I: a tutorial on formulating and using qubo models. Ann. Oper. Res. pp. 1\u201343 (2022)","DOI":"10.1007\/s10479-022-04634-2"},{"key":"2029_CR8","unstructured":"Kolner, T.: Some highlights of a scheduling matrix generator system. In: United Airlines, presented at the Sixth AGIFORS Symposium (1966)"},{"issue":"3","key":"2029_CR9","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1016\/j.cor.2006.04.002","volume":"35","author":"M Lewis","year":"2008","unstructured":"Lewis, M., Kochenberger, G., Alidaee, B.: A new modeling and solution approach for the set-partitioning problem. Comput. Oper. Res. 35(3), 807\u2013813 (2008)","journal-title":"Comput. Oper. Res."},{"key":"2029_CR10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.99.013304","volume":"99","author":"G Nannicini","year":"2019","unstructured":"Nannicini, G.: Performance of hybrid quantum-classical variational heuristics for combinatorial optimization. Phys. Rev. E 99, 013304 (2019). https:\/\/doi.org\/10.1103\/PhysRevE.99.013304","journal-title":"Phys. Rev. E"},{"key":"2029_CR11","doi-asserted-by":"publisher","first-page":"4213","DOI":"10.1038\/ncomms5213","volume":"5","author":"A Peruzzo","year":"2014","unstructured":"Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.H., Zhou, X.Q., Love, P.J., Aspuru-Guzik, A., O\u2019Brien, J.L.: A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213 (2014)","journal-title":"Nat. Commun."},{"key":"2029_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-04520-2","volume-title":"The quadratic unconstrained binary optimization problem","author":"AP Punnen","year":"2022","unstructured":"Punnen, A.P.: The quadratic unconstrained binary optimization problem. Springer, Tech. rep. (2022)"},{"key":"2029_CR13","unstructured":"Svensson, M., Andersson, M., Gr\u00f6nkvist, M., Vikst\u00e5l, P., Dubhashi, D., Ferrini, G., Johansson, G.: A hybrid quantum-classical heuristic to solve large-scale integer linear programs. arXiv preprint arXiv:2103.15433 (2021)"},{"key":"2029_CR14","doi-asserted-by":"publisher","unstructured":"tA\u00a0v, A., ANIS, M.S., Abby-Mitchell, Abraham, H., AduOffei, Agarwal, R., Agliardi, G., Aharoni, M., Ajith, V., Akhalwaya, I.Y., Aleksandrowicz, G., Alexander, T., Amy, M., Anagolum, S., Anthony-Gandon, Araujo, I.F., Arbel, E., Asfaw, A., Ashimine, I.E., Athalye, A., Avkhadiev, A., Azaustre, C., BHOLE, P., Bajpe, V., Banerjee, A., Banerjee, S., Bang, W., Bansal, A., Barkoutsos, P., Barnawal, A., Barron, G., Barron, G.S., Bello, L., Ben-Haim, Y., Bennett, M.C., Bevenius, D., Bhatnagar, D., Bhatnagar, P., Bhobe, A., Bianchini, P., Bishop, L.S., Blank, C., Bolos, S., Bopardikar, S., Bosch, S., Brandhofer, S., Brandon, Bravyi, S., Bryce-Fuller, Bucher, D., Burgholzer, L., Burov, A., Cabrera, F., Calpin, P., Capelluto, L., Carballo, J., Carrascal, G., Carriker, A., Carvalho, I., Chakrabarti, R., Chen, A., Chen, C.F., Chen, E., Chen, J.C., Chen, R., Chevallier, F., Chinda, K., Cholarajan, R., Chow, J.M., Churchill, S., CisterMoke, Claus, C., Clauss, C., Clothier, C., Cocking, R., Cocuzzo, R., Connor, J., Correa, F., Crockett, Z., Cross, A.J., Cross, A.W., Cross, S., Cruz-Benito, J., Culver, C., C\u00f3rcoles-Gonzales, A.D., D, N., Dague, S., Dandachi, T.E., Dangwal, A.N., Daniel, J., DanielAja, Daniels, M., Dartiailh, M., Davila, A.R., Debouni, F., Dekusar, A., Deshmukh, A., Deshpande, M., Ding, D., Doi, J., Dow, E.M., Downing, P., Drechsler, E., Drudis, M.S., Dumitrescu, E., Dumon, K., Duran, I., EL-Safty, K., Eastman, E., Eberle, G., Ebrahimi, A., Eendebak, P., Egger, D., EgrettaThula, ElePT, Elsayed, I., Emilio, Espiricueta, A., Everitt, M., Facoetti, D., Farida, Fern\u00e1ndez, P.M., Ferracin, S., Ferrari, D., Ferrera, A.H., Fouilland, R., Frisch, A., Fuhrer, A., Fuller, B., GEORGE, M., Gacon, J., Gago, B.G., Gambella, C., Gambetta, J.M., Gammanpila, A., Garcia, L., Garg, T., Garion, S., Garrison, J.R., Garrison, J., Gates, T., Gavrielov, N., Gentinetta, G., Georgiev, H., Gil, L., Gilliam, A., Giridharan, A., Glen, Gomez-Mosquera, J., Gonzalo, de\u00a0la Puente\u00a0Gonz\u00e1lez, S., Gorzinski, J., Gould, I., Greenberg, D., Grinko, D., Guan, W., Guijo, D., Guillermo-Mijares-Vilarino, Gunnels, J.A., Gupta, H., Gupta, N., G\u00fcnther, J.M., Haglund, M., Haide, I., Hamamura, I., Hamido, O.C., Harkins, F., Hartman, K., Hasan, A., Havlicek, V., Hellmers, J., Herok, \u0141., Hill, R., Hillmich, S., Hincks, I., Hong, C., Horii, H., Howington, C., Hu, S., Hu, W., Huang, C.H., Huang, J., Huisman, R., Imai, H., Imamichi, T., Ishizaki, K., Ishwor, Iten, R., Itoko, T., Ivrii, A., Javadi, A., Javadi-Abhari, A., Javed, W., Jianhua, Q., Jivrajani, M., Johns, K., Johnstun, S., Jonathan-Shoemaker, JosDenmark, JoshDumo, Judge, J., Kachmann, T., Kale, A., Kanazawa, N., Kane, J., Kang-Bae, Kapila, A., Karazeev, A., Kassebaum, P., Kato, T., Kehrer, T., Kelso, J., Kelso, S., van Kemenade, H., Khanderao, V., King, S., Kobayashi, Y., Kovi11Day, Kovyrshin, A., Krishna, J., Krishnakumar, R., Krishnamurthy, P., Krishnan, V., Krsulich, K., Kumkar, P., Kus, G., LNoorl, LaRose, R., Lacal, E., Lambert, R., Landa, H., Lapeyre, J., Lasecki, D., Latone, J., Lawrence, S., Lee, C., Li, G., Liang, T.J., Lishman, J., Liu, D., Liu, P., Lolcroc, M, A.K., Madden, L., Maeng, Y., Maheshkar, S., Majmudar, K., Malyshev, A., Mandouh, M.E., Manela, J., Manjula, Marecek, J., Marques, M., Marwaha, K., Maslov, D., Maszota, P., Mathews, D., Matsuo, A., Mazhandu, F., McClure, D., McElaney, M., McElroy, J., McGarry, C., McKay, D., McPherson, D., Meesala, S., Meirom, D., Mendell, C., Metcalfe, T., Mevissen, M., Meyer, A., Mezzacapo, A., Midha, R., Millar, D., Miller, D., Miller, H., Minev, Z., Mitchell, A., Mohammad, A., Moll, N., Montanez, A., Monteiro, G., Mooring, M.D., Morales, R., Moran, N., Morcuende, D., Mostafa, S., Motta, M., Moyard, R., Murali, P., Murata, D., M\u00fcggenburg, J., NEMOZ, T., Nadlinger, D., Nakanishi, K., Nannicini, G., Nation, P., Navarro, E., Naveh, Y., Neagle, S.W., Neuweiler, P., Ngoueya, A., Nguyen, T., Nicander, J., Nick-Singstock, Niroula, P., Norlen, H., NuoWenLei, O\u2019Riordan, L.J., Ogunbayo, O., Ollitrault, P., Onodera, T., Otaolea, R., Oud, S., Padilha, D., Paik, H., Pal, S., Pang, Y., Panigrahi, A., Pascuzzi, V.R., Perriello, S., Peterson, E., Phan, A., Pilch, K., Piro, F., Pistoia, M., Piveteau, C., Plewa, J., Pocreau, P., Possel, C., Pozas-Kerstjens, A., Pracht, R., Prokop, M., Prutyanov, V., Puri, S., Puzzuoli, D., Pythonix, P\u00e9rez, J., Quant02, Quintiii, Rahman, R.I., Raja, A., Rajeev, R., Rajput, I., Ramagiri, N., Rao, A., Raymond, R., Reardon-Smith, O., Redondo, R.M.C., Reuter, M., Rice, J., Riedemann, M., Rietesh, Risinger, D., Rivero, P., Rocca, M.L., Rodr\u00edguez, D.M., RohithKarur, Rosand, B., Rossmannek, M., Ryu, M., SAPV, T., Sa, N.R.C., Saha, A., Ash-Saki, A., Salman, A., Sanand, S., Sandberg, M., Sandesara, H., Sapra, R., Sargsyan, H., Sarkar, A., Sathaye, N., Savola, N., Schmitt, B., Schnabel, C., Schoenfeld, Z., Scholten, T.L., Schoute, E., Schuhmacher, J., Schulterbrandt, M., Schwarm, J., Schweigert, P., Seaward, J., Sergi, Serrano, D.E., Sertage, I.F., Setia, K., Shah, F., Shammah, N., Shanks, W., Sharma, R., Shaw, P., Shi, Y., Shoemaker, J., Silva, A., Simonetto, A., Singh, D., Singh, D., Singh, P., Singkanipa, P., Siraichi, Y., Siri, Sistos, J., Sistos, J., Sitdikov, I., Sivarajah, S., Slavikmew, Sletfjerding, M.B., Smolin, J.A., Soeken, M., Sokolov, I.O., Sokolov, I., Soloviev, V.P., SooluThomas, Starfish, Steenken, D., Stypulkoski, M., Suau, A., Sun, S., Sung, K.J., Suwama, M., S\u0142owik, O., Taeja, R., Takahashi, H., Takawale, T., Tavernelli, I., Taylor, C., Taylour, P., Thomas, S., Tian, K., Tillet, M., Tod, M., Tomasik, M., Tornow, C., de\u00a0la Torre, E., Toural, J.L.S., Trabing, K., Treinish, M., Trenev, D., TrishaPe, Truger, F., TsafrirA, Tsilimigkounakis, G., Tsuoka, K., Tulsi, D., Tuna, D., Turner, W., Vaknin, Y., Valcarce, C.R., Varchon, F., Vartak, A., Vazquez, A.C., Vijaywargiya, P., Villar, V., Vishnu, B., Vogt-Lee, D., Vuillot, C., WQ, Weaver, J., Weidenfeller, J., Wieczorek, R., Wildstrom, J.A., Wilson, J., Winston, E., WinterSoldier, Woehr, J.J., Woerner, S., Woo, R., Wood, C.J., Wood, R., Wood, S., Wootton, J., Wright, M., Xing, L., YU, J., Yaiza, Yang, B., Yang, U., Yao, J., Yeralin, D., Yonekura, R., Yonge-Mallo, D., Yoshida, R., Young, R., Yu, J., Yu, L., Yuma-Nakamura, Zachow, C., Zdanski, L., Zhang, H., Zheltonozhskii, E., Zidaru, I., Zimmermann, B., Zindorf, B., Zoufal, C., a\u00a0matsuo, aeddins ibm, alexzhang13, b63, bartek bartlomiej, bcamorrison, brandhsn, nick bronn, chetmurthy, choerst ibm, comet, dalin27, deeplokhande, dekel.meirom, derwind, dime10, ehchen, ewinston, fanizzamarco, fs1132429, gadial, galeinston, georgezhou20, georgios ts, gruu, hhorii, hhyap, hykavitha, itoko, jeppevinkel, jessica angel7, jezerjojo14, jliu45, johannesgreiner, jscott2, kUmezawa, klinvill, krutik2966, ma5x, michelle4654, msuwama, nico lgrs, nrhawkins, ntgiwsvp, ordmoj, sagar pahwa, pritamsinha2304, rithikaadiga, ryancocuzzo, saktar unr, saswati qiskit, sebastian mair, septembrr, sethmerkel, sg495, shaashwat, smturro2, sternparky, strickroman, tigerjack, tsura crisaldo, upsideon, vadebayo49, welien, willhbang, wmurphy collabstar, yang.luh, yuri@FreeBSD, \u010cepulkovskis, M.: Qiskit: An open-source framework for quantum computing (2021). https:\/\/doi.org\/10.5281\/zenodo.2573505","DOI":"10.5281\/zenodo.2573505"},{"issue":"3","key":"2029_CR15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.14.034009","volume":"14","author":"P Vikst\u00e5l","year":"2020","unstructured":"Vikst\u00e5l, P., Gr\u00f6nkvist, M., Svensson, M., Andersson, M., Johansson, G., Ferrini, G.: Applying the quantum approximate optimization algorithm to the tail-assignment problem. Phys. Rev. Appl. 14(3), 034009 (2020)","journal-title":"Phys. Rev. Appl."},{"issue":"17","key":"2029_CR16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.170503","volume":"101","author":"A Young","year":"2008","unstructured":"Young, A., Knysh, S., Smelyanskiy, V.: Size dependence of the minimum excitation gap in the quantum adiabatic algorithm. Phys. Rev. Lett. 101(17), 170503 (2008)","journal-title":"Phys. Rev. Lett."},{"issue":"2","key":"2029_CR17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.104.020502","volume":"104","author":"A Young","year":"2010","unstructured":"Young, A., Knysh, S., Smelyanskiy, V.: First-order phase transition in the quantum adiabatic algorithm. Phys. Rev. Lett. 104(2), 020502 (2010)","journal-title":"Phys. Rev. Lett."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-023-02029-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11590-023-02029-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-023-02029-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T06:23:19Z","timestamp":1704867799000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11590-023-02029-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,23]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["2029"],"URL":"https:\/\/doi.org\/10.1007\/s11590-023-02029-1","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,23]]},"assertion":[{"value":"14 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 June 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 June 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}