{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T09:04:07Z","timestamp":1790154247183,"version":"4.0.1"},"reference-count":78,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T00:00:00Z","timestamp":1789948800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We address the design of global quantum internet topologies that jointly optimise four physical objectives: average end-to-end Werner-state fidelity, entanglement rate, latency and coverage, evaluated with an analytical BDCZ oracle whose path selection is exact under the stated Werner-composition model and whose satellite links respect a single-satellite visibility limit. The search space is heterogeneous (fibre, satellite, free-space optical), comprising 1002=4950 possible edges over 100 cities; direct per-edge categorical optimisation degenerates. We propose a mixed representation of ten physical design parameters plus one stochastic realisation index (eleven decision variables in total) decoding into a topology via k-nearest-neighbour rules. Seven many-objective algorithms (NSGA-II, NSGA-III, MOEA\/D, SMS-EMOA, RVEA, SPEA2, AGE-MOEA-II) are compared at a matched budget over 30 seeds, scored against a shared reference front. NSGA-II attains the highest mean hypervolume (0.353\u00b10.040) but is statistically indistinguishable from SPEA2 and AGE-MOEA-II (0.352, 0.347); after Holm correction across all 63 tests, this top group separates significantly from NSGA-III, SMS-EMOA, RVEA and MOEA\/D, though NSGA-III and SMS-EMOA remain indistinguishable in HV\/IGD (spacing unresolved). NSGA-II\u2019s lead is driven by 6 of its 30 seeds reaching a higher-HV region, a bimodality we report. An eight-variant decoder ablation (NSGA-III) shows fibre is necessary while satellite\u2019s contribution is not detectable, and one classical constructor (a Random Geometric Graph) remains non-dominated; none of the 561 front points connects all 100 cities under the satellite model. On four additional real-city instances (five algorithms), MOEA\/D is last throughout; SMS-EMOA\/RVEA ranks vary by instance, and NSGA-II\/NSGA-III reverses, without significance, twice; the fibre transmittance law is cross-checked against SeQUeNCe (Spearman \u03c1=1.0). The pooled front is released as QI-Bench-Pareto-v1.<\/jats:p>","DOI":"10.3390\/e28091041","type":"journal-article","created":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T14:12:09Z","timestamp":1789999929000},"page":"1041","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Many-Objective Optimisation of Global Quantum Internet Topologies: A Compact Parametric Representation with an Analytical BDCZ Oracle"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0675-2038","authenticated-orcid":false,"given":"Jes\u00fas","family":"Gil Ruiz","sequence":"first","affiliation":[{"name":"Science and Aerospace Department, Universidad Europea de Madrid, Calle Tajo s\/n, Villaviciosa de Od\u00f3n, 28670 Madrid, Spain"},{"name":"Universidad Alfonso X el Sabio, Villanueva de la Ca\u00f1ada, 28691 Madrid, Spain"},{"name":"Universidad Internacional de Valencia (VIU), 46002 Valencia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3808-6754","authenticated-orcid":false,"given":"Diego Rub\u00e9n","family":"Rodr\u00edguez Regadera","sequence":"additional","affiliation":[{"name":"Science and Aerospace Department, Universidad Europea de Madrid, Calle Tajo s\/n, Villaviciosa de Od\u00f3n, 28670 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4091-8265","authenticated-orcid":false,"given":"Rafael","family":"Mu\u00f1oz Gil","sequence":"additional","affiliation":[{"name":"Science and Aerospace Department, Universidad Europea de Madrid, Calle Tajo s\/n, Villaviciosa de Od\u00f3n, 28670 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"eaam9288","DOI":"10.1126\/science.aam9288","article-title":"Quantum internet: A vision for the road ahead","volume":"362","author":"Wehner","year":"2018","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1038\/nature07127","article-title":"The quantum internet","volume":"453","author":"Kimble","year":"2008","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1038\/d41586-018-01835-3","article-title":"The quantum internet has arrived (and it hasn\u2019t)","volume":"554","author":"Castelvecchi","year":"2018","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1109\/MNET.001.1900092","article-title":"Quantum Internet: Networking Challenges in Distributed Quantum Computing","volume":"34","author":"Cacciapuoti","year":"2020","journal-title":"IEEE Netw."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1038\/s41586-020-03093-8","article-title":"An integrated space-to-ground quantum communication network over 4600 kilometres","volume":"589","author":"Chen","year":"2021","journal-title":"Nature"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1038\/s41534-019-0221-4","article-title":"Cambridge quantum network","volume":"5","author":"Dynes","year":"2019","journal-title":"npj Quantum Inf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"10387","DOI":"10.1364\/OE.19.010387","article-title":"Field test of quantum key distribution in the Tokyo QKD network","volume":"19","author":"Sasaki","year":"2011","journal-title":"Opt. Express"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1142\/S0219749908003529","article-title":"Outline of the SECOQC quantum-key-distribution network in Vienna","volume":"6","author":"Poppe","year":"2008","journal-title":"Int. J. Quantum Inf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5932","DOI":"10.1103\/PhysRevLett.81.5932","article-title":"Quantum repeaters: The role of imperfect local operations","volume":"81","author":"Briegel","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1038\/35106500","article-title":"Long-distance quantum communication with atomic ensembles and linear optics","volume":"414","author":"Duan","year":"2001","journal-title":"Nature"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1103\/RevModPhys.83.33","article-title":"Quantum repeaters based on atomic ensembles and linear optics","volume":"83","author":"Sangouard","year":"2011","journal-title":"Rev. Mod. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1038\/nphoton.2010.213","article-title":"From quantum multiplexing to high-performance quantum networking","volume":"4","author":"Munro","year":"2010","journal-title":"Nat. Photonics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"032325","DOI":"10.1103\/PhysRevA.79.032325","article-title":"Quantum repeater with encoding","volume":"79","author":"Jiang","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1109\/JSAC.2020.2969005","article-title":"Optimal Remote Entanglement Distribution","volume":"38","author":"Dai","year":"2020","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"034403","DOI":"10.1116\/5.0287733","article-title":"Inferring quantum network topologies using genetic optimisation of indirect measurements","volume":"7","author":"Campbell","year":"2025","journal-title":"AVS Quantum Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1860","DOI":"10.1109\/TCOMM.2025.3640083","article-title":"RELiQ: Scalable Entanglement Routing via Reinforcement Learning in Quantum Networks","volume":"74","author":"Meuser","year":"2025","journal-title":"IEEE Trans. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1109\/TEVC.2013.2281535","article-title":"An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I","volume":"18","author":"Deb","year":"2014","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_18","unstructured":"Gil Ruiz, J., Su\u00e1rez Medina, L., and Rodr\u00edguez Regadera, D.R. (2026). QI-Bench-100: Benchmarking Graph and Tabular Surrogates for Global Quantum-Internet Topology Evaluation, manuscript submitted for publication."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"15043","DOI":"10.1038\/ncomms15043","article-title":"Fundamental limits of repeaterless quantum communications","volume":"8","author":"Pirandola","year":"2017","journal-title":"Nat. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6787","DOI":"10.1038\/ncomms7787","article-title":"All-photonic quantum repeaters","volume":"6","author":"Azuma","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"160803","DOI":"10.1103\/PhysRevLett.134.160803","article-title":"Repeater-Based Quantum Communication Protocol: Maximizing Teleportation Fidelity with Minimal Entanglement","volume":"134","author":"Ghosal","year":"2025","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"15302","DOI":"10.1038\/s41598-022-19170-z","article-title":"Quantum Zeno repeaters","volume":"12","author":"Bayrakci","year":"2022","journal-title":"Sci. Rep."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Fuentealba, D., Dahn, J., Steck, J., and Behrman, E. (2025). Robust and Scalable Quantum Repeaters Using Machine Learning. Information, 16.","DOI":"10.20944\/preprints202505.0691.v1"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1126\/science.aan3211","article-title":"Satellite-based entanglement distribution over 1200 kilometers","volume":"356","author":"Yin","year":"2017","journal-title":"Science"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"030501","DOI":"10.1103\/PhysRevLett.120.030501","article-title":"Satellite-relayed intercontinental quantum network","volume":"120","author":"Liao","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1038\/nphoton.2017.116","article-title":"Long-distance free-space quantum key distribution in daylight towards inter-satellite communication","volume":"11","author":"Liao","year":"2017","journal-title":"Nat. Photonics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"053021","DOI":"10.1088\/1367-2630\/abfa63","article-title":"Quantum repeaters in space","volume":"23","author":"Liorni","year":"2021","journal-title":"New J. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1038\/s41534-020-00327-5","article-title":"Spooky action at a global distance: Analysis of space-based entanglement distribution for the quantum internet","volume":"7","author":"Khatri","year":"2021","journal-title":"npj Quantum Inf."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"190502","DOI":"10.1103\/PhysRevLett.121.190502","article-title":"Secure quantum key distribution over 421 km of optical fiber","volume":"121","author":"Boaron","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1038\/s41586-018-0066-6","article-title":"Overcoming the rate\u2013distance limit of quantum key distribution without quantum repeaters","volume":"557","author":"Lucamarini","year":"2018","journal-title":"Nature"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1038\/s41566-019-0377-7","article-title":"Experimental quantum key distribution beyond the repeaterless secret key capacity","volume":"13","author":"Minder","year":"2019","journal-title":"Nat. Photonics"},{"key":"ref_32","unstructured":"Schoute, E., Mancinska, L., Islam, T., Kerenidis, I., and Wehner, S. (2016). Shortcuts to quantum network routing. arXiv."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TQE.2021.3058058","article-title":"On the stochastic analysis of a quantum entanglement distribution switch","volume":"2","author":"Vardoyan","year":"2021","journal-title":"IEEE Trans. Quantum Eng."},{"key":"ref_34","unstructured":"Jallow, L., and Khan, M.I. (2025). Adaptive entanglement routing with deep Q-networks in quantum networks. arXiv."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TQE.2022.3148667","article-title":"DQRA: Deep quantum routing agent for entanglement routing in quantum networks","volume":"3","author":"Le","year":"2022","journal-title":"IEEE Trans. Quantum Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"537","DOI":"10.22331\/q-2021-09-07-537","article-title":"Policies for elementary links in a quantum network","volume":"5","author":"Khatri","year":"2021","journal-title":"Quantum"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"033111","DOI":"10.1103\/2g9m-h3jm","article-title":"Optimization of Quantum-Repeater Networks using Stochastic Automatic Differentiation","volume":"7","author":"Avis","year":"2025","journal-title":"Phys. Rev. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1038\/s41534-025-01048-3","article-title":"Surrogate-guided optimization in quantum networks","volume":"11","author":"Prielinger","year":"2025","journal-title":"npj Quantum Inf."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1038\/s41534-021-00501-3","article-title":"Designing quantum networks using preexisting infrastructure","volume":"8","author":"Rabbie","year":"2022","journal-title":"npj Quantum Inf."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Pouryousef, S., Panigrahy, N.K., and Towsley, D. (2023, January 17\u201320). A Quantum Overlay Network for Efficient Entanglement Distribution. Proceedings of the IEEE INFOCOM 2023\u2014IEEE Conference on Computer Communications, New York, NY, USA.","DOI":"10.1109\/INFOCOM53939.2023.10228944"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Liu, J., Liu, X., Wei, X., and Wang, Y. (2024, January 2\u20134). Topology Design with Resource Allocation and Entanglement Distribution for Quantum Networks. Proceedings of the 2024 21st Annual IEEE International Conference on Sensing, Communication, and Networking (SECON), Phoenix, AZ, USA.","DOI":"10.1109\/SECON64284.2024.10934901"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1038\/s41534-022-00628-x","article-title":"A benchmarking procedure for quantum networks","volume":"9","author":"Helsen","year":"2023","journal-title":"npj Quantum Inf."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","article-title":"A fast and elitist multiobjective genetic algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1137\/S1052623496307510","article-title":"Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems","volume":"8","author":"Das","year":"1998","journal-title":"SIAM J. Optim."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/TEVC.2015.2420112","article-title":"A new dominance relation-based evolutionary algorithm for many-objective optimization","volume":"20","author":"Yuan","year":"2016","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1109\/TEVC.2014.2378512","article-title":"A knee point-driven evolutionary algorithm for many-objective optimization","volume":"19","author":"Zhang","year":"2015","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Zitzler, E., and K\u00fcnzli, S. (2004, January 18\u201322). Indicator-based selection in multiobjective search. Proceedings of the Parallel Problem Solving from Nature (PPSN VIII), Birmingham, UK.","DOI":"10.1007\/978-3-540-30217-9_84"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1653","DOI":"10.1016\/j.ejor.2006.08.008","article-title":"SMS-EMOA: Multiobjective selection based on dominated hypervolume","volume":"181","author":"Beume","year":"2007","journal-title":"Eur. J. Oper. Res."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1109\/TEVC.2007.892759","article-title":"MOEA\/D: A multiobjective evolutionary algorithm based on decomposition","volume":"11","author":"Zhang","year":"2007","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Zhang, Q., Liu, W., and Li, H. (2009, January 18\u201321). The performance of a new version of MOEA\/D on CEC09 unconstrained MOP test instances. Proceedings of the IEEE Congress on Evolutionary Computation, Trondheim, Norway.","DOI":"10.1109\/CEC.2009.4982949"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1162\/EVCO_a_00109","article-title":"MOEA\/D with adaptive weight adjustment","volume":"22","author":"Qi","year":"2014","journal-title":"Evol. Comput."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"89497","DOI":"10.1109\/ACCESS.2020.2990567","article-title":"pymoo: Multi-objective optimization in Python","volume":"8","author":"Blank","year":"2020","journal-title":"IEEE Access"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Auger, A., Bader, J., Brockhoff, D., and Zitzler, E. (2009, January 9\u201311). Theory of the hypervolume indicator: Optimal \u03bc-distributions and the choice of the reference point. Proceedings of the Tenth ACM SIGEVO Workshop on Foundations of Genetic Algorithms, Orlando, FL, USA.","DOI":"10.1145\/1527125.1527138"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/TEVC.2003.810758","article-title":"Performance assessment of multiobjective optimizers: An analysis and review","volume":"7","author":"Zitzler","year":"2003","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Coello Coello, C.A., and Reyes Sierra, M. (2004, January 26\u201330). A study of the parallelization of a coevolutionary multi-objective evolutionary algorithm. Proceedings of the Mexican International Conference on Artificial Intelligence, Mexico City, Mexico.","DOI":"10.1007\/978-3-540-24694-7_71"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Bezerra, L.C., L\u00f3pez-Ib\u00e1\u00f1ez, M., and St\u00fctzle, T. (2017, January 19\u201322). An empirical assessment of the properties of inverted generational distance on multi- and many-objective optimization. Proceedings of the International Conference on Evolutionary Multi-Criterion Optimization (EMO), M\u00fcnster, Germany.","DOI":"10.1007\/978-3-319-54157-0_3"},{"key":"ref_57","unstructured":"Schott, J.R. (1995). Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. [Master\u2019s Thesis, Massachusetts Institute of Technology]."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"2568","DOI":"10.1109\/TCYB.2014.2310651","article-title":"Diversity comparison of Pareto front approximations in many-objective optimization","volume":"44","author":"Li","year":"2014","journal-title":"IEEE Trans. Cybern."},{"key":"ref_59","unstructured":"Kipf, T.N., and Welling, M. (2017, January 24\u201326). Semi-Supervised Classification with Graph Convolutional Networks. Proceedings of the ICLR, Toulon, France."},{"key":"ref_60","unstructured":"Veli\u010dkovi\u0107, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., and Bengio, Y. (May, January 30). Graph Attention Networks. Proceedings of the ICLR, Vancouver, BC, Canada."},{"key":"ref_61","unstructured":"Corso, G., Cavalleri, L., Beaini, D., Li\u00f2, P., and Veli\u010dkovi\u0107, P. (2020, January 6\u201312). Principal Neighbourhood Aggregation for Graph Nets. Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), Virtual."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"3080","DOI":"10.1109\/TNET.2023.3269983","article-title":"RouteNet-Fermi: Network modeling with graph neural networks","volume":"31","author":"Rusek","year":"2023","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Geyer, F., and Carle, G. (2018, January 20). Learning and Generating Distributed Routing Protocols Using Graph-Based Deep Learning. Proceedings of the 2018 Workshop on Big Data Analytics and Machine Learning for Data Communication Networks (Big-DAMA\u201918), Budapest, Hungary.","DOI":"10.1145\/3229607.3229610"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1103\/PhysRevA.59.169","article-title":"Quantum repeaters based on entanglement purification","volume":"59","author":"Briegel","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1109\/TEVC.2016.2519378","article-title":"A reference vector guided evolutionary algorithm for many-objective optimization","volume":"20","author":"Cheng","year":"2016","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_66","first-page":"115","article-title":"Simulated binary crossover for continuous search space","volume":"9","author":"Deb","year":"1995","journal-title":"Complex Syst."},{"key":"ref_67","first-page":"30","article-title":"A combined genetic adaptive search (GeneAS) for engineering design","volume":"26","author":"Deb","year":"1996","journal-title":"Comput. Sci. Inform."},{"key":"ref_68","unstructured":"Zitzler, E., Laumanns, M., and Thiele, L. (2001). SPEA2: Improving the Strength Pareto Evolutionary Algorithm, Computer Engineering and Networks Laboratory (TIK), ETH Zurich. Technical Report 103."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Panichella, A. (2022, January 9\u201313). An improved Pareto front modeling algorithm for large-scale many-objective optimization. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO \u201922), Boston, MA, USA.","DOI":"10.1145\/3512290.3528732"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.swevo.2011.02.002","article-title":"A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms","volume":"1","author":"Derrac","year":"2011","journal-title":"Swarm Evol. Comput."},{"key":"ref_71","unstructured":"GeoNames (2026, July 29). GeoNames Geographical Database: Cities15000 Export. 2026. Data File cities15000.zip, Downloaded 2026-07-29; Licensed CC BY 4.0. Available online: https:\/\/download.geonames.org\/export\/dump\/."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1109\/TEVC.2016.2587749","article-title":"Performance of decomposition-based many-objective algorithms strongly depends on Pareto front shapes","volume":"21","author":"Ishibuchi","year":"2017","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1109\/TEVC.2013.2281534","article-title":"An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II","volume":"18","author":"Jain","year":"2014","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Miettinen, K. (1999). Nonlinear Multiobjective Optimization, Springer.","DOI":"10.1007\/978-1-4615-5563-6"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1109\/TEVC.2008.925798","article-title":"Multiobjective optimization problems with complicated Pareto sets, MOEA\/D and NSGA-II","volume":"13","author":"Li","year":"2009","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"045027","DOI":"10.1088\/2058-9565\/ac22f6","article-title":"SeQUeNCe: A customizable discrete-event simulator of quantum networks","volume":"6","author":"Wu","year":"2021","journal-title":"Quantum Sci. Technol."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1038\/s42005-021-00647-8","article-title":"NetSquid, a NETwork Simulator for QUantum Information using Discrete events","volume":"4","author":"Coopmans","year":"2021","journal-title":"Commun. Phys."},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Satoh, R., Hajdu\u0161ek, M., Benchasattabuse, N., Nagayama, S., Teramoto, K., Matsuo, T., Metwalli, S.A., Satoh, T., Suzuki, S., and Van Meter, R. (2022). QuISP: A Quantum Internet Simulation Package. arXiv.","DOI":"10.1109\/QCE53715.2022.00056"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/1041\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T08:20:41Z","timestamp":1790151641000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/1041"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,21]]},"references-count":78,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["e28091041"],"URL":"https:\/\/doi.org\/10.3390\/e28091041","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,21]]}}}