{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T22:51:23Z","timestamp":1768949483662,"version":"3.49.0"},"reference-count":17,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T00:00:00Z","timestamp":1768608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The Lunar Gateway is a planned small space station that will orbit the Moon and serve as a central hub for NASA\u2019s Artemis program to return humans to the lunar surface and to prepare for Mars missions. This work presents a hybrid optimization strategy for designing minimum-fuel transfers from an Earth orbit to a Lunar Near-Rectilinear Halo Orbit. The corresponding optimal control problem\u2014crucial for missions to NASA\u2019s Lunar Gateway\u2014is characterized by a high-dimensional, non-convex solution space due to the multi-body gravitational environment. To tackle this challenge, a two-stage hybrid optimization scheme is employed. The first stage uses a Genetic Algorithm heuristic as a global search strategy, to identify promising feasible trajectory solutions. Subsequently, the initial solution guess (or guesses) produced by GA are improved by a local optimizer based on a Sequential Quadratic Programming method: from a suitable initial guess, SQP rapidly converges to a high-precision feasible solution. The proposed methodology is applied to a representative cargo mission case study, demonstrating its efficiency. Our numerical results confirm that the hybrid optimization strategy can reliably generate mission-grade quality trajectories that satisfy stringent constraints while minimizing propellant consumption. Our analysis validates the combined GA-SQP optimization approach as a robust and efficient tool for space mission design in the cislunar environment.<\/jats:p>","DOI":"10.3390\/a19010080","type":"journal-article","created":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T09:24:34Z","timestamp":1768901074000},"page":"80","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hybrid Optimization Technique for Finding Efficient Earth\u2013Moon Transfer Trajectories"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7074-7738","authenticated-orcid":false,"given":"Lorenzo","family":"Casalino","sequence":"first","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"D\u2019Ottavio","sequence":"additional","affiliation":[{"name":"Thales Alenia Space, Strada Antica di Collegno 253, 10146 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giorgio","family":"Fasano","sequence":"additional","affiliation":[{"name":"Thales Alenia Space, Strada Antica di Collegno 253, 10146 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4909-7619","authenticated-orcid":false,"given":"Janos D.","family":"Pint\u00e9r","sequence":"additional","affiliation":[{"name":"Department of Management Science & Information Systems, Rutgers Business School\u2014New Brunswick, Rutgers University, Piscataway, NJ 08854, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Riccardo","family":"Roberto","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,17]]},"reference":[{"key":"ref_1","unstructured":"European Space Agency (2025, September 15). ESA\u2014European Space Agency. Available online: https:\/\/www.esa.int."},{"key":"ref_2","unstructured":"Vallado, D.A. (2013). Fundamentals of Astrodynamics and Applications, Microcosm Press. [4th ed.]."},{"key":"ref_3","unstructured":"Zimovan-Spreen, E.M., Scheuerle, S.T., Mccarthy, B.P., Davis, D.C., and Howell, K.C. (2023). Baseline orbit generation for near rectilinear halo orbits. Proceedings of the AAS\/AIAA Astrodynamics Specialist Conference, NASA Johnson Space Center."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.2514\/1.41449","article-title":"Hybrid genetic algorithm\u2013collocation method for trajectory optimization","volume":"32","author":"Subbarao","year":"2009","journal-title":"J. Guid. Control. Dyn."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhang, D., and Liu, Y. (2011, January 8\u201311). RLV reentry trajectory optimization through hybridization of an improved GA and an SQP algorithm. Proceedings of the AIAA Guidance, Navigation, and Control Conference, Portland, OR, USA. AIAA Paper 2011\u20136658.","DOI":"10.2514\/6.2011-6658"},{"key":"ref_6","unstructured":"NASA (2025, September 15). CAPSTONE, Available online: https:\/\/www.nasa.gov\/mission\/capstone\/."},{"key":"ref_7","unstructured":"NASA (2025, September 15). Gateway, Available online: https:\/\/www.nasa.gov\/mission\/gateway\/."},{"key":"ref_8","unstructured":"Bryson, A.E., and Ho, Y.-C. (1975). Applied Optimal Control: Optimization, Estimation, and Control, Hemisphere Publishing Corporation\/Taylor & Francis."},{"key":"ref_9","unstructured":"Tr\u00e9lat, E., and Zuazua, E. (2022). Numerical Control. Handbook of Numerical Analysis, Elsevier. Volumes 23 (Part A) and 24 (Part B)."},{"key":"ref_10","unstructured":"NAIF\/JPL Frames and Coordinate Systems; Technical report\/tutorial; Navigation and Ancillary Information Facility (NAIF), Jet Propulsion Laboratory."},{"key":"ref_11","unstructured":"Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Michalewicz, Z. (1996). Genetic Algorithms + Data Structures = Evolution Programs, Springer. [3rd. ed.].","DOI":"10.1007\/978-3-662-03315-9"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Mart\u00ed, R., Pardalos, P.M., and Resende, M.G.C. (2018). Genetic Algorithms. Handbook of Heuristics, Springer International Publishing AG. Chapter 15.","DOI":"10.1007\/978-3-319-07124-4"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/978-3-319-91086-4_8","article-title":"Next Generation Genetic Algorithms: A User\u2019s Guide and Tutorial","volume":"Volume 272","author":"Gendreau","year":"2019","journal-title":"Handbook of Metaheuristics"},{"key":"ref_15","unstructured":"Nocedal, J., and Wright, S.J. (2006). Numerical Optimization, Springer. [2nd ed.]. Chapters 12\u201318 cover SQP and related NLP topics."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Belbruno, E.A., and Carrico, J.P. (2000, January 14\u201317). Calculation of weak stability boundary ballistic lunar transfer trajectories. Proceedings of the AIAA\/AAS Astrodynamics Specialist Conference, Denver, CO, USA.","DOI":"10.2514\/6.2000-4142"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Eiben, A.E., and Smith, J.E. (2015). Introduction to Evolutionary Computing, Springer. [2nd ed.]. Natural Computing Series.","DOI":"10.1007\/978-3-662-44874-8"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/1\/80\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T09:32:55Z","timestamp":1768901575000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/1\/80"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,17]]},"references-count":17,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["a19010080"],"URL":"https:\/\/doi.org\/10.3390\/a19010080","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,17]]}}}