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To address this, we propose an improved directional mutation moth\u2013flame optimization algorithm with gene modification (IDMMFO-GM). We develop a practical reference trajectory optimization model by combining cubic spline interpolation with a standardized parking plane coordinate system. To effectively address the infeasible solutions encountered when parking in a garage, we apply gene modification for collision avoidance and berthing tilt generated from the reference trajectory optimization to enhance the preservation of optimization information. Furthermore, we introduce a non-linear decreasing weight coefficient and a directional mutation strategy into the moth\u2013flame optimization algorithm to significantly improve its overall optimization performance. Taking the automatic parking garage space No. 155 in Dalian Shell Museum as the actual vehicle test object, which is situated within Dalian Xinghai Square, test results demonstrate that the proposed algorithm achieves an accelerated optimization speed, enhanced precision in trajectory optimization, and superior tracking control performance.<\/jats:p>","DOI":"10.3390\/a18060299","type":"journal-article","created":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T07:04:28Z","timestamp":1747897468000},"page":"299","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Improved Directional Mutation Moth\u2013Flame Optimization Algorithm via Gene Modification for Automatic Reverse Parking Trajectory Optimization"],"prefix":"10.3390","volume":"18","author":[{"given":"Yan","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Chizhou University, Chizhou 247000, China"}]},{"given":"Yi","family":"Chen","sequence":"additional","affiliation":[{"name":"Information and Communication Section, Chizhou Public Security Bureau, Chizhou 247000, China"}]},{"given":"Yang","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Dalian Jiaotong University, Dalian 116026, China"}]},{"given":"Longda","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Dalian Jiaotong University, Dalian 116026, China"}]},{"given":"Gang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Inner Mongolia University for the Nationalities, Tongliao 028000, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"124163","DOI":"10.1109\/ACCESS.2023.3330431","article-title":"Fast planning and tracking of complex autonomous parking maneuvers with optimal control and pseudo-neural networks","volume":"11","author":"Pagot","year":"2023","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"104630","DOI":"10.1016\/j.robot.2024.104630","article-title":"Path Planning Algorithms in the Autonomous Driving System: A Comprehensive Review","volume":"174","author":"Reda","year":"2024","journal-title":"Robot. Auton. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"49611","DOI":"10.1109\/ACCESS.2023.3276858","article-title":"An Automatic Parking Algorithm Design Using Multi-Objective Particle Swarm Optimisation","volume":"11","author":"Daniali","year":"2023","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Huang, C., Yang, S., Luo, Y., Wang, Y., and Liu, Z. (2022). Visual Detection and Image Processing of Parking Space Based on Deep Learning. Sensors, 22.","DOI":"10.3390\/s22176672"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"de Almeida, P.R.L., Alves, J.H., Oliveira, L.S., Hochuli, A.G., Frohlich, J.V., and Krauel, R.A. (2023, January 1\u20134). Vehicle Occurrence-Based Parking Space Detection. Proceedings of the 2023 IEEE International Conference on Systems, Man, and Cybernetics (SMC), Honolulu, HI, USA.","DOI":"10.1109\/SMC53992.2023.10394316"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"93841","DOI":"10.1109\/ACCESS.2023.3310256","article-title":"Parallel parking path planning in narrow space based on a Three-stage Curve interpolation method","volume":"11","author":"Li","year":"2023","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"9579","DOI":"10.1016\/j.jfranklin.2023.06.037","article-title":"Automatic parking trajectory planning based on random sampling and nonlinear optimisation","volume":"360","author":"Wang","year":"2023","journal-title":"J. Frankl. 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Sensors, 24.","DOI":"10.3390\/s24072270"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/6\/299\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:38:13Z","timestamp":1760031493000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/6\/299"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,22]]},"references-count":24,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["a18060299"],"URL":"https:\/\/doi.org\/10.3390\/a18060299","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,22]]}}}