Improved Directional Mutation Moth–Flame Optimization Algorithm via Gene Modification for Automatic Reverse Parking Trajectory Optimization

Automatic reverse parking (ARP) faces challenges in finding ideal reference trajectories that avoid collisions, maintain smoothness, and minimize path length. To address this, we propose an improved directional mutation moth–flame 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–flame 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.