For three-dimensional path planning of autonomous underwater vehicles (AUVs) in complex marine environments where sonar detection, mine fields, no-go zones, meso-scale eddy currents and undulating seabed terrain are coupled, an improved subtraction-average-based optimizer (ISABO) is proposed. A passive-sonar detection-probability model with the thermocline shadow-zone effect is established, and a dimensionless normalised fitness function is built from the terrain, a Lamb-Oseen eddy current field and the kinematic constraints, with hard constraints measured by a separate violation degree. Three strategies, namely current-aware adaptive search bias, depth-horizontal cooperative search and sonar-feedback adaptive elite guidance, are proposed, and a conditional global convergence analysis is given. Under a fairness protocol with shared initial populations and an identical evaluation budget, ISABO is compared with fourteen swarm-intelligence algorithms and the A* and RRT* planners? it attains the best solution and the best median among the swarm-intelligence algorithms with a 100% success rate, and lowers the median by 95.4% relative to SABO. A per-evaluation analysis shows that the turning-angle constraint makes the feasible region very thin along coordinate-wise independent perturbations, and that the side-channel refinement of ISABO, which perturbs only a few coordinates at a time, keeps a high feasibility rate of its candidates, which explains why the algorithms ranked highest on CEC2022 fall behind on this problem. Combined with rolling-horizon replanning in a dynamic threat scenario, ISABO lowers the accumulated sonar exposure by 40.9% relative to SABO.