In　this　study,　we　present　a　comprehensive　approach　to　enhancing　submersible　trajectory　prediction　in　deep-sea　environments　by　integrating　grey　relational　analysis　and　reinforcement　learning　techniques.　The　utilization　of　grey　relational　evaluation　models　and　Multi-Agent　Reinforcement　Learning　with　the　MADDPG　method　allows　for　the　optimization　of　search　and　rescue　equipment　selection　for　deep-sea　submersibles.　By　considering　factors　such　as　equipment　availability,　maintenance,　preparation,　and　usage-related　costs,　the　proposed　methodology　aims　to　improve　the　efficiency　and　effectiveness　of　search　and　rescue　operations　in　challenging　underwater　conditions.　Furthermore,　the　integration　of　grey　relational　analysis　and　reinforcement　learning　offers　a　novel　and　advanced　strategy　for　predicting　submersible　trajectories　with　increased　accuracy　and　reliability.　By　leveraging　the　capabilities　of　these　analytical　tools,　this　research　contributes　to　the　development　of　more　robust　and　adaptive　systems　for　deep-sea　exploration　and　recovery　missions.　The　findings　of　this　study　have　significant　implications　for　enhancing　the　safety　and　success　of　submersible　operations　in　complex　underwater　environments,　ultimately　advancing　the　field　of　deep-sea　exploration　and　rescue　efforts.　©　2024　IEEE.