Multi-agent cooperation among Uncrewed Aerial Vehicles (UAVs) has become a key contributor in various application areas such as surveillance, where mission efficiency and reliability are essential. This paper aims to provide a structured work for future progress in cooperative flight by presenting a comprehensive review of the hybrid and modified optimization algorithms developed for multi-agent UAV path planning. Initially, the paper categorizes existing approaches into classical, heuristic, metaheuristic, sampling-based, control-based, and Artificial Intelligence (AI)-based frameworks, with an emphasis on their objectives, constraints, and implementation strategies. Special attention is given to metaheuristic and AI-driven techniques, which demonstrate strong adaptability and scalability in dynamic and uncertain environments. The review further examines the environmental modeling strategies, swarm architectures, and mission types, revealing the predominance of static and known environments in current research and highlighting the limited exploration of dynamic and unknown operational considerations. While performance criteria such as collision avoidance, mission duration, and cumulative path length are commonly assessed, aspects like communication constraints, task allocation, and energy efficiency remain relatively underexplored. Open research challenges and future directions are identified, including the need for real-time adaptive optimization strategies and the incorporation of more realistic agent dynamics to enhance experimental validation and practical deployment.