Multi-agent path planning (MAPP) focuses on finding an optimal set of paths for multiple agents. MAPP can be applied in the fleet management of different modes of mobility, ranging from aircraft and ground vehicles to robots. The challenge in implementing MAPP is obtaining balanced paths for all agents when solving large-scale problems with numerous targets, owing to NP-hardness. Moreover, MAPP can be complicated in practical situations in which agents must their tasks on moving targets at distant positions. To address these limitations, this study proposes a novel path planning algorithm based on clustering and meta-heuristics. In particular, the problem is divided into a combinatorial optimization problem of finding the target visitation orders for agents and a continuous optimization problem of determining the task execution positions of the agents. The first optimization involves clustering targets to prioritise agent target assignments with the aim of balancing the travel times of the agents while accelerating the searches for more promising solutions. In the second problem, our formulation searches for solutions to satisfy the practical constraints on task execution with predicted target movements. Numerical experiments on simulated and real datasets are conducted to examine the effectiveness of the proposed algorithm and demonstrate that the proposed algorithm outperforms existing algorithms indicating its potential for practical implementation.