The complexity of unmanned aerial vehicle (UAV) missions is increasing with the rapid development of UAV technology. Multiple UAVs usually cooperate in the form of teams to improve the efficiency of mission execution. The UAVs are equipped with multiple sensors with complementary functions to adapt to the complex mission constraints. Reasonable task assignment, task scheduling, and UAV trajectory planning are the prerequisites for efficient cooperation of multi-functional heterogeneous UAVs. In this paper, a multi-swarm fruit fly optimization algorithm (MFOA) with dual strategy switching is proposed to solve the multi-functional heterogeneous UAV cooperative mission planning problem with the criterion of simultaneously minimizing the makespan and the total mission time. First, the multi-swarm mechanism is introduced to enhance the global search capability of the fruit fly optimization algorithm. Second, in the smell-based search phase, the local search strategies and large-scale search strategies are designed to drive multiple fruit fly swarms, and the dual strategy switching method is presented. Third, in the vision-based search stage, the greedy selection strategy is adopted. Finally, numerical simulation experiments are designed. The simulation results show that the MFOA algorithm is more effective and stable for solving the multi-functional heterogeneous UAV cooperative mission planning problem compared with other algorithms.