A multi-type task assignment optimization model is established by considering constraints of assignment, payload and range of heterogeneous UAVs, task time window, and task sequence. The Non-dominated Sorting Genetic Algorithm-II (NSGA-II) based on elitist strategy is employed to figure out task assignment problem. Firstly, the multiple optimization objectives are set, including total task completion time, total task reward, and cluster damage level. Secondly, the concept of constraint tolerance is introduced, and the non-dominated sorting mechanism of NSGA-II is improved to distinguish the individuals that do not satisfy the up-mentioned constraints from the satisfied ones. This allows individuals that violate high tolerance constraints to be preserved for the next generation and continue to participate in the evolution, effectively addressing the difficulty of obtaining a convergent Pareto solution set for complex coupled task constraints. Finally, numerical simulation results are compared before and after the algorithm improvement under the same task scale, and the better performance of the proposed algorithm is demonstrated.