In the complex mission environment of Unmanned Aerial Vehicle (UAV) swarms, it is imperative to develop efficient task allocation methods that can be feasibly executed in the presence of heterogeneous UAV operation constraints. This study has developed a competitive hyper-heuristic framework for UAV task allocation that can concurrently execute multiple meta-heuristic optimization methods and select the most balanced task allocation strategy through a normalized multi-objective cost function. The task allocation problem has been modeled as a constrained optimization problem that can handle heterogeneous UAV operation constraints, different types of tasks, time constraints, and resource constraints. It can also optimize travel distance, mission time, energy consumption, priority satisfaction, and workload distribution. The framework uses the Genetic Algorithm, Particle Swarm Optimization, Grey Wolf Optimizer, Simulated Annealing, and Greedy Local Search methods within a fixed computational budget to eliminate algorithm selection biases. It uses a penalty normalization technique to prevent the dominance of constraint violation in the objective function. The experimental results for a mission scenario with six heterogeneous UAVs and twenty spatially distributed tasks show that the UAV task allocation problem does not necessarily minimize individual efficiency metrics for the most feasible task allocation strategy. For example, the Grey Wolf Optimizer has the shortest travel distance of 562.5 km and the least energy consumption. However, the Particle Swarm Optimization algorithm has the least total cost of 0.75 due to the near-optimal performance of the algorithm in solving the problem while minimizing constraint violation.