Mobile crowd-sensing (MCS) has recently become a promising approach for massive data collection, which empowers common people to perform sensing tasks with their smart devices. In MCS, locations of tasks and workers are diverse, and workers need to visit different task venues to perform the tasks. The diversity of task and worker locations, tasks' location accessibility, and required sensor type make the task assignment problem highly challenging. In time-sensitive MCS applications, this task assignment problem becomes even more intractable because of the deadline and a lot of possible movement trajectories of the workers. In this paper, we introduce two types of workers and formulate the task assignment problem, which comprises an embedded structure. Furthermore, a decomposition technique is applied to decompose the original problem into a main problem (the assignment problem) and a set of sub-problems (traveling salesman problems). The assignment problem determines task-worker assignments, and the sub-problems determine trajectories of the workers. This decomposition allows using a simpler solution strategy. Then, a memetic genetic algorithm is proposed to address the assignment problem, while each sub-problem is solved using an asymmetric traveling salesman problem heuristic. Results from simulations verify that the proposed algorithm outperforms the baseline methods under various experimental settings. INDEX TERMS Asymmetric traveling salesman problem, mobile crowd-sensing, memetic genetic algorithm, participatory sensing, task allocation.