In crowdsensing, the diversity of the sensing tasks and an enhancement of the smart devices enable mobile users to accept multiple types of tasks simultaneously. In this study, we propose a new practical framework for dealing with the challenges of task assignment and user incentives posed by complex heterogeneous task scenarios in a crowdsensing market full of competition. First, based on the non-cooperative game property of mobile users, the problem is formulated into a Nash equilibrium problem. Then, to provide an efficient solution, a judgment method based on constraints (sensing time and sensing task dimension) is designed to decompose the problems into different situations according to the complexity. We propose a genetic-algorithm-based approach to find the combination of tasks that maximizes the utility of users and adopts a co-evolutionary model to formulate a stable sensing strategy that maintains the maximum utility of all users. Furthermore, we reveal the impact of competition between users and tasks on user strategies and use a cooperative weight to reflect it mathematically. Based on this, an infeasible solution repair method is designed in the genetic algorithm to reduce the search space, thus effectively accelerating the convergence speed. Extensive simulations demonstrate the effectiveness of the proposed method.