The automatic test task scheduling problem is a key challenge for automatic test system to improve throughput and reduce test time. The constrained Test task scheduling problem(TTSP) contains network precedence constraint relationships between tasks. Constrained optimization and topological sorting are applied to handle the constraints. A chaotic non-dominated sorting genetic algorithm is used to stress exploitation ability and obtain high quality solutions. For two commonly applied realworld instances, comparisons show that topological sorting performs much better than constrained optimization and some existing algorithms. Simulation results demonstrate the effectiveness of CNSGA combined with topological sorting for solving constrained TTSP with multiobjectives. The automatic test task scheduling problem is a key challenge for automatic test system to improve throughput and reduce test time. The constrained Test task scheduling problem (TTSP) contains network precedence constraint relationships between tasks. Constrained optimization and topological sorting are applied to handle the constraints For two commonly applied realworld instances, comparisons show that topological sorting performs much better than constrained optimization and some existing algorithms. Simulation results demonstrate the effectiveness of CNSGA combined with topological sorting for solving constrained TTSP with multiobjectives.