This paper investigates the problem of multi-robot task assignment under AND/OR precedence constraints and deadline constraints, where multiple robots are required to visit a set of target locations before the target deadline while complying with specified complex precedence constraints. The precedence constraints are categorized into two types: AND-type precedence constraints, require that a target location cannot be visited before its AND-type predecessor locations; OR-type precedence constraints, necessitate at least one of its OR-type predecessor locations must be reached before visiting the location. The first optimization objective is to maximize the number of target locations visited by robots before the target deadline, and the second optimization objective is to minimize the completion time of the final target visit. To address this problem, a hybrid algorithm based on Greedy algorithm, Iterative local search, and Simulated Annealing (GISA) is designed. First, the greedy algorithm is used to generate an initial solution; subsequently, perturbations are employed to expand the solution space and improve solution quality; finally, local search further optimizes the solution, where simulated annealing is used to determine whether to execute non-improving moves until the search strategy can no longer improve the solution quality. Numerical simulation experiments show that the proposed GISA algorithm outperforms existing algorithms with excellent performance.