Aimed at the security problem of tasks scheduling in heterogeneous grid system, a security evaluation model is presented based on security control strategy and history behavior of grid nodes, and on this basis a kind of safe and trusted optimization model for dependent tasks scheduling is put forward under grid environment.To solve the model, a new genetic- harmonic algorithm called GASHO is designed,which taks full advantage of the characteristic of global optimization of genetic algorithm and introduces the harmonic operator to overcome the shortage of local optimization. Based on the dependencies of a DAG task graph, the heuristic method is employed to design the operator of genetic and quantum harmonic, thus the GASHO produces a better task scheduling queue to avoid the occurence of illegal solutions in discrete spaces. Then, to improve the convergence efficiency, the earliest finish time operator which is constrained to security factors is used to map from task set to grid nodes. At last, the convergence property and time complexity is analyzed. Compared with other similar algorithm under the same condition, the simulation results show that the proposed algorithm has the advantages on the convergence property, scheduling length and security efficiency.

grid computing; dependent task; security scheduling; genetic-harmonic algorithm