In this paper, an improved model of the immune system to handle constraints in multi-criteria optimization problems has been proposed. The problem that is of interest to us is the new task assignment problem for a distributed computer system. Both a workload of a bottleneck computer and the cost of machines are minimized; in contrast, a reliability of the system is maximized. Moreover, constraints related to memory limits, task assignment and computer locations are imposed on the feasible task assignment. Finally, an evolutionary algorithm based on tabu search procedure and the immune system model is proposed to provide task assignments.