A task assignment in a distributed computer system may reduce the total cost of a program execution and the workload of a bottleneck computer. It can decrease the cost of computers because of the computer sort selection, too. A total amount of system performance is another measure that can be minimized by task scattering. A problem of task allocation is formulated as a multiobjective combinatorial optimization question, which is solved by three evolutionary approaches: a tuned genetic algorithm with ranking procedure, an adaptive evolutionary algorithm, and an evolution strategy. They are applied for finding the subset of Pareto-optimal solutions. Finally, two evolutionary approaches are recommended for finding efficient task assignments.