Volunteer computing systems like BOINC or Comcute are strongly supported by a great number of volunteers who contribute resources of their computers via the Web. So, the high efficiency of such grid system is required, and that is why we have formulated a multi-criterion optimization problem for a volunteer grid system design. In that dilemma, both the cost of the host system and workload of a bottleneck host are minimized. On the other hand, a reliability of this grid structure is maximized. Moreover, genetic programming has been applied to determine the Pareto solutions. Finally, a negative selection procedure to handle constraints has been discussed.