The optimal design of geothermal power plants across the entire spectrum of meaningful geothermal brine temperatures and climates is investigated, while accounting for vital real-world constraints that are typically ignored in the existing literature. The constrained design space of both double-flash and binary geothermal power plants is visualized, and it is seen that inclusion of real-world constraints is vital to determining the optimal feasible design of a geothermal power plant. The effect of varying condenser temperature on optimum plant performance and optimal design specifications is analyzed. It is shown that condenser temperature has a significant effect on optimal plant design as well. The optimum specific work output and corresponding optimal design of geothermal power plants across the entire range of brine temperatures and condenser temperatures is illustrated and tabulated, allowing a scientifically sound assessment of both feasibility and appropriate plant design under any set of conditions. The performance of genetic algorithms and particle swarm optimization are compared with respect to the constrained, non-linear, simulation-based optimization of a prototypical geothermal power plant, and particle swarm optimization is shown to perform significantly better than genetic algorithms. The Pareto-optimal front of specific work output and specific heat exchanger area is visualized and tabulated for binary and double-flash plants across the full range of potential geothermal brine inlet conditions and climates, allowing investigation of the specific trade-offs required between specific work output and specific heat exchanger area. In addition to the novel data, this dissertation research illustrates the development and use of a sophisticated analysis tool, based on multi-objective particle swarm optimization, for the optimal design of geothermal power plants.