Genetic algorithms and their hybrids are increasingly being applied to produce near‐optimal solutions to difficult optimization problems. Simple genetic algorithms encode a problem's parameters using concatentated, fixed‐length, unsigned‐integer bit‐strings, but the precision obtainable using this coding scheme is inherently limited. For this reason, genetic algorithms which employ real‐valued parameters are of interest. A new hybrid algorithm is described which improves obtainable precision by combining a simple genetic algorithm with a systematic reduction of the search region, real‐valued parameter encodings, and redefined genetic operators. The resulting multistage genetic algorithm is used to obtain approximate solutions to a pair of 20‐segment brachistochrone problems. The results obtained using this new algorithm are compared to those obtained using a multistage Monte Carlo method.