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A genetic algorithm for generating beam weights is described. The algorithm improves an objective measure of the dose distribution while respecting dose volume constraints placed on critical structures. The algorithm was used to select beam weights for treatment of abdominal tumors. Weights were selected for up to 36 beams. Dose volume limits were placed on normal organs and a dose inhomogeneity limit was placed on tumor. Volumes were represented as sets of several hundred discrete points. The algorithm searched for the beam weights that would make the minimum tumor dose as high as the constraints would allow. The results were checked using dose volume histograms with standard sized grids. Nineteen trials were created using six patient cases by changing the required field margin or allowed beam position in each case. The sampling of points was sufficiently dense to yield solutions that strictly satisfied the constraints when the prescribed dose was renormalized by a factor of less than 6%. The genetic algorithm supplied solutions in 49 min on average, and in a maximum time of 87 min. The randomized search does not guarantee optimality, but high tumor doses were obtained. An example is shown for which the solution of the genetic algorithm gave a minimum tumor dose 7 Gy higher than the solution given by a simulated annealing algorithm under the same set of constraints. The genetic algorithm can be generalized to admit nonlinear functions of the beam intensities in the objective or in the constraints. These can include tumor control and normal tissue complication probabilities. The genetic algorithm is an attractive procedure for assigning beam weights in multifield plans. It improves the dose distribution while respecting specified rules for tissue tolerance.