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Antenna design variables, such as size, have continuous values while others, such as permittivity, have a finite number of values. Having both variable types in one problem requires a mixed integer optimization algorithm. This paper describes a genetic algorithm (GA) that works with real and/or binary values in the same chromosome. The algorithm is demonstrated on designing low side-lobe phase tapers, circularly polarized patch antennas, and identically thinned subarrays