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We report on the use of a genetic algorithm (GA) in the design optimization of electrically small wire antennas, taking into account of bandwidth, efficiency and antenna size. For the antenna configuration, we employ a multisegment wire structure. The Numerical Electromagnetics Code (NEC) is used to predict the performance of each wire structure. To efficiently map out this multiobjective problem, we implement a Pareto GA with the concept of divided range optimization. In our GA implementation, each wire shape is encoded into a binary chromosome. A two-point crossover scheme involving three chromosomes and a geometrical filter are implemented to achieve efficient optimization. An optimal set of designs, trading off bandwidth, efficiency, and antenna size, is generated. Several GA designs are built, measured and compared to the simulation. Physical interpretations of the GA-optimized structures are provided and the results are compared against the well-known fundamental limit for small antennas. Further improvements using other geometrical design freedoms are discussed.