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The design of an antipodal Vivaldi antenna for ultra wideband (UWB) applications is presented. The main purpose of this design is the reduction of three parameters of transient distortion, reflection coefficient and cross polarization level. Multi-objective particle swarm optimization (MOPSO) is applied to handle these objectives simultaneously. All antenna simulations are performed using the CST MWS software. Several design cases of the resultant Pareto fronts are compared, and finally, a sample of the Pareto front is fabricated. To assess the time domain performance of the antenna, two identical antennas are placed in an end-to-end orientation. The simulated correlation factor in this scenario is more than 93%. Measurement results show that the |S11| of the developed antenna is less than -10 dB, the cross polarization level is below -11.5 dB and the gain is between 4.5 dBi and 9 dBi over the whole UWB frequency band.