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An ultrawideband (UWB) antenna array was designed to optimize the beamwidth of the time-domain radiation pattern as well as the side lobe level. Multi-objective particle swarm optimization (MOPSO) was applied in dealing with these two conflicting objectives and finding the optimum trade-offs (Pareto front). Mutual coupling was not considered in the array design. However, the multiple solutions that resulted from MOPSO enable the designer to consider the minimum inter-element spacing as an additional constraint for selecting the appropriate array configuration with negligible mutual coupling effect. Each element of the array was an antipodal Vivaldi antenna. The optimization template was applied for three different timedomain pattern descriptors. In comparison to the arrays with the same number of elements reported in the literature, the Pareto fronts obtained in this study provide lower beamwidth and side lobe level. A 4-element sample from resultant Pareto fronts was simulated by using CST microwave studio software. This array shows a 13.7–17.2 dBi gain over the whole frequency band from 3–11 GHz and 7.2 ° beamwidth and −12 dB side lobe level for the energy pattern.