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A method to obtain optimum tradeoffs (Pareto front) between sidelobe level (SLL) and beamwidth (BW) in time domain for ultrawideband (UWB) antenna arrays is presented. Multiobjective particle swarm optimization (MOPSO) is used to deal with these two conflicting objectives. In the optimization process, mutual coupling effects between elements are not considered. However, the multiple solutions obtained from MOPSO enable the designer to consider the mutual coupling effect as an additional constraint. Each element of the array is an antipodal Vivaldi antenna. The optimization template is applied for three different time-domain pattern descriptors. In comparison to arrays with the same number of elements reported in literature, the Pareto fronts obtained in this study provide lower BW and SLL. A four-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, 7.2° BW, and -12 dB SLL for energy pattern.