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Multiobjective genetic algorithm optimizations of a single-shot ultrafast electron diffraction beam line comprised of a 100  MV/m 1.6-cell normal conducting rf (NCRF) gun, as well as a nine-cell 2π/3 bunching cavity placed between two solenoids, have been performed. These include optimization of the normalized transverse emittance as a function of bunch charge, as well as optimization of the transverse coherence length as a function of the rms bunch length of the beam at the sample location for a fixed charge of 10^{6} electrons. Analysis of the resulting solutions is discussed in terms of the relevant scaling laws, and a detailed description of one of the resulting solutions from the coherence length optimizations is given. For a charge of 10^{6} electrons and final beam sizes of σ_{x}≥25  μm and σ_{t}≈5  fs, we found a relative coherence length of L_{c,x}/σ_{x}≈0.07 using direct optimization of the coherence length. Additionally, based on optimizations of the emittance as a function of final bunch length, we estimate the relative coherence length for bunch lengths of 30 and 100 fs to be roughly 0.1 and 0.2  nm/μm, respectively. Finally, using the scaling of the optimal emittance with bunch charge, for a charge of 10^{5} electrons, we estimate relative coherence lengths of 0.3, 0.5, and 0.92  nm/μm for final bunch lengths of 5, 30 and 100 fs, respectively.