The goal of this paper was to design a trajectory from Earth to Jupiter using a single flyby of either Venus or Earth to obtain a trajectory which is lower in terms of Δv than the Hohmann transfer. The Hohmann transfer Δv from Earth to Jupiter is 14.43 km/s, and its minimum time of arrival (TOA) is 1081 Earth days after the epoch time of 01 January, 2005 00:00 UT. Using two Evolutionary Algorithms (EAs): Differential Evolution (DE) and Particle Swarm Optimization (PSO), two trajectories were identified which were lower than the Hohmann Δv with one requiring an Earth swing-by, and the second a Venusian swing-by. The trajectory requiring the Venusian fly-by required a total Δv of 11.82 km/s, and its TOA was 1250 Earth days. This trajectory requires 18% less Δv than the Hohmann transfer, but its drawback is that the vehicle arrives 169 Earth days later. The second transfer required an Earth flyby, and its total Δv is 13.43 km/s, with a TOA of 1700 Earth days. This transfer also requires less fuel than the Hohmann transfer, but its TOA is 450 Earth days later, which is certainly substantial. Both DE and PSO were used to determine the optimal trajectory, and PSO outperformed DE because it was able to arrive at the optimal trajectory in much fewer function evaluations.