Is it possible to build a honeycombed vacuum balloon?
You can load a decent titanium alloy to about $500 \mathrm{MPa}$ (the ultimate compression strength is quoted at least $850 MPa$, but you need to stay below the elastic limit and have some safety margin). That is $5000$ times more than the pressure at sea level. Therefore, the supporting elements have to take about $\frac{1}{5000}$ of the volume. At density about $4500 \frac{\mathrm{kg}}{\mathrm{m}^3}$, the average density comes at least $0.9 \frac{\mathrm{kg}}{\mathrm{m}^3}$. That is just slightly better than the $1.225 \frac{\mathrm{kg}}{\mathrm{m}^3}$ of air, but way worse than the $0.09 \frac{\mathrm{kg}}{\mathrm{m}^3}$ of hydrogen or the $~0.17 \frac{\mathrm{kg}}{\mathrm{m}^3}$ or helium. And this is only weight of the support—for containing vacuum, the skin will be much heavier as well.

Therefore there is no way this could be better than traditional hydrogen or helium-filled aerostats and it's unlikely to get off the ground at all in practice though the above back-of-the-envelope estimate suggests it just barely might.