Table 1.

The formulations for our objective functions.

	Objective function
Average dose	$\underset{v\in {\mathcal{V}}_r}{\mathrm{mean}}\left(d_v\right)$
Maximum dose	$\underset{v\in {\mathcal{V}}_r}{\max }\left(d_v\right)$
Average dose over threshold	$\underset{v\in {\mathcal{V}}_r}{\mathrm{mean}}{\left(d_v-f\right)}^{+}$
Average dose under threshold	$\underset{v\in {\mathcal{V}}_r}{\mathrm{mean}}{\left(f-d_v\right)}^{+}$