TABLE I.

Targets, Boundaries and Results of MOO and BF Methods

Acoustic variables	Two layer VF					Three layer VF
	Target	Min	Max	X from opt	X from BF	Target	Min	Max	X from opt	X from BF
${\overline{F}}_0$ (Hz)	80	50	110	93	97	130	90	170	135	156
$\overline{\mathit{\text{SPL}}}$ (dB)	110	90	130	no	110	70	50	90	78	81
${{\mu }^{\prime }}_2/{{\mu }^{\prime }}_1$	N/A	0.05	20	0.8 $\left({\overline{F}}_0\right)$ 0.85 $\left(\overline{\mathit{\text{SPL}}}\right)$	0.94 $\left({\overline{F}}_0\right)$ 1.24 $\left(\overline{\mathit{\text{SPL}}}\right)$	N/A	0.05	20	0.85 $\left({\overline{F}}_0\right)$ 0.85 $\left(\overline{\mathit{\text{SPL}}}\right)$	0.95 $\left(\overline{\mathit{\text{SPL}}}\right)$ 1.05 $\left({\overline{F}}_0\right)$
${{\mu }^{\prime }}_3/{{\mu }^{\prime }}_2$	N/A	N/A	N/A	N/A	N/A	N/A	0.05	20	0.65 $\left(\overline{\mathit{\text{SPL}}}\right)$ 0.7 $\left({\overline{F}}_0\right)$	0.8 $\left({\overline{F}}_0\right)$ 0.8 $\left(\overline{\mathit{\text{SPL}}}\right)$

MOO was tested on two vocal fold designs. A two-layer vocal fold is based on morphological and mechanical data collected from tiger larynges and vocal folds [37], [31]. The three-layer vocal fold is based on human data from various sources [16]. The table lists two variables in the objective domain ( ${\overline{F}}_0$, $\overline{\text{SPL}}$) and two translayer ratios of longitudinal shear modulus of different layers ( ${{\mu }^{\prime }}_2/{{\mu }^{\prime }}_1$ and ${{\mu }^{\prime }}_3/{{\mu }^{\prime }}_2$) implemented in the finite element model. VF-vocal fold, opt-NSGA-II optimization, BF-brute force, X-centroid of the highest density cluster for optimization and brute force method, respectively, and for ( ${\overline{F}}_0$) and ( $\overline{\text{SPL}}$), respectively.