$t_0$	Thickness of the piezoelectric material
$t_e$	Thickness of the matching layer
$C_0$	Piezoceramic clamped capacity
$S$	Area of the transducer
${\epsilon }_{33}^S$	Ceramic permittivity with zero or constant strain
$Z_0$	Acoustic impedance of the piezoelectric layer
$\rho$	Density of the piezoelectric material
$c$	Longitudinal velocity of the piezoelectric material
$\mathsf{\Phi }$	Ratio of transformer
$k_t$	Effective piezoelectric coupling coefficient
${\omega }_0$	Resonant frequency
$X$	Reactance of piezoelectric element
$Z_{p1}$	Input impedance of the acoustic transmission line looking towards the front acoustic port
$Z_{p2}$	Input impedance of the acoustic transmission line looking towards the back acoustic port
$k_0$	Wave number of the piezoelectric material
$k_e$	Wave number of the matching layer
$Z_e$	Acoustic impedance of the matching layer
$Z_f$	Acoustic impedance of front load(acoustic impedance of water)
$Z_b$	Acoustic impedance of the backing
$CF$	Center frequency
$BW$	Bandwidth
$f_1$	Lower frequency at which the amplitude drops to the −6 dB peak
$f_2$	Upper frequency at which the amplitude drops to the −6 dB peak
$J$	Optimality criteria of ultrasonic transducer
$C{F}_{\mathrm{des}}$	Desired CF
$B{W}_{\mathrm{des}}$	Desired BW
$\alpha$	Weight coefficients of CFdes
$\beta$	Weight coefficients of BWdes
$C{F}_{\min }$	Minimum values of CF
$C{F}_{\max }$	Maximum values of CF
$B{W}_{\min }$	Minimum values of BW
$B{W}_{\max }$	Maximum values of BW
$v_i$	The ith particle’s velocity and position
$x_i$	The ith particle’s position
$w$	Inertia weight
$c_1$, $c_2$	Two constants
$p_i$	Best previous positions of the ith individual in current generation
$p_g$	Best previous positions of the ith all particles in current generation
$r_1$, $r_2$	Two random values distributed in the range of [0, 1]
$iter$	Current iteration
$ite{r}_{\max }$	Maximum of the current iteration
$w_{\max }$	Maximum of inertia weight
$w_{\min }$	Minimum of inertia weight