An Error Bound Particle Swarm Optimization for Analog Circuit Sizing

An Error-Bound Particle Swarm Optimization (EB-PSO) is proposed in this work. The objective function is evaluated for each particle in each iteration. The velocity update equation is modified by introducing two new parameters
$\zeta _{1}$
and
$\zeta _{2}$
. These parameters varies exponentially, within the bounds (
$\zeta _{1,min}$
,
$\zeta _{2,min}$
) and (
$\zeta _{1,max}$
,
$\zeta _{2,max}$
), with respect to the number of iterations. Initially, a higher value of
$\zeta _{2}$
and minimum value of
$\zeta _{1}$
is chosen to facilitate a global search. Once the global error (
$\varepsilon _{2}$
) is less than the desired value,
$\zeta _{1}$
is allowed to increase from its minimum value and
$\zeta _{2}$
is held constant at
$\zeta _{2,max}$
. This leads to local exploitation of the search space. The proposed algorithm is implemented on Python platform. To verify the effectiveness of the proposed EB-PSO algorithm in analog circuit sizing, a case study on the performance and optimization of two-stage op-amp is presented, whose validation is done in Cadence-Virtuoso environment at 45-nm CMOS technology. The results show that the proposed EB-PSO algorithm converges in 11 iterations for two-stage op-amp, whereas it takes 23, 29, and 41 iterations to converge for conventional GA, DE, and PSO algorithms respectively.