This paper investigates the impact of permanent magnet (PM) displacement and flux barrier extension on cogging torque in flux-intensifying permanent magnet-assisted synchronous reluctance machines (FI-PMa-SynRMs) with surface-inset PMs. Unlike prior work centred on average torque, torque ripple, or inductance, we focus on cogging torque, a key driver of noise and vibration. Four rotor configurations are evaluated via finite element analysis of ∼20,000 designs per configuration generated during NSGA-II multi-objective optimisation. To avoid bias from near-duplicate designs, we introduce Euclidean distance-based medoid filtering, which enforces a minimum separation of models within each configuration. The cross-configuration similarity is measured by Euclidean distance over common design variables. Results show that PM displacement alone does not substantially reduce cogging torque, while flux barrier extension alone yields reductions of up to ∼25%. Combining PM displacement with flux barrier extension achieves up to a ∼30% reduction in cogging torque, often maintaining average torque and lowering torque ripple. This study provides a comparative framework for mitigating cogging torque in FI-PMa-SynRMs and clarifies the trade-offs revealed by similarity-based analyses.