With the widespread application of clustering algorithms in intelligent measurement systems, multi-source sensor data analysis, and embedded state recognition, ensuring fairness with respect to sensitive attributes while maintaining clustering quality has become a key challenge that limits their effectiveness in critical measurement tasks. To address this issue, we propose a population optimization combined with robust distance metric for fair K-means clustering method (PODM-Kmeans). The proposed method balances clustering quality and fairness by incorporating an enhanced Cuckoo Search algorithm to achieve a trade-off between global and local search capabilities during the initialization of cluster centers, thereby improving clustering stability. Furthermore, fairness constraints and cluster size constraints are effectively integrated into the iterative clustering objective function. A flexible weighted Euclidean norm is adopted as the distance metric to mitigate the negative impact of outliers, contributing to improved fairness. Extensive experiments conducted on five synthetic and five real-world datasets demonstrate the superior performance of PODM-Kmeans compared to existing methods. Notably, on the Adult, Bank, Census1990, and CreditCard datasets, PODM-Kmeans achieves a fairness ratio (FR) exceeding 0.95 while maintaining high clustering quality.