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The advent of decentralised systems and the continuous collection of personal data managed by public and private entities require the application of measures to guarantee the privacy of individuals. Due to the necessity to preserve both the privacy and the utility of such data, different techniques have been proposed in the literature. Microaggregation, a family of data perturbation methods, relies on the principle of k-anonymity to aggregate personal data records. While several microaggregation heuristics exist, those based on the Travelling Salesman Problem (TSP) have been shown to outperform the state of the art when considering the trade-off between privacy protection and data utility. However, TSP-based heuristics suffer from scalability issues. Intuitively, methods that may reduce the computational time of TSP-based heuristics may incur a higher information loss. Nevertheless, in this article, we propose a method that improves the performance of TSP-based heuristics and can be used in both small and large datasets effectively. Moreover, instead of focusing only on the computational time perspective, our method can preserve and sometimes reduce the information loss resulting from the microaggregation. Extensive experiments with different benchmarks show how our method is able to outperform the current state of the art, considering the trade-off between information loss and computational time.