The k-anonymity concept introduced in (Samarati and Sweeney 1998) proposes a good trade-off between the privacy and the utility of the data published for exploitation. However, minimizing the loss of information throughout the k-anonymization of a database is known to be NP-Hard (Meyerson and Williams 2004). Several previous works defined metrics to measure and to optimize this process according to different priorities or different ways of looking at things. In this paper, we first present a unified modeling of the optimization metrics for the k-anonymization of a database. Then, we propose different new metrics for this optimization problem. Finally, we evaluate three metrics of the literature and our new metrics using a greedy algorithm along the anonymization process for 21 values of k.