Using biased data to train Artificial Intelligence (AI) algorithms will lead to biased decisions, discriminating against certain groups or individuals. Bias can be explicit (one or several protected features directly influence the decisions) or implicit (one or several protected features indirectly influence the decisions). Unsurprisingly, biased patterns are difficult to detect and mitigate. This paper investigates the extent to which explicit and implicit against one or more protected features in structured classification data sets can be mitigated simultaneously while retaining the (...) data’s discriminatory power. The main contribution of this paper concerns an optimization-based bias mitigation method that reweights the training instances. The algorithm operates with numerical and nominal data and can mitigate implicit and explicit bias against several protected features simultaneously. The trade-off between bias mitigation and accuracy loss can be controlled using parameters in the objective function. The numerical simulations using real-world data sets show a reduction of up to 77% of implicit bias and a complete removal of explicit bias against protected features at no cost of accuracy of a wrapper classifier trained on the data. Overall, the proposed method outperforms the state-of-the-art bias mitigation methods for the selected data sets. (shrink)