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This paper studies the economically significant problem of the optimization of customs fraud control, which is a critical issue for many countries. The European Union (EU) alone handles 4693 tons of goods every minute (2018 figures). Even though 70% of goods are imported at zero tariff, the EU raised EUR 25.4 billions in 2018, and customs-related income transferred by member states to the EU accounts for nearly 13% of its overall budget. In this field, (a) the conflicting objectives are qualitative and cannot be reduced to a common measure (security and terrorism, health, drug market access control, taxes, etc.); (b) each submitted item has dozens of characteristics; (c) there are constraints; and (d) risk analysis systems have to make decisions in real time. Although the World Customs Organization has promoted the use of artificial intelligence to increase the precision of controls, the problem is very complex due to the data characteristics and interpretability, which is a requirement established by customs officers. In this paper, we propose a new Bayesian-based hybrid approach combining machine learning and multi-objective linear programming (MOLP), called multi-objective Bayesian with dynamic optimization (MOBADO). We demonstrate that it is possible to more than double (with a 237% increase) the precision of current inspection systems, freeing up almost 50% of human resources, and outperform past results with respect to each of the above objectives. MOBADO is an optimization technique that could be combined with any artificial intelligence approach capable of optimizing the quality of multi-objective risk analysis in real time. [ABSTRACT FROM AUTHOR]