Autonomous Driving Systems (ADSs) are complex systems that must satisfy multiple requirements such as safety, compliance to traffic rules, and comfortableness. However, satisfying all these requirements may not always be possible due to emerging environmental conditions. Therefore, the ADSs may have to make trade-offs among multiple requirements during the ongoing operation, resulting in one or more requirements violations. For ADS engineers, it is highly important to know which combinations of requirements violations may occur, as different combinations can expose different types of failures. However, there is currently no testing approach that can generate scenarios to expose different combinations of requirements violations. To address this issue, in this paper, we introduce the notion of requirements violation pattern to characterize a specific combination of requirements violations. Based on this notion, we propose a testing approach named EMOOD that can effectively generate test scenarios to expose as many requirements violation patterns as possible. EMOOD uses a prioritization technique to sort all possible patterns to search for, from the most to the least critical ones. Then, EMOOD iteratively includes an evolutionary many-objective optimization algorithm to find different combinations of requirements violations. In each iteration, the targeted pattern is determined by a dynamic prioritization technique to give preferences to those patterns with higher criticality and higher likelihood to occur. We apply EMOOD to an industrial ADS under two common traffic situations. Evaluation results show that EMOOD outperforms three baseline approaches in generating test scenarios by discovering more requirements violation patterns.