Test case prioritization (TP) prioritizes test cases into an optimal order for achieving specific criteria (e.g., higher fault detection capability) as early as possible. However, the existing TP techniques usually only produce a static test case order before the execution without taking runtime test case execution results into account. In this paper, we propose an approach for black-box dynamic TP using rule mining and multi-objective search (named as REMAP). REMAP has three key components: 1) Rule Miner, which mines execution relations among test cases from historical execution data; 2) Static Prioritizer, which defines two objectives (i.e., fault detection capability (FDC) and test case reliance score (TRS)) and applies multi-objective search to prioritize test cases statically; and 3) Dynamic Executor and Prioritizer, which executes statically-prioritized test cases and dynamically updates the test case order based on the runtime test case execution results. We empirically evaluated REMAP with random search, greedy based on FDC, greedy based on FDC and TRS, static search-based prioritization, and rule-based prioritization using two industrial and three open source case studies. Results showed that REMAP significantly outperformed the other approaches for 96% of the case studies and managed to achieve on average 18% higher Average Percentage of Faults Detected (APFD).