Utility-oriented mining which integrates utility theory and data mining is a useful tool for understanding economic consumer behavior. Traditional algorithms for mining high-utility patterns (HUPs) applies a single/uniform minimum high-utility threshold (minutil) to obtain the set of HUPs, but in some real-life circumstances, some specific products may bring lower utilities compared with others, but their profit may offer some vital information. However, if minutil is set high, the patterns with low minutil are missed; if minutil is set low, the number of patterns becomes unmanageable. In this paper, an efficient one-phase utility-oriented pattern mining algorithm, called HIMU, is proposed for mining HUPs with varied item-specific minimum utility. A novel tree structure called a multiple item utility set-enumeration tree (MIU-tree), the global sorted and the conditional downward closure properties are introduced in HIMU. In addition, we extended the compact utility-list structure to keep the necessary information, and thus this one-phase HIMU model greatly reduces the computational costs and memory requirements. Moreover, two pruning strategies are then extended to enhance the performance. We conducted extensive experiments in several synthetic and real-world datasets; the results indicates that the designed one-phase HIMU algorithm can address the "rare item problem" and has better performance than the state-of-the-art algorithms in terms of runtime, memory usage, and scalability. Furthermore, the enhanced algorithms outperform the non-optimized HIMU approach.