Learning hash functions have been widely applied for large-scale image retrieval. Existing methods usually use CNNs to process an entire image at once, which is efficient for single-label images but not for multi-label images. First, these methods cannot fully exploit independent features of different objects in one image, resulting in some small object features with important information being ignored. Second, the methods cannot capture different semantic information from dependency relations among objects. Third, the existing methods ignore the impacts of imbalance between hard and easy training pairs, resulting in suboptimal hash codes. To address these issues, we propose a novel deep hashing method, termed multi-label hashing for dependency relations among multiple objectives (DRMH). We first utilize an object detection network to extract object feature representations to avoid ignoring small object features and then fuse object visual features with position features and further capture dependency relations among objects using a self-attention mechanism. In addition, we design a weighted pairwise hash loss to solve the imbalance problem between hard and easy training pairs. Extensive experiments are conducted on multi-label datasets and zero-shot datasets, and the proposed DRMH outperforms many state-of-the-art hashing methods with respect to different evaluation metrics.

In a practical development environment, the completion of a job often necessitates the coordinated allocation of multiple resources. However, resource constraints such as molds are seldom taken into account in the multi-resource job shop scheduling problem. These molds have sequence-dependent setup times and are fully occupied during processing. Therefore, this study focuses on the Flexible Job Shop Scheduling Problem with Mold Resource Setup Time Optimization (FJSP-MRST), which aims to minimize setup time and makespan. Considering the characteristics of mold setup time, this paper introduces a Mold-Machine Double Fusion Insertion Method to optimize the mold-machine usage order and enhance the mold changeover time calculation method. This innovative approach improves the overall scheduling process by efficiently managing the utilization of molds and machines. Furthermore, we propose a Mold-Operation Layer Loading Method to compress setup time, offering a novel strategy for reducing the setup time for mold resources. These two pioneering methods are integrated with an enhanced multi-objective differential evolution algorithm to obtain the optimal solution for FJSP-MRST. Experimental results demonstrate that the proposed methods can render the arrangement of machines and molds under the current process sequence more reasonable and effectively eliminate implicit setup time.