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AbstractInremanufacturing, a vital segment of the sustainable, low-carbon circular economy, existing versions of the traditional unequal-areas facility layout problem (UA-FLP) model face significant limitations in designing layouts. To be specific, in the process of minimizing the material-handling cost (MHC), these models also alter departmental dimensions, often diverging from construction specifications. This poses a difficulty, as critical equipment required for remanufacturing, e.g., sorting and cleaning machines, have unalterable dimensions, which implies that departmental dimensions cannot be changed from specifications provided. To address this, a novelFlexible Envelope UA-FLP(FE-UA-FLP) model is proposed in this work for designing layouts wherein department dimensions and shapes arenotaltered while simultaneously theMHCis reduced. The new model offers two additional advantages in that (a) it diminishes the dead space between the departments, generating avisually appealing, compactlayout, and (b) it uses an updatable interaction matrix, which allows it to beadaptable to changing demand, making the design process suitable forsmart systems. Numerical testing with three meta-heuristics on simulated factory data demonstrates the effectiveness of the FE-UA-FLP model in achieving these objectives. The numerical results also highlight the model’s ability torapidlygenerate solutions, which is a key requirement for smart manufacturing. Future work can extend this model to three-dimensional optimization and job shop settings. Graphical abstract 

Preferences within a group of people are not uniform but follow a distribution. While existing alignment methods like Direct Preference Optimization (DPO) attempt to steer models to reflect human preferences, they struggle to capture the distributional pluralistic preferences within a group. These methods often skew toward dominant preferences, overlooking the diversity of opinions, especially when conflicting preferences arise. To address this issue, we propose Group Distributional Preference Optimization (GDPO), a novel framework that aligns language models with the distribution of preferences within a group by incorporating the concept of beliefs that shape individual preferences. GDPO calibrates a language model using statistical estimation of the group's belief distribution and aligns the model with belief-conditioned preferences, offering a more inclusive alignment framework than traditional methods. In experiments using both synthetic controllable opinion generation and real-world movie review datasets, we show that DPO fails to align with the targeted belief distributions, while GDPO consistently reduces this alignment gap during training. Additionally, our evaluation metrics demonstrate that GDPO outperforms existing approaches in aligning with group distributional preferences, marking a significant advance in pluralistic alignment. 

Much work on the cultural awareness of large language models (LLMs) focuses on the models' sensitivity to geo-cultural diversity. However, in addition to cross-cultural differences, there also exists common ground across cultures. For instance, a bridal veil in the United States plays a similar cultural-relevant role as a honggaitou in China. In this study, we introduce a benchmark dataset CUNIT for evaluating decoder-only LLMs in understanding the cultural unity of concepts. Specifically, CUNIT consists of 1,425 evaluation examples building upon 285 traditional cultural-specific concepts across 10 countries. Based on a systematic manual annotation of cultural-relevant features per concept, we calculate the cultural association between any pair of cross-cultural concepts. Built upon this dataset, we design a contrastive matching task to evaluate the LLMs' capability to identify highly associated cross-cultural concept pairs. We evaluate 3 strong LLMs, using 3 popular prompting strategies, under the settings of either giving all extracted concept features or no features at all on CUNIT Interestingly, we find that cultural associations across countries regarding clothing concepts largely differ from food. Our analysis shows that LLMs are still limited to capturing cross-cultural associations between concepts compared to humans. Moreover, geo-cultural proximity shows a weak influence on model performance in capturing cross-cultural associations.