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Multi-objective machine learning (ML) methods are widely used in the field of materials because material optimizations are always multi-objective. Traditional multi-objective optimization methods mainly use a combination of hierarchical single-objective optimization. However, this strategy often has difficulty in finding features that can optimize multiple objectives simultaneously. In this work, taking the two objectives of ductility and thermoelectric performance as examples, interpretable and explainable ML strategies are used to find features that can simultaneously optimize multiple objectives. Specifically, SHAP and SISSO are applied for qualitative analysis and quantitative analysis between key features and target values. Both SISSO and SHAP show that EN(ab)A/B and V are both positively correlated with zT and negatively correlated with Pugh's ratio. Furthermore, domain knowledge helps to rationalize the two favorable features. The compounds with large EN(ab)A/B tend to have high band degeneracies, resulting in high zT. High EN(ab)A/B correspond to weak B–X bonds, reducing the G and Pugh's ratio, and improving the ductility of materials. On the other hand, large V will cause small G, which is beneficial to small Pugh's ratio and large zT (via low κL). The present work demonstrates the significance of multi-objective optimization and domain knowledge in the development of materials informatics.
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