<p>Label correlations, as important prior information, are essential to enhance the classification performance in Multi-Instance Multi-Label (MIML) algorithms, but existing models always leverage global label correlations which are less informative. Furthermore, classifier optimization is also crucial for MIML classification results, previous works do not frequently seek to optimize multi objectives simultaneously which may easily result in poor performance on some important metrics. In this paper, a MIML algorithm encoded with local label correlations with an improved Multi-Objective Particle Swarm Optimization (MIML-MOPSO-LLC) is proposed to address the above problems. Specifically, a framework is proposed by taking consideration into both global discrimination fitting and local label correlation sensitivity in the bag level simultaneously in the standard MIML. Subsequently, the loss function of the framework is solved by an alternating optimization process where Support Vector Machine (SVM) classifiers are constructed for optimization. Ultimately, an improved MOPSO is employed to optimize the SVM classifiers by searching for more reliable Pareto front solutions. The experimental results demonstrate that the proposed method achieves competitive performance compared with the classical and state-of-the-art MIML models from the perspective of several classification indicators. Notably, the proposed method which explores the local label correlations exhibits superiority over methods relying on global ones. Furthermore, the study reveals that proposed methods demonstrates enhanced effectiveness in MIML classification and optimizing SVM classifiers compared to conventional single and multi objective optimization approaches.</p> Graphical Abstract <p></p>