With the ability to process many real-world problems, multi-label classification has received a large attention in recent years and the instance-based ML-kNN classifier is today considered as one of the most efficient. But it is sensitive to noisy and redundant features and its performances decrease with increasing data dimensionality. To overcome these problems, dimensionality reduction is an alternative but current methods optimize reduction objectives which ignore the impact on the ML-kNN classification. We here propose ML-ARP, a novel dimensionality reduction algorithm which, using a variable neighborhood search meta-heuristic, learns a linear projection of the feature space which specifically optimizes the ML-kNN classification loss. Numerical comparisons have confirmed that ML-ARP outperforms ML-kNN without data processing and four standard multi-label dimensionality reduction algorithms.