Graph-based dimensionality reduction has attracted a lot of attention in recent years. Such methods aim to exploit the graph representation in order to catch some structural information hidden in data. They usually consist of two steps: graph construction and projection. Although graph construction is crucial to the performance, most research work in the literature has focused on the development of heuristics and models to the projection step, and only very recently, attention was paid to network construction. In this work, graph construction is considered in the context of supervised dimensionality reduction. To be specific, using a nature-inspired optimization framework, this work investigates if an optimized graph is able to provide better projections than well-known general-purpose methods. The proposed method is compared with widely used graph construction methods on a range of real-world image classification problems. Results show that the optimization framework has achieved considerable dimensionality reduction rates as well as good predictive performance.