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Connection patterns among Local Optima Networks (LONs) can inform heuristic design for optimisation. LON research has predominantly required complete enumeration of a fitness landscape, thereby restricting analysis to problems diminutive in size compared to real-life situations. LON sampling algorithms are therefore important. In this paper, we study LON construction algorithms for the Quadratic Assignment Problem (QAP). Using machine learning, we use estimated LON features to predict search performance for competitive heuristics used i