BiQAP: Neural Bi-level Optimization-based Framework for Solving Quadratic Assignment Problems

The Quadratic Assignment Problem (QAP) has attracted lasting attention for its wide applications and computational challenges. Despite the rich literature in machine learning for QAP, most works often address the problem in the setting of image matching, whereby deep networks could play a vital role in extracting useful features for the subsequent matching. While its power on pure numerical QAP instances is limited in node embedding, often with a vanilla graph neural network. This paper tries to tap the potential of deep nets for QAP, specifically by modifying the input instance, which is orthogonal to previous efforts. Specifically, we develop a bi-level unsupervised framework, where the inner optimization involves trying to solve the modified instance with entropic regularization that can be solved iteratively using the Sinkhorn algorithm without affecting backpropagation by truncating gradients during training. The outer minimization deals with the quadratic objective function of the original QAP. In particular, seeing the intractable scale of the most general form, i.e., Lawler's QAP and the practical utility of the more efficient Koopmans-Beckmann QAP (KBQAP) form for solving other graph and combinatorial problems like TSP and graph edit distance, we embody our network on the KBQAP, and show its strong performance on various benchmarks in our experiments.