Quadratic Assignment Problem

The Quadratic Assignment Problem (QAP) is a computationally hard combinatorial optimization problem focused on optimally assigning a set of facilities to a set of locations, considering pairwise interaction costs. Current research emphasizes developing scalable algorithms, including those based on deep learning (e.g., transformer networks and reinforcement learning), convex relaxations, and quantum-hybrid solvers, to tackle the NP-hard nature of the problem and address larger instances. QAP's significance stems from its wide applicability in diverse fields like computer vision (image matching), machine learning (data alignment), and operations research (facility layout), with ongoing efforts to improve solution quality and efficiency for real-world applications.