Paper: Solving the Quadratic Assignment Problem With Deep Reinforcement Learning (ICLR-2024)

Reviewer comment (Novelty):
It seems that from the DRL based heuristic perspective, the objective function in QAP does not make difference compared with the ones in ILP, both of which are just captured by a reward in DRL. In this sense, the QAP in this paper is almost the same as the vehicle and customer assignment in VRPs with linear objectives, such as [a] Deep Reinforcement Learning for Solving the Heterogeneous Capacitated Vehicle Routing Problem. IEEE T Cybernetics; [b] Learning to Solve Vehicle Routing Problems with Time Windows through Joint Attention. Arxiv; [c] Solving NP-hard Min-max Routing Problems as Sequential Generation with Equity Context. Arxiv. Those works also involve sequentially or parallelly selecting vehicles and customers, while using (advanced) Transformers rather than pointer network.

Author response:
Thank you for the feedback. While we focus on a facility location motivation, it is true that the quadratic assignment problem can be viewed as a generalization of several other combinatorial optimization problems such as the traveling salesman problem and some vehicle routing problems – indeed, we feel this is motivation for developing a DRL methodology to solve it. We have added the suggested references to our literature review, and we are working to implement these suggestions (as well as those made by other referees) to improve performance and narrow the gap with our baseline methods.

Reviewer comment (Novelty):
The motivation and contribution of the work is not clear.

Author response:
Thank you for your feedback. We have expanded the literature review to include some additional relevant references suggested by the referees, as well as clarified the motivation and contribution in the introduction. Regarding the evaluation, we feel that adding further baselines is difficult, since to our knowledge there are no other RL frameworks for QAP. We are working on improving performance relative to the swap heuristic by making tweaks to our model architecture, following the suggestions of other reviewers. We are also working to improve scalability by reducing model size where it is possible to do so without compromising performance.

Reviewer comment (Experiments):
The experimental evaluation is not sufficient; only Gurobi and a swap-based local search heuristic are compared, which makes the paper less convincing.

Author response:
Thank you for your feedback. Regarding the evaluation, we feel that adding further baselines is difficult, since to our knowledge there are no other RL frameworks for QAP. We are working on improving performance relative to the swap heuristic by making tweaks to our model architecture, following the suggestions of other reviewers. We are also working to improve scalability by reducing model size where it is possible to do so without compromising performance.

Reviewer comment (Experiments):
The size of QAP used in the experiment is quite small.

Author response:
Thank you for your feedback. We are also working to improve scalability by reducing model size where it is possible to do so without compromising performance.

Reviewer comment (Experiments):
The performance is quite poor, and it cannot outperform simple heuristics such as SWAP.

Author response:
Thank you for your feedback. We are working on improving performance relative to the swap heuristic by making tweaks to our model architecture, following the suggestions of other reviewers.