Title: Ranking Cost: One-Stage Circuit Routing by Directly Optimizing Global Objective Function. Abstract: Circuit routing has been a historically challenging problem in designing electronic systems such as very large-scale integration (VLSI) and printed circuit boards (PCBs). The main challenge is that connecting a large number of electronic components under specific design rules and constraints involves a very large search space, which is proved to be NP-complete. 
Early solutions are typically designed with hard-coded heuristics, which suffer from problems of non-optimum solutions and lack of flexibility for new design needs. Although a few learning-based methods have been proposed recently, their methods are cumbersome and hard to extend to large-scale applications. In this work, we propose a new algorithm for circuit routing, named as Ranking Cost (RC),  which innovatively combines search-based methods (i.e., A* algorithm) and learning-based methods (i.e., Evolution Strategies) to form an efficient and trainable router under a proper parameterization. Different from two-stage routing methods ( i.e., first global routing and then detailed routing), our method involves a one-stage procedure that directly optimizes the global objective function, thus it can be easy to adapt to new routing rules and constraints. In our method, we introduce a new set of variables called cost maps, which can help the A* router to find out proper paths to achieve the global object. We also train a ranking parameter, which can produce the ranking order and further improve the performance of our method. Our algorithm is trained in an end-to-end manner and does not use any artificial data or human demonstration. In the experiments, we compare our method with the sequential A* algorithm and a canonical reinforcement learning approach, and results show that our method outperforms these baselines with higher connectivity rates and better scalability. Our ablation study shows that our trained cost maps can capture the global information and guide the routing result to approach global optimum.