A gradual neural network approach for FPGA segmented channel routing problems

A novel neural network approach called gradual neural network (GNN) is presented for segmented channel routing in field programmable gate arrays (FPGA's). FPGA's contain predefined segmented channels for net routing, where adjacent segments in a track can be interconnected through programmable switches for longer segments. The goal of the FPGA segmented channel routing problem, known to be NP-complete, is to find a conflict-free net routing with the minimum routing cost. The GNN for the N-net-M-track problem consists of a neural network of N x M binary neurons and a gradual expansion scheme. The neural network satisfies the constraints of the problem, while the gradual expansion scheme seeks the cost minimization by gradually increasing activated neurons. The energy function and the motion equation are newly defined with heuristic methods. The performance is verified through solving 30 instances, where GNN finds better solutions than existing algorithms within a constant number of iteration steps.