A Parallel Hardware Architecture based on Node-Depth Encoding to Solve Network Design Problems

Many problems involving network design can be found in the real world, such as electric power circuit planning, telecommunications and phylogenetic trees. In general, solutions for these problems are modeled as forests represented by a graph manipulating thousands or millions of input variables, making it hard to obtain the solutions in a reasonable time. To overcome this restriction, Evolutionary Algorithms (EAs) with dynamic data structures (encodings) have been widely investigated to increase the performance of EAs for Network Design Problems (NDPs). In this context, this paper proposes a parallelization of the node-depth encoding (NDE), a data structure especially designed for NDPs. Based on the NDE the authors have developed a parallel algorithm and a hardware architecture implemented on FPGA (Field-Programmable Gate Array), denominated Hardware Parallelized NDE (HP-NDE). The running times obtained in a general purpose processor (GPP) and the HP-NDE are compared. The results show a significant speedup in relation to the GPP solution, solving NDP in a time limited by a constant. Such time upper bound can be satisfied for any size of network until the hardware resources available on the FPGA are depleted. The authors evaluated the HP-NDE on a Stratix IV FPGA with networks containing up to 2048 nodes.