In this paper, a system of searching for optimal paths is developed and concreted on a FPGA. It is based on a memristive emulator, used as a delay element, by configuring the test graph as a memristor network. A parallel algorithm is applied to reduce computing time and increase efficiency. The operation of the algorithm in Matlab is checked beforehand and then exported to two different Intel FPGAs: a DE0-Nano board and an Arria 10 GX 220 FPGA. In both cases reliable results are obtained quickly and conveniently, even for the case of a 300x300 nodes maze.