Integrated photonic traveling salesman problem probabilistic solver with polynomial calculation time complexity

Abstract

Abstract The traveling salesman problem (TSP) is an NP hard problem, where the solution time becomes unrealistically large as the number of points increases. We propose and simulate a photonic integrated circuit-based TSP solver which uses the delay time of light to express the delay caused by traveling between the points. The solver is comprised of semiconductor optical amplifiers and tunable delay lines, therefore it is reconfigurable. A probabilistic algorithm is used, which enables polynomial calculation and footprint complexity with an error rate of less than 1e-12. The calculation time is 388 ms and footprint is within 10 cm squared for a TSP of 100 points.