Traveling Salesman Problem solution using Magnonic Combinatorial Device

Abstract

Abstract Traveling Salesman Problem (TSP) is a decision-making problem that is essential for a number of practical applications. Today, this problem is solved on digital computers exploiting Boolean-type architecture by checking one by one a number of possible routes. In this work, we describe a special type of hardware for the TSP solution. It is a magnonic combinatorial device comprising magnetic and electric parts connected in the active ring circuit. There is a number of possible propagation routes in the magnetic mesh made of phase shifters, frequency filters, and attenuators. The phase shifters mimic cities in TSP while the distance between the cities is encoded in the signal attenuation. The set of frequency filters makes the waves on different frequencies propagate through the different routes. The principle of operation is based on the classical wave superposition. There is a number of waves coming in all possible routes in parallel accumulating different phase shifts and amplitude damping. However, only the wave(s) that accumulates the certain phase shift will be amplified by the electric part. The amplification comes first to the waves that possess the minimum propagation losses. It makes this type of device suitable for TSP solution, where waves are similar to the salesmen traveling in all possible routes at a time. We present the results of numerical modeling illustrating the TSP solutions for four and six cities. Also, we present experimental data for the TSP solution with four cities. The prototype device is built of commercially available components including magnetic phase shifters/filters, coaxial cables, splitters, attenuators, and a broadband amplifier. The device literally shows the shortest route between the four selected cities. There are three examples of finding the shortest route between the cities for three different sets of city-to-city distances. The ability to exploit classical wave superposition is the most appealing property of the demonstrated device. It allows us to check a number of possible routes in parallel without any time overhead. It provides a fundamental advantage over conventional digital computers in functional throughput. The proposed approach is scalable to TSP with a larger number of cities. The estimated functional throughput of the combinatorial device for TSP with 25 cities exceeds 1035 Ops/s∙m2 which is above the limits of the existing supercomputers combined. Physical limits and challenges are also discussed.