Optical processor for solving the traveling salesman problem (TSP)

Natan T. Shaked; Gil Simon; Tal Tabib; Stephane Mesika; Shlomi Dolev; Joseph Rosen

doi:10.1117/12.683979

30 August 2006 Optical processor for solving the traveling salesman problem (TSP)

Natan T. Shaked, Gil Simon, Tal Tabib, Stephane Mesika, Shlomi Dolev, Joseph Rosen

Proceedings Volume 6311, Optical Information Systems IV; 63110G (2006) https://doi.org/10.1117/12.683979
Event: SPIE Optics + Photonics, 2006, San Diego, California, United States

Abstract

This paper introduces an optical solution to (bounded-length input instances of) an NP-complete problem called the traveling salesman problem using a pure optical system. The solution is based on the multiplication of a binary-matrix, representing all feasible routes, by a weight-vector, representing the weights of the problem. The multiplication of the binary-matrix by the weight-vector can be implemented by any optical vector-matrix multiplier. In this paper, we show that this multiplication can be obtained by an optical correlator. In order to synthesize the binary-matrix, a unique iterative algorithm is presented. This algorithm synthesizes an N-node binary-matrix using rather small number of vector duplications from the (N-1)-node binary-matrix. We also show that the algorithm itself can be implemented optically and thus we ensure the entire optical solution to the problem. Simulation and experimental results prove the validity of the optical method.

Citation Download Citation

Natan T. Shaked, Gil Simon, Tal Tabib, Stephane Mesika, Shlomi Dolev, and Joseph Rosen "Optical processor for solving the traveling salesman problem (TSP)", Proc. SPIE 6311, Optical Information Systems IV, 63110G (30 August 2006); https://doi.org/10.1117/12.683979

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