Efficient convex-elastic net algorithm to solve the Euclidean traveling salesman problem

• Published in: IEEE transactions on systems, man and cybernetics. Part B, Cybernetics Vol. 28; no. 4; pp. 618 - 620
• Main Authors: Al-Mulhem, M., Al-Maghrabi, T.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.1998
• Subjects: Cities and towns; Costs; Euclidean distance; Iterative algorithms; Neural networks; NP-hard problem; Operations research; Polynomials; Space exploration; Traveling salesman problems
• ISSN: 1083-4419
• DOI: 10.1109/3477.704301

This paper describes a hybrid algorithm that combines an adaptive-type neural network algorithm and a nondeterministic iterative algorithm to solve the Euclidean traveling salesman problem (E-TSP). It begins with a brief introduction to the TSP and the E-TSP. Then, it presents the proposed algorithm with its two major components: the convex-elastic net (CEN) algorithm and the nondeterministic iterative improvement (NII) algorithm. These two algorithms are combined into the efficient convex-elastic net (ECEN) algorithm. The CEN algorithm integrates the convex-hull property and elastic net algorithm to generate an initial tour for the E-TSP. The NII algorithm uses two rearrangement operators to improve the initial tour given by the CEN algorithm. The paper presents simulation results for two instances of E-TSP: randomly generated tours and tours for well-known problems in the literature. Experimental results are given to show that the proposed algorithm ran find the nearly optimal solution for the E-TSP that outperform many similar algorithms reported in the literature. The paper concludes with the advantages of the new algorithm and possible extensions.