### New Traveling Salesman Problem Approximation Algorithm

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#### Abstract

The travelling salesman problem (TSP) has been studied by many researchers and a great variety of heuristics and implementations with varying solution quality/running time tradeoffs have been proposed. In this paper, we introduce a heuristic algorithm that uses nearest neighbour heuristic first to find an initial tour and then uses a local search component to improve the quality of the solution. The implementation of our algorithm is given. The local search consists of utilizing a combination of brute force and 2-Optimal techniques on small parts of the tour. The results of our implementation are compared with corresponding results using nearest insertion heuristic on the same instances. The effectiveness of our algorithm derives from the improved tour quality achieved with reasonable running times. *Copyright © 2016 Praise Worthy Prize - All rights reserved.*

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