An Improvement to the 2-Opt Heuristic Algorithm for Approximation of Optimal TSP Tour

Abstract

The travelling salesman problem (TSP) is perhaps the most researched problem in the field of Computer Science and Operations. It is a known NP-hard problem and has significant practical applications in a variety of areas, such as logistics, planning, and scheduling. Route optimisation not only improves the overall profitability of a logistic centre but also reduces greenhouse gas emissions by minimising the distance travelled. In this article, we propose a simple and improved heuristic algorithm named 2-Opt++, which solves symmetric TSP problems using an enhanced 2-Opt local search technique, to generate better results. As with 2-Opt, our proposed method can also be applied to the Vehicle Routing Problem (VRP), with minor modifications. We have compared our technique with six existing algorithms, namely ruin and recreate, nearest neighbour, genetic algorithm, simulated annealing, Tabu search, and ant colony optimisation. Furthermore, to allow for the complexity of larger TSP instances, we have used a graph compression/candidate list technique that helps in reducing the computational complexity and time. The comprehensive empirical evaluation carried out for this research work shows the efficacy of the 2-Opt++ algorithm as it outperforms the other well-known algorithms in terms of the error margin, execution time, and time of convergence.

Keywords

• travelling salesman problem
• combinatorial optimisation
• VRP
• route optimisation
• heuristic algorithms
• TSPLIB