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An investigation of the robustness in the Travelling Salesman problem routes using special structured matrices

Aziz, A. A ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1080/23302674.2018.1551584
  3. Publisher: Taylor and Francis , 2020
  4. Abstract:
  5. In this study, the robustness of the Travelling Salesman Problem (TSP) routes is investigated by recognising the special combinatorial structures of Kalmanson matrices. A recognition algorithm encompassing three procedures based on combinatorial and linear programming (LP) is developed and executed on several randomly generated instances. These procedures produce three lower bounds which provide guarantees on the optimality of the solutions. Computational experiments show that the proposed LP-based procedure performs efficiently well across all problem dimensions and provides the best lower bounds to the TSP. This is supported by an average deviation of less than 7% between the TSP tour lengths and the lower bounds of the Kalmanson matrices. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group
  6. Keywords:
  7. Combinatorial ; Kalmanson ; Linear programming ; Robustness ; Special structured matrices ; Travelling salesman problem
  8. Source: International Journal of Systems Science: Operations and Logistics ; Volume 7, Issue 2 , 2020 , Pages 172-181
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/23302674.2018.1551584?journalCode=tsyb20