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A Fast GRASP Metaheuristic for the Trigger Arc TSP with MIP-Based Construction and Multi-Neighborhood Local Search

Joan Salvà Soler, Grégoire de Lambertye

TL;DR

The paper tackles the TA-TSP, a path-dependent variant of the TSP where trigger arcs dynamically alter target arc costs. It introduces a GRASP-based metaheuristic that combines a MIP-based construction phase with a multi-neighborhood local search (2-Opt, Swap, Relocate) and a delta-evaluation strategy that guides efficient exploration of the complex state-dependent landscape. Empirical results on RG, C1, and C2 datasets from MESS 2024 show competitive average gaps (e.g., 0.77% for C1 and 0.40% for C2 within 60 seconds) and outperformance of the Gurobi solver on smaller synthetic instances, with the approach achieving a top-three finish at MESS 2024. The work demonstrates that a carefully tuned GRASP framework with MIP-based construction can deliver high-quality, real-time solutions for TA-TSP, offering practical impact for warehouse routing and other state-dependent routing applications. It also provides a solid foundation for further enhancements through advanced perturbation strategies and tailored neighborhood structures.

Abstract

The Trigger Arc Traveling Salesman Problem (TA-TSP) extends the classical TSP by introducing dynamic arc costs that change when specific "trigger" arcs are traversed, modeling scenarios such as warehouse operations with compactable storage systems. This paper introduces a GRASP-based metaheuristic that combines multiple construction heuristics with a multi-neighborhood local search. The construction phase uses mixed-integer programming (MIP) techniques to transform the TA-TSP into a sequence of tailored TSP instances, while the improvement phase applies 2-Opt, Swap, and Relocate operators. Computational experiments on MESS 2024 competition instances achieved average optimality gaps of 0.77% and 0.40% relative to the best-known solutions within a 60-second limit. On smaller, synthetically generated datasets, the method produced solutions 11.3% better than the Gurobi solver under the same time constraints. The algorithm finished in the top three at MESS 2024, demonstrating its suitability for real-time routing applications with state-dependent travel costs.

A Fast GRASP Metaheuristic for the Trigger Arc TSP with MIP-Based Construction and Multi-Neighborhood Local Search

TL;DR

The paper tackles the TA-TSP, a path-dependent variant of the TSP where trigger arcs dynamically alter target arc costs. It introduces a GRASP-based metaheuristic that combines a MIP-based construction phase with a multi-neighborhood local search (2-Opt, Swap, Relocate) and a delta-evaluation strategy that guides efficient exploration of the complex state-dependent landscape. Empirical results on RG, C1, and C2 datasets from MESS 2024 show competitive average gaps (e.g., 0.77% for C1 and 0.40% for C2 within 60 seconds) and outperformance of the Gurobi solver on smaller synthetic instances, with the approach achieving a top-three finish at MESS 2024. The work demonstrates that a carefully tuned GRASP framework with MIP-based construction can deliver high-quality, real-time solutions for TA-TSP, offering practical impact for warehouse routing and other state-dependent routing applications. It also provides a solid foundation for further enhancements through advanced perturbation strategies and tailored neighborhood structures.

Abstract

The Trigger Arc Traveling Salesman Problem (TA-TSP) extends the classical TSP by introducing dynamic arc costs that change when specific "trigger" arcs are traversed, modeling scenarios such as warehouse operations with compactable storage systems. This paper introduces a GRASP-based metaheuristic that combines multiple construction heuristics with a multi-neighborhood local search. The construction phase uses mixed-integer programming (MIP) techniques to transform the TA-TSP into a sequence of tailored TSP instances, while the improvement phase applies 2-Opt, Swap, and Relocate operators. Computational experiments on MESS 2024 competition instances achieved average optimality gaps of 0.77% and 0.40% relative to the best-known solutions within a 60-second limit. On smaller, synthetically generated datasets, the method produced solutions 11.3% better than the Gurobi solver under the same time constraints. The algorithm finished in the top three at MESS 2024, demonstrating its suitability for real-time routing applications with state-dependent travel costs.

Paper Structure

This paper contains 31 sections, 5 equations, 2 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Variants of the
  4. Metaheuristics for the TSP
  5. Greedy Randomized Adaptive Search Procedures ()
  6. Methodology
  7. Problem Definition
  8. A for the
  9. Construction Heuristics
  10. Simple Randomized Construction
  11. Randomized Greedy Construction
  12. -based Random Perturbation
  13. -based Biased Perturbation
  14. Local search
  15. 2-Opt
  16. ...and 16 more sections

Figures (2)

  • Figure 1: Performance comparison of RGC on the three datasets. Each plot shows average gap (%) and success rate across different values of $\alpha$ for a specific dataset.
  • Figure 2: Performance comparison of -based biased perturbation with parameters $\alpha$ and $\beta$ on different datasets. Results show the average gap (%) across different parameter combinations.