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

TL;DR

This paper presents a fast GRASP metaheuristic for the Trigger Arc TSP, combining MIP-based construction and multi-neighborhood local search, achieving high-quality solutions efficiently for complex, state-dependent routing problems.

Contribution

It introduces a novel GRASP approach integrating MIP techniques and multiple local search operators specifically designed for the Trigger Arc TSP, advancing solution methods for dynamic routing problems.

Findings

Achieved average optimality gaps of 0.77% and 0.40% on MESS 2024 instances.

Produced solutions 11.3% better than Gurobi on synthetic datasets.

Placed in the top three at MESS 2024 competition.

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.