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

2025-08-11

AI Summary

This paper addresses the Triggered-Arc Traveling Salesman Problem (TA-TSP), a dynamic variant of the TSP where traversing designated “trigger arcs” causes real-time updates to the costs of other arcs—modeling scenarios such as compactable-storage warehouse routing. We propose a MIP-driven GRASP metaheuristic: its construction phase employs a customized mixed-integer program to generate high-quality initial solutions; its enhanced multi-neighborhood local search integrates 2-Opt, Swap, and Relocate operators for efficient solution-space exploration. By decomposing the TA-TSP into a sequence of adapted TSP subproblems, our approach balances solution accuracy and computational efficiency. Evaluated on the MESS 2024 competition benchmarks, the method achieves an average optimality gap of only 0.77% within 60 seconds; on small-scale instances, it outperforms Gurobi by up to 11.3%. It ranked among the top three overall in the competition, demonstrating state-of-the-art performance and practical applicability for dynamic warehouse routing.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Topic discovery and tracking

Abstract

The Trigger Arc Traveling Salesman Problem (TA-TSP) extends the classical TSP by introducing dynamic arc costs that change when specific extit{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.

Problem

• Solves dynamic arc cost TSP with trigger arcs
• Optimizes warehouse routing with compactable storage
• Improves real-time solutions for state-dependent travel

Innovation

• GRASP metaheuristic with MIP-based construction
• Multi-neighborhood local search operators
• Transforms TA-TSP into tailored TSP instances