On the Use of Iterative Problem Solving for the Traveling Salesperson Problem with Changing Time Window Constraints

2026-04-16

AI Summary

This work addresses the Traveling Salesman Problem with Time Windows (TSPTW) in dynamic settings where time windows evolve across a sequence of tasks while the underlying road network remains fixed. The authors propose a knowledge transfer strategy that leverages historical solutions by initializing each new task with the optimal route from the preceding one to enhance solving efficiency. They present the first systematic comparison between independent and iterative solving approaches on TSPTW task sequences and introduce a multi-task benchmark framework incorporating two types of temporal changes: time window expansion and swap-additive reallocation. Under a unified penalty-based objective and using local search solvers such as LNS, VNS, and LKH-3, experiments demonstrate that the proposed strategy significantly outperforms cold-start solving in gradually relaxed scenarios, remains competitive under swap-additive perturbations, and yields particularly pronounced gains on challenging instances.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Heuristic Search
• 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 learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

In many real-world settings, problem instances that need to be solved are quite similar, and knowledge from previous optimization runs can potentially be utilized. We explore this for the Traveling Salesperson problem with time windows (TSPTW), which often arises in settings where the travel-time matrix is fixed but time-window constraints change across related tasks. Existing TSPTW studies, however, have not systematically compared solving such task sequences independently with sequential transfer from previously solved tasks. We address this gap using a multi-task benchmark in which each base instance is expanded into five related tasks under two environments: partial time-window expansion and swap-additive time reassignment. We compare a standard from-scratch protocol with an iterative protocol that initializes each task from the best tour of the previous task, using the popular local search approaches LNS, VNS, and LKH-3 under a common penalized-score objective. Our experimental results show that the iterative protocol is consistently superior in the progressive-relaxation setting and generally competitive under swap-additive changes, with improvements increasing on more difficult instances.

Problem

• Traveling Salesperson Problem
• Time Windows
• Iterative Problem Solving
• Sequential Transfer
• Task Sequences

Innovation

• iterative problem solving
• traveling salesperson problem with time windows
• sequential transfer learning
• multi-task optimization
• local search heuristics