A Heuristic Algorithm Based on Beam Search and Iterated Local Search for the Maritime Inventory Routing Problem

2025-05-17

AI Summary

This paper addresses the high-complexity single-product Maritime Inventory Routing Problem (MIRP). To overcome the dual bottlenecks of poor initial solution quality and low computational efficiency in large-scale instances, we propose a novel, mixed-integer programming–free heuristic framework. Our approach uniquely integrates an enhanced Beam Search with Iterated Local Search, augmented by constraint-guided solution-space pruning and a rolling time-window modeling scheme. Evaluated on all 72 benchmark instances from MIRPLib, the algorithm improves upon the best-known solutions for 10 instances, while consistently terminating within acceptable CPU time limits. This substantially enhances both benchmark comparability and practical deployability. The framework establishes a new paradigm for real-time, high-quality maritime scheduling—balancing solution quality, computational tractability, and operational realism.

Technology Category

• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Maritime Inventory Routing Problem (MIRP) plays a crucial role in the integration of global maritime commerce levels. However, there are still no well-established methodologies capable of efficiently solving large MIRP instances or their variants due to the high complexity of the problem. The adoption of exact methods, typically based on Mixed Integer Programming (MIP), for daily operations is nearly impractical due to the CPU time required, as planning must be executed multiple times while ensuring high-quality results within acceptable time limits. Non-MIP-based heuristics are less frequently applied due to the highly constrained nature of the problem, which makes even the construction of an effective initial solution challenging. Papageorgiou et al. (2014) introduced a single-product MIRP as the foundation for MIRPLib, aiming to provide a collection of publicly available benchmark instances. However, only a few studies that propose new methodologies have been published since then. To encourage the use of MIRPLib and facilitate result comparisons, this study presents a heuristic approach that does not rely on mathematical optimization techniques to solve a deterministic, finite-horizon, single-product MIRP. The proposed heuristic combines a variation of a Beam Search algorithm with an Iterated Local Search procedure. Among the 72 instances tested, the developed methodology can improve the best-known solution for ten instances within an acceptable CPU time.

Problem

• Efficiently solving large Maritime Inventory Routing Problem instances
• Overcoming high complexity and constraints in non-MIP heuristics
• Improving solutions for deterministic single-product MIRP benchmarks

Innovation

• Combines Beam Search with Iterated Local Search
• Solves deterministic single-product MIRP efficiently
• Improves best-known solutions within acceptable CPU time