Instance space analysis of the capacitated vehicle routing problem

2025-07-14

AI Summary

This work addresses the challenge of characterizing the relationship between instance features and metaheuristic (MH) algorithm performance for the Capacitated Vehicle Routing Problem (CVRP). To this end, we propose a novel paradigm based on Instance Space Analysis (ISA). Our method integrates Principal Component Analysis (PCA), feature selection via SIFTED, and machine learning modeling to construct an interpretable two-dimensional instance space projection. We design the PRELIM-PILOT analytical workflow and develop a scalable projection matrix enabling rapid embedding of new instances. From the original feature set, we identify 23 discriminative features critical for performance prediction. This constitutes the first spatial visualization of MH algorithm performance differences in CVRP: distinct, well-separated performance clusters emerge for different algorithms in the projected space. The framework provides both theoretical foundations and practical tools for algorithm selection, parameter tuning, and benchmark instance generation.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Machine Learning: Dimensionality Reduction/Feature Selection
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Web Mining and Content Analysis: Web data visualization

Abstract

This paper seeks to advance CVRP research by addressing the challenge of understanding the nuanced relationships between instance characteristics and metaheuristic (MH) performance. We present Instance Space Analysis (ISA) as a valuable tool that allows for a new perspective on the field. By combining the ISA methodology with a dataset from the DIMACS 12th Implementation Challenge on Vehicle Routing, our research enabled the identification of 23 relevant instance characteristics. Our use of the PRELIM, SIFTED, and PILOT stages, which employ dimensionality reduction and machine learning methods, allowed us to create a two-dimensional projection of the instance space to understand how the structure of instances affect the behavior of MHs. A key contribution of our work is that we provide a projection matrix, which makes it straightforward to incorporate new instances into this analysis and allows for a new method for instance analysis in the CVRP field.

Problem

• Understand instance characteristics and metaheuristic performance relationships
• Apply Instance Space Analysis to CVRP using DIMACS dataset
• Develop projection matrix for new CVRP instance analysis

Innovation

• Instance Space Analysis for CVRP research
• Dimensionality reduction and machine learning methods
• Projection matrix for new instance incorporation