Instance Space Analysis for the Car Sequencing Problem

TL;DR

This paper uses instance space analysis to understand what makes car sequencing problem instances hard, introduces new diverse benchmark instances, and develops a machine learning-based algorithm selection model to improve solving efficiency.

Contribution

It presents a novel instance space analysis approach for the car sequencing problem, creates more diverse benchmark instances, and proposes a machine learning model for algorithm selection.

Findings

New insights into instance characteristics affecting difficulty

Introduction of more challenging and diverse benchmark instances

Development of a machine learning-based algorithm selection model

Abstract

We investigate an important research question for solving the car sequencing problem, that is, which characteristics make an instance hard to solve? To do so, we carry out an instance space analysis for the car sequencing problem, by extracting a vector of problem features to characterize an instance. In order to visualize the instance space, the feature vectors are projected onto a two-dimensional space using dimensionality reduction techniques. The resulting two-dimensional visualizations provide new insights into the characteristics of the instances used for testing and how these characteristics influence the behaviours of an optimization algorithm. This analysis guides us in constructing a new set of benchmark instances with a range of instance properties. We demonstrate that these new instances are more diverse than the previous benchmarks, including some instances that are significantly more difficult to solve. We introduce two new algorithms for solving the car sequencing problem and compare them with four existing methods from the literature. Our new algorithms are shown to perform competitively for this problem but no single algorithm can outperform all others over all instances. This observation motivates us to build an algorithm selection model based on machine learning, to identify the niche in the instance space that an algorithm is expected to perform well on. Our analysis helps to understand problem hardness and select an appropriate algorithm for solving a given car sequencing problem instance.