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Automatic Feature Learning for Essence: a Case Study on Car Sequencing

Alessio Pellegrino, Özgür Akgün, Nguyen Dang, Zeynep Kiziltan, Ian Miguel

TL;DR

This paper considers the task of building machine learning models to automatically select the best combination for a problem instance and contributes to automatic learning of instance features directly from the high-level representation of a problem instance using a language model.

Abstract

Constraint modelling languages such as Essence offer a means to describe combinatorial problems at a high-level, i.e., without committing to detailed modelling decisions for a particular solver or solving paradigm. Given a problem description written in Essence, there are multiple ways to translate it to a low-level constraint model. Choosing the right combination of a low-level constraint model and a target constraint solver can have significant impact on the effectiveness of the solving process. Furthermore, the choice of the best combination of constraint model and solver can be instance-dependent, i.e., there may not exist a single combination that works best for all instances of the same problem. In this paper, we consider the task of building machine learning models to automatically select the best combination for a problem instance. A critical part of the learning process is to define instance features, which serve as input to the selection model. Our contribution is automatic learning of instance features directly from the high-level representation of a problem instance using a language model. We evaluate the performance of our approach using the Essence modelling language with a case study involving the car sequencing problem.

Automatic Feature Learning for Essence: a Case Study on Car Sequencing

TL;DR

This paper considers the task of building machine learning models to automatically select the best combination for a problem instance and contributes to automatic learning of instance features directly from the high-level representation of a problem instance using a language model.

Abstract

Constraint modelling languages such as Essence offer a means to describe combinatorial problems at a high-level, i.e., without committing to detailed modelling decisions for a particular solver or solving paradigm. Given a problem description written in Essence, there are multiple ways to translate it to a low-level constraint model. Choosing the right combination of a low-level constraint model and a target constraint solver can have significant impact on the effectiveness of the solving process. Furthermore, the choice of the best combination of constraint model and solver can be instance-dependent, i.e., there may not exist a single combination that works best for all instances of the same problem. In this paper, we consider the task of building machine learning models to automatically select the best combination for a problem instance. A critical part of the learning process is to define instance features, which serve as input to the selection model. Our contribution is automatic learning of instance features directly from the high-level representation of a problem instance using a language model. We evaluate the performance of our approach using the Essence modelling language with a case study involving the car sequencing problem.
Paper Structure (15 sections, 1 equation, 8 figures, 1 table)

This paper contains 15 sections, 1 equation, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Methodology
  4. Feature Learning Using a Language Model
  5. Algorithm Selection Using the Learnt Features
  6. A Case Study with the Car Sequencing Problem
  7. Problem Description and Instance Set
  8. Combinations of Models and Solvers
  9. Dataset and Algorithm Complementarity
  10. Experimental Evaluation
  11. Neural Network Training
  12. Feature Learning and Algorithm Selection: Combining vs Splitting
  13. Learnt Features vs fzn2feat
  14. Feature Extraction Cost
  15. Conclusions

Figures (8)

  • Figure 1: Two possible algorithm selection approaches: entirely NN-based (top) versus hybrid of an NN and an ML-based algorithm selector (bottom).
  • Figure 2: Essence model of the car sequencing problem.
  • Figure 3: PAR10 value of each algorithm and the VBS on the instance set (lower is better), where the algorithms are grouped by their models (left) or solvers (right).
  • Figure 4: Average participation to VBS (left) and average competitiveness (right).
  • Figure 5: Training progress of the combined learning approach in one fold, shown by the cross entropy loss (top left), accuracy and F1 score (top right), and PAR10 score (bottom). The PAR10 score is normalised into the range $[0,1]$ using $M_2$-Chuffed (the best overall algorithm) and the VBS.
  • ...and 3 more figures