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Enhancing Genetic Algorithms with Graph Neural Networks: A Timetabling Case Study

Laura-Maria Cornei, Mihaela-Elena Breabăn

TL;DR

This work tackles Staff Rostering timetabling by blending a Graph Neural Network with a multi-modal Genetic Algorithm, using the GNN as an improvement operator to guide GA search. The GNN learns domain patterns from timetabling data and outputs higher-quality schedules, while the GA maintains diverse exploration of the search space. Across extensive experiments, the GA+GNN hybrid achieves statistically significant gains in both speed and solution quality compared to standalone GA or GNN baselines. The study demonstrates a pioneering integration of GNNs and GAs for timetabling, with potential applicability to broader scheduling problems and future improvements in generalization and hybrid strategies.

Abstract

This paper investigates the impact of hybridizing a multi-modal Genetic Algorithm with a Graph Neural Network for timetabling optimization. The Graph Neural Network is designed to encapsulate general domain knowledge to improve schedule quality, while the Genetic Algorithm explores different regions of the search space and integrates the deep learning model as an enhancement operator to guide the solution search towards optimality. Initially, both components of the hybrid technique were designed, developed, and optimized independently to solve the tackled task. Multiple experiments were conducted on Staff Rostering, a well-known timetabling problem, to compare the proposed hybridization with the standalone optimized versions of the Genetic Algorithm and Graph Neural Network. The experimental results demonstrate that the proposed hybridization brings statistically significant improvements in both the time efficiency and solution quality metrics, compared to the standalone methods. To the best of our knowledge, this work proposes the first hybridization of a Genetic Algorithm with a Graph Neural Network for solving timetabling problems.

Enhancing Genetic Algorithms with Graph Neural Networks: A Timetabling Case Study

TL;DR

This work tackles Staff Rostering timetabling by blending a Graph Neural Network with a multi-modal Genetic Algorithm, using the GNN as an improvement operator to guide GA search. The GNN learns domain patterns from timetabling data and outputs higher-quality schedules, while the GA maintains diverse exploration of the search space. Across extensive experiments, the GA+GNN hybrid achieves statistically significant gains in both speed and solution quality compared to standalone GA or GNN baselines. The study demonstrates a pioneering integration of GNNs and GAs for timetabling, with potential applicability to broader scheduling problems and future improvements in generalization and hybrid strategies.

Abstract

This paper investigates the impact of hybridizing a multi-modal Genetic Algorithm with a Graph Neural Network for timetabling optimization. The Graph Neural Network is designed to encapsulate general domain knowledge to improve schedule quality, while the Genetic Algorithm explores different regions of the search space and integrates the deep learning model as an enhancement operator to guide the solution search towards optimality. Initially, both components of the hybrid technique were designed, developed, and optimized independently to solve the tackled task. Multiple experiments were conducted on Staff Rostering, a well-known timetabling problem, to compare the proposed hybridization with the standalone optimized versions of the Genetic Algorithm and Graph Neural Network. The experimental results demonstrate that the proposed hybridization brings statistically significant improvements in both the time efficiency and solution quality metrics, compared to the standalone methods. To the best of our knowledge, this work proposes the first hybridization of a Genetic Algorithm with a Graph Neural Network for solving timetabling problems.
Paper Structure (17 sections, 8 equations, 2 figures, 2 tables)

This paper contains 17 sections, 8 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Staff Rostering - an Integer Programming model
  4. Graph Neural Network
  5. GNN learning procedure
  6. Datasets generation
  7. GNN structure, model and embeddings
  8. GNN hyper-parameter tuning
  9. Genetic Algorithm
  10. Overview of the algorithm
  11. Solution representation, initial population and fitness function
  12. Stopping conditions
  13. Variation operators
  14. Crowding distances computation and selection
  15. Optimizing the Genetic Algorithm
  16. ...and 2 more sections

Figures (2)

  • Figure 1: Overview of the GNN learning procedure (left side) and structure of the graph and the embeddings of the used GNN (right side)
  • Figure 2: Comparative evaluation of the $GA\_v1$ and $GA\_v1+GNN$ methods for the fitness, hard & soft penalty scores, and number of feasible schedules metrics