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An island-parallel ensemble metaheuristic algorithm for large graph coloring problems

Tansel Dokeroglu, Tayfun Kucukyilmaz, Ahmet Cosar

TL;DR

This work tackles large graph coloring problems by introducing PEM-Color, an island-parallel ensemble metaheuristic that fuses HHO, ABC, and TLBO under an MPI framework, with TabuCol guiding exploitation. By distributing three populations across a 64-processor cluster and coordinating through a master node, the method achieves near-linear speedups while delivering competitive and often best-known solution quality on the DIMACS benchmarks. The study demonstrates the effectiveness of parallel ensemble strategies for NP-hard problems, achieving strong scalability and outperforming 13 state-of-the-art algorithms on many large instances. The results suggest significant practical impact for rapid, high-quality graph coloring in large-scale applications and point to promising avenues for further parallelization and generalization to other combinatorial problems.

Abstract

Graph Coloring Problem (GCP) is an NP-Hard vertex labeling problem in graphs such that no two adjacent vertices can have the same color. Large instances of GCP cannot be solved in reasonable execution times by exact algorithms. Therefore, soft computing approaches, such as metaheuristics, have proven to be very efficient for solving large instances of GCP. In this study, we propose a new island-parallel ensemble metaheuristic algorithm (PEM-Color) to solve large GCP instances. Ensemble learning is a new machine learning approach based on combining the output of multiple models instead of using a single one. We use Message Passing Interface (MPI) parallel computation libraries to combine recent state-of-the-art metaheuristics: Harris Hawk Optimization (HHO), Artificial Bee Colony (ABC), and Teaching Learning Based (TLBO) to improve the quality of their solutions further. To the best of our knowledge, this is the first study that combines metaheuristics and applies to the GCP using an ensemble approach. We conducted experiments on large graph instances from the well-known DIMACS benchmark using 64 processors and achieved significant improvements in execution times. The experiments also indicate an almost linear speed-up with a strong scalability potential. The solution quality of the instances is promising, as our algorithm outperforms 13 state-of-the-art algorithms.

An island-parallel ensemble metaheuristic algorithm for large graph coloring problems

TL;DR

This work tackles large graph coloring problems by introducing PEM-Color, an island-parallel ensemble metaheuristic that fuses HHO, ABC, and TLBO under an MPI framework, with TabuCol guiding exploitation. By distributing three populations across a 64-processor cluster and coordinating through a master node, the method achieves near-linear speedups while delivering competitive and often best-known solution quality on the DIMACS benchmarks. The study demonstrates the effectiveness of parallel ensemble strategies for NP-hard problems, achieving strong scalability and outperforming 13 state-of-the-art algorithms on many large instances. The results suggest significant practical impact for rapid, high-quality graph coloring in large-scale applications and point to promising avenues for further parallelization and generalization to other combinatorial problems.

Abstract

Graph Coloring Problem (GCP) is an NP-Hard vertex labeling problem in graphs such that no two adjacent vertices can have the same color. Large instances of GCP cannot be solved in reasonable execution times by exact algorithms. Therefore, soft computing approaches, such as metaheuristics, have proven to be very efficient for solving large instances of GCP. In this study, we propose a new island-parallel ensemble metaheuristic algorithm (PEM-Color) to solve large GCP instances. Ensemble learning is a new machine learning approach based on combining the output of multiple models instead of using a single one. We use Message Passing Interface (MPI) parallel computation libraries to combine recent state-of-the-art metaheuristics: Harris Hawk Optimization (HHO), Artificial Bee Colony (ABC), and Teaching Learning Based (TLBO) to improve the quality of their solutions further. To the best of our knowledge, this is the first study that combines metaheuristics and applies to the GCP using an ensemble approach. We conducted experiments on large graph instances from the well-known DIMACS benchmark using 64 processors and achieved significant improvements in execution times. The experiments also indicate an almost linear speed-up with a strong scalability potential. The solution quality of the instances is promising, as our algorithm outperforms 13 state-of-the-art algorithms.

Paper Structure

This paper contains 14 sections, 3 equations, 4 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. PEM-Color Framework
  4. Parameter tuning of the metaheuristics
  5. Harris Hawk Optimization Metaheuristic for the GCP
  6. Artificial Bee Colony Optimization Metaheuristic for the GCP
  7. Teaching Learning-Based Optimization Metaheuristic for the GCP
  8. Tabu Search Algorithm, TabuCol
  9. Evaluation of experimental results and discussion
  10. The performance of PEM-Color algorithm on small problem instances
  11. The performance of PEM-Color algorithm on large problem instances
  12. Comparisons with state-of-the-art algorithms
  13. The scalability and speed-up analysis
  14. Conclusions and future work

Figures (4)

  • Figure 1: Illustration of GCP: an undirected graph (having 20 vertices) labeled using four colors.
  • Figure 2: The representation of the GCP solution in Figure \ref{['colored-graph']}. The indices represent vertex IDs in the graph.
  • Figure 3: The parallel computation framework of PEM-Color algorithm. Master and slave nodes and how they interact is presented in this drawing.
  • Figure 4: Harris Hawk (HH) metaheuristic hunting strategy summary. The HH metaheuristic exhibits distinct stages that depend on the energy levels of the hawks. These stages correspond to various behaviors and strategies adopted by the hawks, which are influenced by their energy conditions.