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Combining Monte Carlo Tree Search and Heuristic Search for Weighted Vertex Coloring

Cyril Grelier, Olivier Goudet, Jin-Kao Hao

TL;DR

This work tackles WVCP, an NP-hard generalization of graph coloring, by applying Monte Carlo Tree Search (MCTS) with problem-specific heuristics and vertex-ordering. It develops a constructive tree representation for WVCP, and augments MCTS with greedy and local-search-based simulations to improve solution quality. Experimental results on 188 benchmark instances show that MCTS variants, especially when paired with local search (notably RedLS), outperform pure greedy approaches and can obtain new best-known scores on difficult cases. The findings highlight the value of combining MCTS with targeted heuristics for WVCP, with distinct strategies recommended for large versus small instances and clear avenues for adaptive or learning-guided enhancements.

Abstract

This work investigates the Monte Carlo Tree Search (MCTS) method combined with dedicated heuristics for solving the Weighted Vertex Coloring Problem. In addition to the basic MCTS algorithm, we study several MCTS variants where the conventional random simulation is replaced by other simulation strategies including greedy and local search heuristics. We conduct experiments on well-known benchmark instances to assess these combined MCTS variants. We provide empirical evidence to shed light on the advantages and limits of each simulation strategy. This is an extension of the work of Grelier and al. presented at EvoCOP2022.

Combining Monte Carlo Tree Search and Heuristic Search for Weighted Vertex Coloring

TL;DR

This work tackles WVCP, an NP-hard generalization of graph coloring, by applying Monte Carlo Tree Search (MCTS) with problem-specific heuristics and vertex-ordering. It develops a constructive tree representation for WVCP, and augments MCTS with greedy and local-search-based simulations to improve solution quality. Experimental results on 188 benchmark instances show that MCTS variants, especially when paired with local search (notably RedLS), outperform pure greedy approaches and can obtain new best-known scores on difficult cases. The findings highlight the value of combining MCTS with targeted heuristics for WVCP, with distinct strategies recommended for large versus small instances and clear avenues for adaptive or learning-guided enhancements.

Abstract

This work investigates the Monte Carlo Tree Search (MCTS) method combined with dedicated heuristics for solving the Weighted Vertex Coloring Problem. In addition to the basic MCTS algorithm, we study several MCTS variants where the conventional random simulation is replaced by other simulation strategies including greedy and local search heuristics. We conduct experiments on well-known benchmark instances to assess these combined MCTS variants. We provide empirical evidence to shed light on the advantages and limits of each simulation strategy. This is an extension of the work of Grelier and al. presented at EvoCOP2022.
Paper Structure (27 sections, 3 equations, 4 figures, 16 tables, 1 algorithm)

This paper contains 27 sections, 3 equations, 4 figures, 16 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Constructive approach with a tree for the weighted graph coloring problem
  3. Partial and legal search space
  4. Tree search for weighted vertex coloring
  5. Predefined vertex order
  6. Monte Carlo Tree Search for weighted vertex coloring
  7. General framework
  8. Selection
  9. Expansion
  10. Simulation
  11. Update
  12. Pruning
  13. Toy example
  14. Combining MCTS with Local Search
  15. Basic tabu search
  16. ...and 12 more sections

Figures (4)

  • Figure 1: This figure shows an application of the WVCP for scheduling jobs into batches in a multiprocessor environment with restricted access to certain resources.
  • Figure 2: Toy example of one MCTS iteration
  • Figure 3: Toy example of the search tree pruning
  • Figure 4: Plots of the evolution of the means of the scores over time for different values of the coefficient $c$ between 0 and 5, for the instances DSJC500.5, latin_square_10, le450_25a, wap01a, C2000.5, and C2000.9. For each configuration, 20 runs are launched with the MCTS+Greedy-Random variant for 5h and 15h for the C2000 instances.