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Discovering new robust local search algorithms with neuro-evolution

Mohamed Salim Amri Sakhri, Adrien Goëffon, Olivier Goudet, Frédéric Saubion, Chaïmaâ Touhami

TL;DR

The paper tackles the challenge of designing effective local search moves for discrete optimization by learning a neural policy that operates on the same input as classic local search. It frames local search as a memoryless episodic process and trains a neural network policy (Neuro-LS) with CMA-ES on NK landscapes across varied sizes $N$ and ruggedness $K$. Four observation schemes are compared, with ranking-based inputs ($o^3$ or $o^4$) yielding the strongest and most robust strategies, including a two-mode behavior in rugged landscapes (small steps followed by a worst-improvement jump). The learned Neuro-LS policies outperform baseline deterministic LS (Best/First improvement and $(1,\lambda)$-ES) on NK ensembles and show robustness in out-of-distribution tests to QUBO risks, highlighting the potential to auto-discover robust local search heuristics for black-box combinatorial optimization.

Abstract

This paper explores a novel approach aimed at overcoming existing challenges in the realm of local search algorithms. Our aim is to improve the decision process that takes place within a local search algorithm so as to make the best possible transitions in the neighborhood at each iteration. To improve this process, we propose to use a neural network that has the same input information as conventional local search algorithms. In this paper, which is an extension of the work presented at EvoCOP2024, we investigate different ways of representing this information so as to make the algorithm as efficient as possible but also robust to monotonic transformations of the problem objective function. To assess the efficiency of this approach, we develop an experimental setup centered around NK landscape problems, offering the flexibility to adjust problem size and ruggedness. This approach offers a promising avenue for the emergence of new local search algorithms and the improvement of their problem-solving capabilities for black-box problems. The last version of this article is published in the journal SN Computer Science (Springer).

Discovering new robust local search algorithms with neuro-evolution

TL;DR

The paper tackles the challenge of designing effective local search moves for discrete optimization by learning a neural policy that operates on the same input as classic local search. It frames local search as a memoryless episodic process and trains a neural network policy (Neuro-LS) with CMA-ES on NK landscapes across varied sizes and ruggedness . Four observation schemes are compared, with ranking-based inputs ( or ) yielding the strongest and most robust strategies, including a two-mode behavior in rugged landscapes (small steps followed by a worst-improvement jump). The learned Neuro-LS policies outperform baseline deterministic LS (Best/First improvement and -ES) on NK ensembles and show robustness in out-of-distribution tests to QUBO risks, highlighting the potential to auto-discover robust local search heuristics for black-box combinatorial optimization.

Abstract

This paper explores a novel approach aimed at overcoming existing challenges in the realm of local search algorithms. Our aim is to improve the decision process that takes place within a local search algorithm so as to make the best possible transitions in the neighborhood at each iteration. To improve this process, we propose to use a neural network that has the same input information as conventional local search algorithms. In this paper, which is an extension of the work presented at EvoCOP2024, we investigate different ways of representing this information so as to make the algorithm as efficient as possible but also robust to monotonic transformations of the problem objective function. To assess the efficiency of this approach, we develop an experimental setup centered around NK landscape problems, offering the flexibility to adjust problem size and ruggedness. This approach offers a promising avenue for the emergence of new local search algorithms and the improvement of their problem-solving capabilities for black-box problems. The last version of this article is published in the journal SN Computer Science (Springer).
Paper Structure (29 sections, 2 equations, 12 figures, 3 tables)

This paper contains 29 sections, 2 equations, 12 figures, 3 tables.

Table of Contents

  1. Introduction
  2. General framework
  3. Pseudo-Boolean Optimization Problems and Local Search
  4. Local Search as an Episodic Task Process
  5. States
  6. Observations
  7. Deterministic policy and actions
  8. Transitions and trajectory
  9. Reward
  10. Policy Learning for a Set of Instances
  11. Deterministic local search policies for pseudo-Boolean optimization
  12. Neural network local search policy
  13. Basic local search policies
  14. Best improvement hill climber [+jump] (${\rm BHC}^{+}$).
  15. First improvement hill climber [+jump] (${\rm FHC}^{+}$).
  16. ...and 14 more sections

Figures (12)

  • Figure 1: Global View of the Process.
  • Figure 2: Neuro-LS policy .
  • Figure 3: Evolution of the average score on the validation set for NK instances with $N = 64$ and $K=8$ over the generations of CMA-ES obtained by Neuro-LS with the four different observation matrices as input.
  • Figure 4: Fitness evolution curve and strategy used by Neuro-LS using $o^1$ observations for the resolution of an instance with smooth NK landscape ($N=64$ and $K=2$).
  • Figure 5: Fitness evolution curve and strategy used by Neuro-LS using $o^3$ observations for the resolution of an instance with significantly rugged NK landscape ($N=64$ and $K=8$).
  • ...and 7 more figures