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Loop-Extrusion Linkage: Spectral Ordering and Interval-Based Structure Discovery for Continuous Optimization

Eren Unlu

Abstract

The rapid growth of nature-inspired metaheuristics has exposed a persistent gap between metaphorical novelty and genuine algorithmic advancement. Motivated by the biophysics of chromatin loop extrusion -- a well-characterized genome-folding process driven by SMC motor complexes and conditional barriers -- we introduce the Loop-Extrusion Linkage (LEL) operator, a structure-learning wrapper that combines online variable-interaction estimation, spectral seriation via the Fiedler vector, and adaptive interval-based subspace search. LEL constructs a sparse interaction graph from successful optimization steps, derives a heuristic one-dimensional variable ordering, and generates overlapping evaluation subsets through stochastic interval growth modulated by learned boundary-crossing probabilities. We evaluate LEL on six synthetic diagnostic functions at d=96 designed to probe specific structural hypotheses -- contiguous blocks, permuted blocks, overlapping windows, banded chains, separable controls, and dense rotated couplings -- across 10^4 and 5 x 10^4 evaluation budgets with 15 independent seeds. Results are assessed via the Wilcoxon signed-rank test with Holm-Bonferroni correction and Vargha-Delaney A12 effect sizes. At 10^4 evaluations, Full LEL achieves the best median log-gap on 3 of 6 functions significantly outperforming all ablations and jSO on the structured tasks. At 5 x 10^4 evaluations, simpler ablations and baselines often surpass the full method, indicating that the adaptive barrier mechanism may over-constrain late-stage search on uniformly partitioned landscapes. The strongest supported finding is that learned spectral ordering consistently improves over graph-only grouping and random variable ordering, suggesting that interaction-graph seriation is the most valuable component of the proposed framework.

Loop-Extrusion Linkage: Spectral Ordering and Interval-Based Structure Discovery for Continuous Optimization

Abstract

The rapid growth of nature-inspired metaheuristics has exposed a persistent gap between metaphorical novelty and genuine algorithmic advancement. Motivated by the biophysics of chromatin loop extrusion -- a well-characterized genome-folding process driven by SMC motor complexes and conditional barriers -- we introduce the Loop-Extrusion Linkage (LEL) operator, a structure-learning wrapper that combines online variable-interaction estimation, spectral seriation via the Fiedler vector, and adaptive interval-based subspace search. LEL constructs a sparse interaction graph from successful optimization steps, derives a heuristic one-dimensional variable ordering, and generates overlapping evaluation subsets through stochastic interval growth modulated by learned boundary-crossing probabilities. We evaluate LEL on six synthetic diagnostic functions at d=96 designed to probe specific structural hypotheses -- contiguous blocks, permuted blocks, overlapping windows, banded chains, separable controls, and dense rotated couplings -- across 10^4 and 5 x 10^4 evaluation budgets with 15 independent seeds. Results are assessed via the Wilcoxon signed-rank test with Holm-Bonferroni correction and Vargha-Delaney A12 effect sizes. At 10^4 evaluations, Full LEL achieves the best median log-gap on 3 of 6 functions significantly outperforming all ablations and jSO on the structured tasks. At 5 x 10^4 evaluations, simpler ablations and baselines often surpass the full method, indicating that the adaptive barrier mechanism may over-constrain late-stage search on uniformly partitioned landscapes. The strongest supported finding is that learned spectral ordering consistently improves over graph-only grouping and random variable ordering, suggesting that interaction-graph seriation is the most valuable component of the proposed framework.

Paper Structure

This paper contains 27 sections, 9 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Metaheuristic Design and Evaluation Standards
  4. Linkage Learning and Variable Grouping
  5. Spectral Seriation
  6. Biological Substrate: Chromatin Loop Extrusion
  7. Algorithm Design: Loop-Extrusion Linkage
  8. Phase 1: Interaction Graph Estimation
  9. Phase 2: Spectral Variable Ordering
  10. Phase 3: Adaptive Barrier Learning
  11. Phase 4: Stochastic Interval Extrusion
  12. Phase 5: Blockwise Variation (Base Evaluator)
  13. Computational Complexity
  14. Experimental Evaluation
  15. Synthetic Diagnostic Functions
  16. ...and 12 more sections

Figures (2)

  • Figure 1: Final log-gap distributions at $10^4$ evaluations. Full LEL achieves the best median on S2, S3, and S6, and is competitive on S5. On S1 and S4, DG2+CC achieves the best median.
  • Figure 2: Final log-gap distributions at $5 \cdot 10^4$ evaluations. With additional budget, simpler ablations (A3, A5) and baselines (DG2+CC, jSO) often surpass Full LEL, suggesting that the adaptive barrier mechanism may over-constrain late-stage search.