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

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.

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