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.
Figures & tables
Figure 1: Final log-gap distributions at 104 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⋅104 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.
Function
Algorithm
Med LogGap
IQR
A^12 vs LEL
p -value
S1: Sep. Sphere
DG2_CC
-2.0627
0.6948
0.00
<0.001 ***
Full_LEL
0.0532
0.1642
-
-
jSO
1.6662
0.0811
1.00
<0.001 ***
S2: Contig. Rosen.
A1_GraphOnly
3.4968
0.1330
1.00
<0.001 ***
A2_RandomOrder
2.8895
0.1817
0.99
<0.001 ***
A3_NoBarriers
3.2311
0.0581
1.00
<0.001 ***
Table 1: Synthetic benchmark results ( 104 evaluations). Metric: final log-gap (lower is better). Best median per function in bold . Significance stars: *** p<0.001 , ** p<0.01 , * p<0.05 (Wilcoxon signed-rank vs. Full_LEL, Holm–Bonferroni corrected). A^12 : probability that the row algorithm produces a worse log-gap than Full LEL.
Function
Algorithm
Med LogGap
IQR
A^12 vs LEL
p -value
S1: Sep. Sphere
DG2_CC
-7.3724
1.9388
0.00
<0.001 ***
Full_LEL
-0.4979
0.0959
-
-
jSO
-0.4425
0.1165
0.62
0.679
S2: Contig. Rosen.
A1_GraphOnly
3.4868
0.1309
1.00
<0.001 ***
A2_RandomOrder
2.8240
0.1709
1.00
<0.001 ***
A3_NoBarriers
1.8876
0.0442
0.00
<0.001 ***
Table 2: Synthetic benchmark results ( 5⋅104 evaluations). Metric: final log-gap (lower is better). Best median per function in bold . Significance stars: *** p<0.001 , ** p<0.01 , * p<0.05 (Wilcoxon signed-rank vs. Full_LEL, Holm–Bonferroni corrected). A^12 : probability that the row algorithm produces a worse log-gap than Full LEL.
Continuous optimisation methods need to balance sharing information and maintaining alternative search directions. In this paper, we introduce Mycelial Search (Myco), a graph-structured metaheuristic designed around active tips, community-weighted flow, adaptive cord plasticity, and anchor-based injection. Candidate solutions form an evolving spatial graph in which a Louvain partition distinguishes within-community from cross-community information exchange. Adaptive cord plasticity subsequently modifies active tip-to-tip edges according to their alignment with the local flow. An anchor-based injection mechanism supplements the graph-driven tip dynamics. We evaluated Myco on the CEC 2022 single-objective bound-constrained benchmark suite at dimensions D=10 and D=20, using 30 independent runs per algorithm-function pair. The comparison includes eleven established optimisers from several search families. Myco reaches competitive results on selected functions across both dimensions. The ablation analysis further shows that community structure regulates the range of graph-based information exchange, whereas cord plasticity controls the persistence of local directional influence. These findings indicate that graph-structured local interaction can support continuous optimisation, while its effectiveness depends on landscape structure and information transfer across local search regions.
Permutation optimization arises whenever the components of a system are fixed but their ordering affects performance. We introduce PRISM, a predictive protocol for permutation optimization that measures a fitness landscape before selecting a search strategy. PRISM uses inexpensive landscape diagnostics, including one-step move autocorrelation and fitness-distance correlation, to predict useful mutation operators, identify when structured search is likely to outperform random sampling, and detect regimes in which search provides little advantage. Across synthetic permutation landscapes, neural architecture benchmarks, scientific machine learning pipelines, and large-language-model instruction ordering, the protocol makes testable predictions about search behavior before optimization begins. Exhaustive instruction-ordering experiments reveal substantial performance variation induced solely by permutation, while cross-model experiments show that useful ordering structure can transfer across model families and task difficulty. Additional experiments demonstrate that instruction ordering remains consequential after prompt wording is optimized, indicating that content optimization and ordering optimization are complementary. The results position PRISM not as a universally superior optimizer, but as a framework for determining when permutation search is useful, which representation and operator should be used, and when simpler alternatives are preferable.
In evolutionary algorithms powered by language models, the LLM acts as a single operator that simultaneously updates structural components (like control flow) and continuous parameters. While LLMs can be good at the first, they are not efficient at the second, wasting tokens taking discrete jumps inside a trial and error loop. We resolve this by formalizing a hybrid nested search, in which an outer loop has the LLM propose a structural sketch, with numeric gaps, and an inner numerical optimizer tunes the sketch. Both the outer and inner solvers are pluggable: any text-based optimizer can be combined with a zero-order optimizer (CMA-ES), gradient-based routines, or MCMC samplers. We validate our framework across three scientific domains: (i) meta-optimizers on closed-form test functions, (ii) code-based policies for systems research and social dilemmas; and (iii) approximate Bayesian inference tasks. Across all three, the hybrid optimizer is superior to both vanilla LLM-driven search and pure numerical optimization baselines. Code at: https://github.com/vicgalle/hybrid-nested-search