SKROA — Sympodial Kawayan Rhizome Optimization Algorithm

KRNA (krna on PyPI) is a gradient-free, swarm-style framework for continuous optimization, inspired by the growth habit of running bamboo (kawayan): a biphasic strategy that alternates between wide exploration (rhizome creep via Lévy flights) and focused exploitation (vertical shoot, guided by finite-difference gradients), with two additional operators:

• Sympodial Clamping — agents that crowd together repel each other, which keeps the swarm spread out and delays premature convergence.
• Culm-Abortion — exploiting agents that stop improving for several consecutive steps are pruned and respawned near the current best, freeing their search budget.

The package also ships a multi-objective variant (MO-SKROA) that maps Pareto fronts of the ZDT suite, a baseline PSO for comparison, benchmark landscapes (Rastrigin, Ackley, Rosenbrock), a sensitivity-sweep harness, and a hyperparameter tuner for scikit-learn estimators.

Installation

pip install krna

Core features need only NumPy. Plotting (benchmark/sensitivity harnesses) adds Matplotlib, and the ML tuner adds scikit-learn:

pip install "krna[plots]"   # + matplotlib
pip install "krna[ml]"      # + scikit-learn (implies plots)

Quick start

import numpy as np
from krna import SKROA
from krna.benchmarks import rastrigin

optimizer = SKROA(
    evaluator=rastrigin,       # maps (N, D) candidate matrix -> (N,) fitness
    bounds=(-5.12, 5.12),      # same box bounds on every dimension
    dim=10,
    n_agents=50,
    max_iters=500,
    seed=42,                   # fully reproducible runs
)
result = optimizer.optimize()

print("best fitness :", result["g_best_fit"])
print("best position:", result["g_best_pos"])
# result["convergence_curve"] is a per-iteration history of the best fitness

Your evaluator receives a (n_agents, dim) float array and must return a (n_agents,) array of fitness values to minimize. Batch evaluation like this keeps the whole swarm vectorized — don't loop over agents in Python if your objective can be written with NumPy.

Hyperparameters

Parameter	Default	Role
n_agents	50	swarm size
max_iters	1000	iteration budget
delta_threshold	None	fitness cutoff for the exploit state; None uses the swarm median (keeps ~50% exploiting)
tau_stagnation	1e-4	minimum per-step improvement before an exploiting agent counts as stalled
max_stagnation_steps	10	stalled steps tolerated before Culm-Abortion respawns the agent
epsilon_clamp	1e-2	repulsion distance for Sympodial Clamping
gamma_lr	0.05	gradient-step learning rate (relative to the domain span)
levy_scale	0.01	Lévy-flight step scale (relative to the domain span)
sigma_jitter	1e-4	Gaussian jitter added to gradient steps
seed	42	RNG seed for reproducibility

Multi-objective optimization

from krna import MOSKROA
from krna.mo_benchmarks import ZDT1_BENCHMARK

opt = MOSKROA(evaluator=ZDT1_BENCHMARK.evaluator, bounds=(0.0, 1.0), dim=30)
res = opt.optimize()  # res["pareto_front_fitness"] -> (A, 2) objective matrix

MO-SKROA maintains a non-dominated archive; exploiting agents descend along randomly scalarized gradients so different agents cover different regions of the front.

Hyperparameter tuning for scikit-learn models

from sklearn.svm import SVC
from sklearn.datasets import load_breast_cancer
from krna.ml_tuning import SKROAMLTuner

data = load_breast_cancer()
space = {
    "C":     {"type": "log_float", "min": 1e-3, "max": 1e3},
    "gamma": {"type": "log_float", "min": 1e-4, "max": 1e1},
    "kernel": {"type": "categorical", "values": ["linear", "rbf", "sigmoid"]},
}
tuner = SKROAMLTuner(model_class=SVC, param_space=space,
                     X=data.data, y=data.target, seed=101)
print(tuner.tune())

Supported parameter types: int, float, log_float, categorical.

Tuning a random forest

The same interface works for any scikit-learn estimator — the tuner detects automatically whether the model accepts a random_state argument. Here is a RandomForestClassifier on the same dataset, mixing integer, log-scaled and categorical hyperparameters in one search space:

from sklearn.ensemble import RandomForestClassifier
from sklearn.datasets import load_breast_cancer
from krna.ml_tuning import SKROAMLTuner

data = load_breast_cancer()
space = {
    "n_estimators": {"type": "int", "min": 25, "max": 400},
    "max_depth":    {"type": "int", "min": 2, "max": 20},
    "max_features": {"type": "categorical", "values": ["sqrt", "log2"]},
    "min_samples_leaf": {"type": "log_float", "min": 1e-3, "max": 0.3},
}

tuner = SKROAMLTuner(model_class=RandomForestClassifier, param_space=space,
                     X=data.data, y=data.target, cv_folds=5,
                     n_agents=20, max_iters=30, seed=101)
result = tuner.tune()
print(result["best_hyperparams"])         # decoded hyperparameter dict
print(f"CV accuracy: {result['best_accuracy_percent']:.2f}%")

Continuous coordinates are decoded with a log scale for log_float parameters, so the swarm explores min_samples_leaf between 1e-3 and 0.3 evenly across orders of magnitude — the same trick RandomizedSearchCV uses. Candidate models are cross-validated in parallel (n_jobs=-1); invalid combinations score worst instead of crashing the run.

Command line

krna benchmark      # SKROA vs PSO on Rastrigin/Ackley/Rosenbrock, CSV + plots
krna tune           # SKROA hyperparameter search on an SVM (breast cancer)
krna mo-benchmark   # MO-SKROA on ZDT1/ZDT2 Pareto fronts

Outputs land in results/logs/ (CSV telemetry) and results/plots/ (convergence curves, 3D surfaces, Pareto fronts, sensitivity heatmaps).

Benchmark results

Full head-to-head run of krna benchmark --trials 30: SKROA vs. baseline PSO on three classical landscapes — 30 independent trials per algorithm per landscape (seeds 1000–1029), D=10, 50 agents, 500 iterations, identical budgets and seeds for both algorithms. Statistics are two-sided Wilcoxon rank-sum tests with Cohen's r effect size (krna.stats), reported exactly as the suite prints them.

Landscape	SKROA best fitness (mean ± std)	PSO best fitness (mean ± std)	Wilcoxon p	Effect size r	Verdict (α=0.05)
Rastrigin	14.196 ± 3.012	7.368 ± 2.966	5.97e-09	0.75	PSO significantly better
Ackley	3.598 ± 0.257	1.3e-07 ± 1.2e-07	3.02e-11	0.86	PSO significantly better
Rosenbrock	1855.12 ± 839.79	4.381 ± 1.983	3.02e-11	0.86	PSO significantly better

Reading the table honestly:

• The baseline PSO wins on all three landscapes at this 500-iteration budget, and it also reaches a comparable fitness in roughly 1/6 of the wall-clock time (~0.4 s vs ~2.2 s per run). SKROA spends most of its budget on exploration, so with equal iteration counts it converges more slowly on these unimodal/mildly multimodal 10-D problems.
• Both comparisons share one subtlety of any iteration-matched benchmark: per iteration, SKROA's finite-difference gradient probes cost extra function evaluations that PSO does not pay. That is the standard iteration-budget convention, but evaluation-matched comparisons may narrow the gap.
• The p-values and large effect sizes say the differences are real, not noise — which is exactly why we report them rather than cherry-picking a favorable setting. We publish the suite's output as-is and treat the gap as a target for parameter tuning (see krna sensitivity harness) rather than a headline.

Reproduce with:

krna benchmark --trials 30          # ~5 min on a laptop; CSV + plots in results/

Raw telemetry for this table: results/logs/benchmark_metrics.csv.

Ablation studies and stronger opponents

Every SKROA operator can be switched off at construction (use_biphasic, use_clamping, use_culm_abortion), and krna ablation --trials 30 runs the full study — full SKROA vs. each crippled variant on every landscape, seeded identically, tested with the same Wilcoxon machinery (results/logs/ablation_metrics.csv). How the algorithm works under the hood: algorithms/SKROA.md.

The benchmark suite can also field SciPy Differential Evolution and CMA-ES (install pip install scipy cma) alongside PSO:

krna benchmark --trials 30   # SKROA vs PSO + SciPy-DE + CMA-ES (when installed)

Each opponent's CSV row carries its mean evaluation count, so iteration-budget and evaluation-budget readings are both possible.

Statistical significance testing

Comparing two metaheuristics by eyeballing mean fitness is not publishable — differences can be noise. The benchmark suite therefore reports, for every landscape, a two-sided Wilcoxon rank-sum test (Mann-Whitney U) between the SKROA and PSO final best-fitness samples, with tie correction and continuity correction, plus Cohen's r effect size. Both are implemented in krna.stats with NumPy only and are cross-checked against scipy.stats.mannwhitneyu in the test suite.

Each benchmark_metrics.csv row for PSO carries P_Value_RankSum, Effect_Size_r, and a plain-language Statistical_Verdict; the console prints a [STATS] line per landscape. Use at least 30 independent runs (--trials 30) for stable estimates.

You can also test your own samples:

from krna import wilcoxon_rank_sum, cohens_r, bonferroni_correct

result = wilcoxon_rank_sum(fitness_a, fitness_b)  # >= 8 runs per sample
print(result.u_statistic, result.p_value, result.is_significant)
print("effect size r =", cohens_r(fitness_a, fitness_b))
adjusted = bonferroni_correct([result.p_value, 0.02])  # family-wise control

For multi-problem studies, adjust for multiple comparisons (Bonferroni is provided; Holm or Friedman + Imany–Davenport are common stronger choices).

Methodology and reproducibility

• Minimization everywhere. Evaluators map an (n_agents, dim) array of candidate positions to an (n_agents,) array of fitness values; lower is better.
• Seeded runs. All stochastic operators draw from a NumPy Generator seeded at construction. Two runs with the same seed produce bit-identical convergence curves (verified by test).
• Bounds are a hard contract. No point is ever handed to your evaluator outside [low, high] — gradient probes fold inward at boundaries (krna.gradient).
• Exploration/exploitation split. Agents below the fitness threshold (default: the swarm median, delta_threshold=None) exploit via finite-difference gradient descent; the rest explore via Lévy flights. Stalled exploiting agents are respawned near the best solution after max_stagnation_steps non-improving iterations (Culm-Abortion).
• Fair benchmarking. SKROA and PSO receive identical iteration budgets, swarm sizes, seeds, and evaluation functions per trial.

Running the tests

python -m unittest discover -s tests -v

Contributing

See CONTRIBUTING.md for development setup, ground rules, and pull-request checks. Notable changes are recorded in CHANGELOG.md.

License

MIT — see LICENSE.