hdim-opt: High-Dimensional Optimization Toolkit
Numerical optimization package to accelerate convergence in complex, high-dimensional problems. Includes the QUASAR evolutionary algorithm, HDS QMC sampler, Sobol sensitivity analysis, data analysis / transformations, signal waveform decomposition.
All core functions, listed below, are single-line executable and require three essential parameters: [obj_function, bounds, n_samples]:
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quasar: QUASAR optimization for high-dimensional problems.
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hyperellipsoid: Generate a non-uniform hyperellipsoid density sequence.
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uniform: Generate uniform QMC sample distributions (via Scipy.stats.qmc).
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isotropize/deisotropize: Isotropize the input data using zero-phase component analysis (ZCA).
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sensitivity: Sensitivity analysis to quantify each variable's influence on the objective (via SALib).
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analyze: Numerically analyze any given dataset.
-
lorentzian: Fit a Lorentzian/Cauchy kernel density estimation to the data.
-
waveform: Decompose the input waveform signal array into a diagnostic summary.
Installation
Installed via hdim_opt directly from PyPI:
pip install hdim_opt
Example Usage:
import hdim_opt as h
# Parameter Space
n_dimensions = 30
n_samples = 1000
bounds = [(-100,100)] * n_dimensions
obj_func = h.test_functions.rastrigin # Test function
# Sampling
ellipsoid_samples = h.hyperellipsoid(n_samples, bounds, verbose=True) # Hyperellipsoid sampling
uniform_samples = h.uniform(n_samples, bounds, method='sobol') # Uniform sampling
iso_samples, iso_params = h.isotropize(ellipsoid_samples) # Isotropize dataset
h.analyze(ellipsoid_samples) # Analyze any dataset
# Optimization
solution, fitness = h.quasar(obj_func, bounds, init=ellipsoid_samples) # Evolutionary optimization
local_sol, local_fit = h.minimize(obj_func, bounds, init=solution) # Local minimization
Si, S2 = h.sensitivity(obj_func, bounds) # Sensitivity analysis
kde = h.lorentzian(solution, sigma=150.0, ensemble=ellipsoid_samples, verbose=True) # Lorentzian KDE
# Waveforms
t, signal = h.waveform_analysis.e1_waveform(noise=0.1) # Waveform generation
summary = h.waveform(t,signal) # Waveform analysis
QUASAR Optimizer
QUASAR (Quasi-Adaptive Search with Asymptotic Reinitialization) is a quantum-inspired evolutionary algorithm, highly efficient for minimizing high-dimensional, non-differentiable, and non-parametric objective functions.
- Benefit: Significant improvements in convergence speed and solution quality compared to contemporary optimizers. (Reference: [https://arxiv.org/abs/2511.13843]).
HDS Sampler
HDS (Hyperellipsoid Density Sampling) is a non-uniform Quasi-Monte Carlo sampling method, specifically designed to exploit promising regions of the search space.
- Benefit: Provides control over the sample distribution. Results in higher average optimization solution quality when used for population initialization compared to uniform QMC methods. (Reference: [https://arxiv.org/abs/2511.07836]).
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