hdim-opt: High-Dimensional Optimization Toolkit
hdim_opt is a lightweight and comprehensive Python toolkit to streamline numerical optimization, sampling, and analysis of high-dimensional function landscapes and datasets. Several cohesive methods are provided for random & quasi-Monte Carlo sampling, gradient-based & non-parametric optimization, statistical analyses & visualizations of function landscapes & datasets.
All core functions, listed below, are single-line executable and depend on three essential parameters: [obj_function, bounds, n_samples]:
Sampling
- uniform: Generate uniform QMC sample sequences (via Scipy.stats.qmc).
- hyperellipsoid: Generate hyperellipsoidal sample sequence; may accelerate optimization.
- isotropize: Isotropize the input data via zero-phase component analysis (ZCA).
- encode_bipolar: Bipolar-logarithmic transform, when negative values and exponents are present.
Optimization
- quasar: Optimization using the QUASAR evolutionary algorithm.
- minimize: Optimization using gradient-based minimization (via SciPy.minimize).
- symbolic: Symbolic regression to approximate the input data or function (via gplearn).
- stepAIC: Stepwise feature selection for linear or logistic regression (R's MASS:stepAIC).
Risk
- volatility: Quantifies the volatility of a given solution within its local landscape.
- risk_analysis: Analyzes the conditional value at risk for a given 1-D distribution.
Analysis
- sensitivity: Sensitivity analysis to quantify each dimension's influence (via SALib).
- hyperslice: Create a hyperslice of the function's underlying solution space.
- waveform: Decompose any 2D waveform.
- analyze: Analyze any input dataset.
Installation
Install hdim_opt from PyPI:
pip install hdim_opt
Example Usage
import hdim_opt as h
### Parameter Space
n_samples = 2**10
n_dimensions = 100
bounds = [(-100,100)] * n_dimensions # Parameter bounds
obj_func = h.test_functions.rastrigin # Test function
### Sampling
uniform_samples = h.uniform(n_samples, bounds, method='sobol') # Uniform sampling
ellipsoid_samples = h.hyperellipsoid(n_samples, bounds, verbose=True) # Hyperellipsoid sampling
iso_samples, iso_params = h.isotropize(ellipsoid_samples) # Isotropize data (ZCA)
bipolar_log_samples = h.encode_bipolar(iso_samples, [b[0] for b in bounds]) # Bipolar-logarithm transform
### Optimization
solution, fitness = h.quasar(obj_func, bounds, init=ellipsoid_samples) # Evolutionary optimization
local_sol, local_fit = h.minimize(obj_func, bounds, init=solution) # Gradient-based optimization
all_expr, best_expr = h.symbolic(obj_func, bounds) # Symbolic regression
opt_features, opt_model = h.stepAIC(iso_samples, solution) # R's stepAIC for feature selection & linear regression
### Risk
vol_data, vol_stats = h.volatility(obj_func, bounds, solution, noise=0.01) # Local instability of a solution
risk_stats = h.risk_analysis(vol_data['objective']) # Conditional value at risk for a 1-D distribution
### Analysis
Si, S2 = h.sensitivity(obj_func, bounds) # Sensitivity analysis
slice_data, slice_stats = h.hyperslice(obj_func, bounds, slice_dims=(0,1), n_samples=2**7) # Estimate solution space
signal_results = h.waveform(slice_data['x0'], slice_data['objective']) # Analyze 2D waveform
h.analyze(slice_data) # Analyze any numerical dataset
Issues & Support
Bug reports are highly appreciated and will be handled timely.
QUASAR Optimization
Quasi-Adaptive Search with Asymptotic Reinitialization is an evolutionary algorithm highly efficient for minimizing high-dimensional, non-differentiable, and non-parametric objective functions. ([https://arxiv.org/abs/2511.13843]).
Hyperellipsoid Sampling
Hyperellipsoid Density Sampling is a non-uniform Quasi-Monte Carlo sampling method, designed to exploit promising regions of the parameter space ([https://arxiv.org/abs/2511.07836]).
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Release files for hdim-opt 1.7.0
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