hdim-opt: High-Dimensional Optimization Toolkit
Numerical optimization package for complex, high-dimensional problems. hdim_opt is a lightweight and comprehensive suite to streamline sampling, optimization, and analysis. Home of the QUASAR evolutionary algorithm and Hyperellipsoid quasi-Monte Carlo sampling.
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.
- lorentzian: Fit a Lorentzian/Cauchy kernel density estimation (KDE) to the data.
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).
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 directly from PyPI:
pip install hdim_opt
Example Usage
import hdim_opt as h
### Parameter Space
n_samples = 2**10
n_dimensions = 10
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
kde = h.lorentzian(iso_samples, 1.0, iso_samples, verbose=True) # Lorentzian multivariate KDE
### 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 linear/logistic regression
### Analysis
Si, S2 = h.sensitivity(obj_func, bounds) # Sensitivity analysis
slice_data, stats = h.hyperslice(obj_func, bounds, slice_dims=(0,1)) # Estimate/hyperslice the solution space
signal_results = h.waveform(uniform_samples[:,0], slice_data.iloc[:,1]) # Analyze 2D waveform
h.analyze(slice_data) # Analyze any numerical dataset
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 for high-dimensional spaces compared to standard optimization algorithms like Differential Evolution and L-SHADE. (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 parameter space.
- Benefit: Provides control over high-dimensional sample distributions. Results in higher average solution quality when initializing optimization. (Reference: [https://arxiv.org/abs/2511.07836]).
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