hdim-opt: High-Dimensional Optimization Toolkit
Numerical optimization package for complex, high-dimensional problems. Includes the QUASAR evolutionary algorithm, Hyperellipsoid QMC sampling, and several useful functions streamlined from existing libraries.
All core functions, listed below, are single-line executable and depend on three essential parameters: [obj_function, bounds, n_samples]:
Sampling
- hyperellipsoid: Generate hyperellipsoidal sample sequence; may accelerate optimization.
- uniform: Generate uniform QMC sample sequences (via Scipy.stats.qmc).
- isotropize: Isotropize the input data via zero-phase component analysis (ZCA).
- lorentzian: Fit a Lorentzian/Cauchy kernel density estimation 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).
Analysis
- sensitivity: Sensitivity analysis to quantify each dimension's influence (via SALib).
- hyperslice: Generate a 1D or 2D hyperslice of a function's underlying solution space.
- waveform: Decompose an input signal waveform.
- analyze: Numerically analyze any given 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
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 data
kde = h.lorentzian(iso_samples, 150.0, 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
### Analysis
Si, S2 = h.sensitivity(obj_func, bounds) # Sensitivity analysis
slice_data, stats = h.hyperslice(obj_func, bounds, slice_dims=()) # Hyperslice of the solution space
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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