hdim-opt 1.3.2

High-dimensional numerical optimization and sampling toolkit for complex, non-differentiable problems.

hdim-opt: High-Dimensional Optimization Toolkit

Modern optimization package to accelerate convergence in complex, high-dimensional problems. Includes the QUASAR evolutionary algorithm, HDS exploitative QMC sampler, Sobol sensitivity analysis, signal waveform decomposition, and data transformations.

All core functions, listed below, are single-line executable and require three essential parameters: [obj_function, bounds, n_samples].

• quasar: QUASAR optimization for high-dimensional, non-differentiable problems.
• hyperellipsoid: Generate a non-uniform Hyperellipsoid Density sequence, to focus sample distributions.
• sobol: Generate a uniform Sobol sequence (via SciPy).
• sensitivity: Perform Sobol sensitivity analysis to measure each variable's importance on objective function results (via SALib).
• isotropize: Isotropizes the input matrix.
• waveform: Decompose the input waveform array (handles time- and frequency-domain via FFT / IFFT) 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
bounds = [(-100,100)] * n_dimensions
n_samples = 1000
obj_func = h.test_functions.rastrigin
time, pulse = h.waveform_analysis.e1_waveform()

# Functions
solution, fitness = h.quasar(obj_func, bounds)
sens_matrix = h.sensitivity(obj_func, bounds)

hds_samples = h.hyperellipsoid(n_samples, bounds)
sobol_samples = h.sobol(n_samples, bounds)
isotropic_samples = h.isotropize(sobol_samples)

signal_data = h.waveform(x=time,y=pulse)

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]).