QUASAR: An Evolutionary Algorithm to Accelerate High-Dimensional Optimization

High-dimensional numerical optimization presents a persistent challenge. This paper introduces Quasi-Adaptive Search with Asymptotic Reinitialization (QUASAR), an evolutionary algorithm to accelerate convergence in complex, non-differentiable problems afflicted by the curse of dimensionality. Evaluated on the notoriously difficult CEC2017 benchmark suite of 29 functions, QUASAR achieved the lowest overall rank sum (150) using the Friedman test, significantly outperforming L-SHADE (229) and standard DE (305) in the dimension-variant trials. QUASAR also proves computationally efficient, with run times averaging $1.4 \text{x}$ faster than DE and $7.8 \text{x}$ faster than L-SHADE ($p \ll 0.001$) in the population-variant trials. Building upon Differential Evolution (DE), QUASAR introduces a highly stochastic architecture to dynamically balance exploration and exploitation. Inspired by the probabilistic behavior of quantum particles in a stellar core, the algorithm implements three primary components that augment standard DE mechanisms: 1) probabilistically selected mutation strategies and scaling factors; 2) rank-based crossover rates; 3) asymptotically decaying reinitialization that leverages a covariance matrix of the best solutions to introduce high-quality genetic diversity. QUASAR's performance establishes it as an effective, user-friendly optimizer for complex high-dimensional problems.

Hyperellipsoid Density Sampling: Exploitative Sequences to Accelerate High-Dimensional Optimization

The curse of dimensionality presents a pervasive challenge in optimization problems, with exponential expansion of the search space rapidly causing traditional algorithms to become inefficient or infeasible. An adaptive sampling strategy is presented to accelerate optimization in this domain as an alternative to uniform quasi-Monte Carlo (QMC) methods. This method, referred to as Hyperellipsoid Density Sampling (HDS), generates its sequences by defining multiple hyperellipsoids throughout the search space. HDS uses three types of unsupervised learning algorithms to circumvent high-dimensional geometric calculations, producing an intelligent, non-uniform sample sequence that exploits statistically promising regions of the parameter space and improves final solution quality in high-dimensional optimization problems. A key feature of the method is optional Gaussian weights, which may be provided to influence the sample distribution towards known locations of interest. This capability makes HDS versatile for applications beyond optimization, providing a focused, denser sample distribution where models need to concentrate their efforts on specific, non-uniform regions of the parameter space. The method was evaluated against Sobol, a standard QMC method, using differential evolution (DE) on the 29 CEC2017 benchmark test functions. The results show statistically significant improvements in solution geometric mean error (p < 0.05), with average performance gains ranging from 3% in 30D to 37% in 10D. This paper demonstrates the efficacy of HDS as a robust alternative to QMC sampling for high-dimensional optimization.