QUASAR: An Evolutionary Algorithm to Accelerate High-Dimensional Optimization
Julian Soltes
TL;DR
QUASAR tackles the challenge of high-dimensional optimization by extending Differential Evolution with a quasi-adaptive, stochastic framework that uses three mutation strategies, a rank-based binomial crossover, and an asymptotically decaying covariance-guided reinitialization. Its Sobol-based initial population, dynamic mutation selection, and covariance-informed reinitialization enable robust exploration and exploitation, achieving substantial improvements on the CEC2017 benchmark with a Friedman rank sum of 150 versus 229 for L-SHADE and 305 for DE, and producing significant speedups in run times. The method demonstrates strong, statistically supported gains across dimension and population-size regimes, with GMERF values up to 18.5× and p-values well below 0.001 in many comparisons, highlighting both quality and efficiency benefits. QUASAR is released as an open-source package (hdim-opt) with minimal user effort required, making it a practical choice for non-differentiable, high-dimensional optimization tasks and setting a foundation for future self-adaptive enhancements and broader verification. The work underscores covariance-guided reinitialization as a powerful mechanism to inject high-quality diversity and sustain search progress in large-scale spaces.
Abstract
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.