QUASAR: An Evolutionary Algorithm to Accelerate High-Dimensional Optimization
It addresses the curse of dimensionality for researchers and practitioners in optimization, offering an incremental improvement over existing methods like Differential Evolution.
This paper tackles the challenge of high-dimensional numerical optimization by introducing QUASAR, an evolutionary algorithm that accelerates convergence in complex, non-differentiable problems, achieving the lowest overall rank sum (150) on the CEC2017 benchmark and running 1.4x faster than standard DE and 7.8x faster than L-SHADE.
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.