High-dimensional numerical optimization presents a persistent challenge in computational science. 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. QUASAR expands upon the core principles of Differential Evolution (DE), introducing quasi-adaptive mechanisms to dynamically balance exploration and exploitation in its search. Inspired by the behavior of quantum particles, the algorithm utilizes three highly stochastic mechanisms that augment standard DE: 1) probabilistic mutation strategies and scaling factors; 2) rank-based crossover rates; 3) asymptotically decaying covariance reinitializations. Evaluated on the notoriously difficult CEC2017 benchmark suite of 29 test functions, QUASAR achieved the lowest overall rank sum (367) using the Friedman test, outperforming DE (735) and L-SHADE (452). Geometric mean comparisons show average final solution quality improvements of $3.85 \times$ and $2.07 \times$ compared to DE and L-SHADE, respectively ($p \ll 0.001$), with average optimization speed averaging $1.40 \times$ and $5.16 \times$ faster. QUASAR's performance establishes it as an effective, efficient, and user-friendly evolutionary algorithm for complex high-dimensional problems.