On averaging the best samples in evolutionary computation
This work addresses a long-standing issue in evolutionary computation for researchers and practitioners, offering a theoretical improvement in selection rates for optimization tasks.
The paper tackles the problem of selecting the optimal selection rate in evolutionary computation for continuous unconstrained optimization, proving mathematically that a single parent leads to sub-optimal regret on the sphere function and providing a theoretically-based selection rate that achieves a provable regret of O(λ^{-1}), compared to O(λ^{-2/d}) for the single-parent case.
Choosing the right selection rate is a long standing issue in evolutionary computation. In the continuous unconstrained case, we prove mathematically that a single parent $μ=1$ leads to a sub-optimal simple regret in the case of the sphere function. We provide a theoretically-based selection rate $μ/λ$ that leads to better progress rates. With our choice of selection rate, we get a provable regret of order $O(λ^{-1})$ which has to be compared with $O(λ^{-2/d})$ in the case where $μ=1$. We complete our study with experiments to confirm our theoretical claims.