Large Population Sizes and Crossover Help in Dynamic Environments

Runtime analysis of the (mu+1)-EA on the Dynamic BinVal function

“…So for any c > c 0 , increasing the population size to a large constant will decrease the runtime from exponential to quasi-linear. This is consistent with the experimental findings in [9] for µ = {1, 2, 3, 5}, and it proves that population size can compensate for arbitrarily large mutation parameters.…”

“…In particular, it proves that there are ε, c > 0 such that the runtime is O(n log n) if the algorithm is started in an ε-neighborhood of the optimum, but that it takes exponential time to reach this ε-neighborhood. Thus we formally prove that the hardest part of optimization is not around the optimum, as was already experimentally concluded from Monte Carlo simulations in [9]. Related Work.…”

“…In the mostly experimental paper [9,10], Lengler and Meier defined the dynamic binary value function DynBV as a limiting case of dynamic linear functions. In DynBV, in each generation a uniformly random permutation π k : {1, .…”

“…Lengler and Meier observed that the proof in [11] for the (1 + 1)-EA extends to DynBV with threshold c * = c 0 , i.e., the (1 + 1)-EA needs time O(n log n) for mutation parameter c < c 0 , and exponential time for c > c 0 . In this sense, DynBV is the hardest dynamic linear function, in a limiting sense that is made precise in [10].…”

“…The papers [9,10] studied the (µ+1)-EA (using only mutation) and (µ+1)-GA (using randomly mutation or crossover) for µ ∈ {1, 2, 3, 5} on DynBV by runtime simulations and found two main results. As they increased the population size µ from 1 to 5, the efficiency threshold c 0 increased moderately for the (µ + 1)-EA (from 1.6 to 3.4, and strongly for the (µ + 1)-GA (from 1.6 to more than 20).…”