Stategies to Increase Efficiency

1. Componentwise updating. The idea behind componentwise updating is, as the name suggests, to update at each iteration. The order in which the components are updated can be either according to some fixed permutation or according to some other (possibly random) permutation. In our numerical experiments we chose the second option. Componentwise updating is often used in simulated annealing; see e.g., [3].

2. FACE. The FACE (fully adapted CE) algorithm is described in detail in [6]. In the FACE algorithm the parameters rho and N of the standard CE algorithm are updated adaptively, keeping the number of elite samples constant.

3. No storage of trajectories (increase memory efficiency). Sometimes it is not feasible -- due to memory problems -- to store all trajectories or vectors generated at Step 2 of the CE Algorithm. A memory-efficient alternative is to determine the gamma parameter using a relatively small sample size. Once gamma is determined, Step 3 of the algorithm can be carried out using a new sample, updating the parameters ``online'' while ignoring each trajectory for which the performance is less than gamma.