  A commonly used strategy for improving optimization algorithms is to restart
the algorithm when it is believed to be trapped in an inferior part of the
search space. Building on the recent success of Bet-and-Run approaches for
restarted local search solvers, we introduce an improved generic Bet-and-Run
strategy. The goal is to obtain the best possible results within a given time
budget t using a given black-box optimization algorithm. If no prior knowledge
about problem features and algorithm behavior is available, the question about
how to use the time budget most efficiently arises. We propose to first start
k>=1 independent runs of the algorithm during an initialization budget t1<t,
pausing these runs, then apply a decision maker D to choose 1<=m<=k runs from
them (consuming t2>=0 time units in doing so), and then continuing these runs
for the remaining t3=t-t1-t2 time units. In previous Bet-and-Run strategies,
the decision maker D=currentBest would simply select the run with the best-
so-far results at negligible time. We propose using more advanced methods to
discriminate between "good" and "bad" sample runs, with the goal of increasing
the correlation of the chosen run with the a-posteriori best one. We test
several different approaches, including neural networks trained or polynomials
fitted on the current trace of the algorithm to predict which run may yield the
best results if granted the remaining budget. We show with extensive
experiments that this approach can yield better results than the previous
methods, but also find that the currentBest method is a very reliable and
robust baseline approach.
