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Estimation-of-distribution algorithms (EDAs) are optimization algorithms thatlearn a distribution on the search space from which good solutions can besampled easily. A key parameter of most EDAs is the sample size (populationsize). If the population size is too small, the update of the probabilisticmodel builds on few samples, leading to the undesired effect of genetic drift.Too large population sizes avoid genetic drift, but slow down the process.  Building on a recent quantitative analysis of how the population size leadsto genetic drift, we design a smart-restart mechanism for EDAs. By stoppingruns when the risk for genetic drift is high, it automatically runs the EDA ingood parameter regimes.  Via a mathematical runtime analysis, we prove a general performance guaranteefor this smart-restart scheme. This in particular shows that in many situationswhere the optimal (problem-specific) parameter values are known, the restartscheme automatically finds these, leading to the asymptotically optimalperformance.  We also conduct an extensive experimental analysis. On four classic benchmarkproblems, we clearly observe the critical influence of the population size onthe performance, and we find that the smart-restart scheme leads to aperformance close to the one obtainable with optimal parameter values. Ourresults also show that previous theory-based suggestions for the optimalpopulation size can be far from the optimal ones, leading to a performanceclearly inferior to the one obtained via the smart-restart scheme. We alsoconduct experiments with PBIL (cross-entropy algorithm) on two combinatorialoptimization problems from the literature, the max-cut problem and thebipartition problem. Again, we observe that the smart-restart mechanism findsmuch better values for the population size than those suggested in theliterature, leading to a much better performance.

From Understanding Genetic Drift to a Smart-Restart Mechanism for Estimation-of-Distribution Algorithms