From Understanding Genetic Drift to a Smart-Restart Mechanism for Estimation-of-Distribution Algorithms (2206.09090v5)

Abstract: Estimation-of-distribution algorithms (EDAs) are optimization algorithms that learn a distribution on the search space from which good solutions can be sampled easily. A key parameter of most EDAs is the sample size (population size). If the population size is too small, the update of the probabilistic model 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 leads to genetic drift, we design a smart-restart mechanism for EDAs. By stopping runs when the risk for genetic drift is high, it automatically runs the EDA in good parameter regimes. Via a mathematical runtime analysis, we prove a general performance guarantee for this smart-restart scheme. This in particular shows that in many situations where the optimal (problem-specific) parameter values are known, the restart scheme automatically finds these, leading to the asymptotically optimal performance. We also conduct an extensive experimental analysis. On four classic benchmark problems, we clearly observe the critical influence of the population size on the performance, and we find that the smart-restart scheme leads to a performance close to the one obtainable with optimal parameter values. Our results also show that previous theory-based suggestions for the optimal population size can be far from the optimal ones, leading to a performance clearly inferior to the one obtained via the smart-restart scheme. We also conduct experiments with PBIL (cross-entropy algorithm) on two combinatorial optimization problems from the literature, the max-cut problem and the bipartition problem. Again, we observe that the smart-restart mechanism finds much better values for the population size than those suggested in the literature, leading to a much better performance.