关于稳态进化算法和选择压力：为什么生殖试验的逆秩分配是最好的
On Steady-State Evolutionary Algorithms and Selective Pressure: Why Inverse Rank-Based Allocation of Reproductive Trials is Best
摘要：
我们分析了稳态EA的全局优化能力的选择性压力的影响。对于标准的双峰基准函数\twomax，我们严格证明，使用统一的父选择导致指数运行时，以高概率找到两个最优的标准（$μ$ +1）~EA和（$μ$ +1）~RLS与任何多项式的人口规模。另一方面，我们证明了选择最差的个人作为父母导致有效的全局优化与压倒性的概率合理的人口规模。由于总是选择最差的个人可能会有不利影响，从局部最优逃脱，我们考虑的性能随机父选择算子的低选择压力的函数类称为\textsc{TruncatedTwoMax}，其中一个斜率比其他短。实验分析表明，EA配备逆比赛选择，其中失败者被选择用于复制和小比赛大小，全局优化\textsc{TwoMax}有效地和有效地逃脱局部最优的\textsc{TruncatedTwoMax}具有高概率。因此，他们有效地确定了两个最优选择，而统一（或更强）的选择在理论和实践中都失败了。然后，我们展示了逆选择的力量，从文献中的人口是必不可少的，通过提供严格的证明或实验证据，它优于统一的选择配备或不重新启动策略。最后，我们通过对经典MaxSat和多维背包问题的标准基准的不同选择压力的实证分析来证实我们的理论见解。
英文摘要：
We analyse the impact of the selective pressure for the global optimisation capabilities of steady-state EAs. For the standard bimodal benchmark function \twomax we rigorously prove that using uniform parent selection leads to exponential runtimes with high probability to locate both optima for the standard ($μ$+1)~EA and ($μ$+1)~RLS with any polynomial population sizes. On the other hand, we prove that selecting the worst individual as parent leads to efficient global optimisation with overwhelming probability for reasonable population sizes. Since always selecting the worst individual may have detrimental effects for escaping from local optima, we consider the performance of stochastic parent selection operators with low selective pressure for a function class called \textsc{TruncatedTwoMax} where one slope is shorter than the other. An experimental analysis shows that the EAs equipped with inverse tournament selection, where the loser is selected for reproduction and small tournament sizes, globally optimise \textsc{TwoMax} efficiently and effectively escape from local optima of \textsc{TruncatedTwoMax} with high probability. Thus they identify both optima efficiently while uniform (or stronger) selection fails in theory and in practice. We then show the power of inverse selection on function classes from the literature where populations are essential by providing rigorous proofs or experimental evidence that it outperforms uniform selection equipped with or without a restart strategy. We conclude the paper by confirming our theoretical insights with an empirical analysis of the different selective pressures on standard benchmarks of the classical MaxSat and Multidimensional Knapsack Problems.
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