混合动态规划和Monte Carlo模拟的进化算法运行时间边界
Blending Dynamic Programming with Monte Carlo Simulation for Bounding the Running Time of Evolutionary Algorithms
摘要：
为了提供最佳运行时间的绝对下限，这可以通过$(1+λ)$型搜索算法在常见的基准问题上实现，我们最近提出了一种动态规划方法，该方法计算最佳预期运行时间和偏离最佳参数选择时推断出的遗憾值。我们以前的工作仅限于不同状态之间的转移概率可以用相对简单的数学表达式表示的问题。随着目标，以涵盖更广泛的问题集，我们建议在这项工作中的动态规划方法的扩展设置中的转移概率不一定是精确计算的，但它们可以近似数值，任意精度，通过蒙特卡罗采样。我们应用我们的混合蒙特卡罗动态规划方法的级联跳跃函数，并演示如何获得的界限可以用来获得更深入的了解到参数控制方案。
英文摘要：
With the goal to provide absolute lower bounds for the best possible running times that can be achieved by $(1+λ)$-type search heuristics on common benchmark problems, we recently suggested a dynamic programming approach that computes optimal expected running times and the regret values inferred when deviating from the optimal parameter choice. Our previous work is restricted to problems for which transition probabilities between different states can be expressed by relatively simple mathematical expressions. With the goal to cover broader sets of problems, we suggest in this work an extension of the dynamic programming approach to settings in which the transition probabilities cannot necessarily be computed exactly, but in which they can be approximated numerically, up to arbitrary precision, by Monte Carlo sampling. We apply our hybrid Monte Carlo dynamic programming approach to a concatenated jump function and demonstrate how the obtained bounds can be used to gain a deeper understanding into parameter control schemes.
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