This paper introduces a multi-level (m-lev) mechanism into Evolution Strategies (ESs) in order to address a class of global optimization problems that could benefit from fine discretization of their decision variables. Such problems arise in engineering and scientific applications, which possess a multi-resolution control nature, and thus may be formulated either by means of low-resolution variants (providing coarser approximations with presumably lower accuracy for the general problem) or by high-resolution controls. A particular scientific application concerns practical Quantum Control (QC) problems, whose targeted optimal controls may be discretized to increasingly higher resolution, which in turn carries the potential to obtain better control yields. However, state-of-the-art derivative-free optimization heuristics for high-resolution formulations nominally call for an impractically large number of objective function calls. Therefore, an effective algorithmic treatment for such problems is needed. We introduce a framework with an automated scheme to facilitate guided-search over increasingly finer levels of control resolution for the optimization problem, whose on-the-fly learned parameters require careful adaptation. We instantiate the proposed m-lev self-adaptive ES framework by two specific strategies, namely the classical elitist single-child (1+1)-ES and the non-elitist multi-child derandomized \((\mu _W,\lambda )\)-sep-CMA-ES. We first show that the approach is suitable by simulation-based optimization of QC systems which were heretofore viewed as too complex to address. We also present a laboratory proof-of-concept for the proposed approach on a basic experimental QC system objective.

本文将多级 (m-lev) 机制引入进化策略 (ES)，以解决一类全局优化问题，这些问题可以从其决策变量的精细离散化中受益。此类问题出现在具有多分辨率控制性质的工程和科学应用中，因此可以通过低分辨率变体（为一般问题提供可能较低精度的粗略近似）或高分辨率控制来表述. 一个特定的科学应用涉及实际的量子控制 (QC) 问题，其目标最优控制可能被离散化为越来越高的分辨率，这反过来又具有获得更好控制产量的潜力。然而，用于高分辨率公式的最先进的无导数优化启发式方法名义上需要大量不切实际的目标函数调用。因此，需要对此类问题进行有效的算法处理。我们引入了一个带有自动化方案的框架，以促进优化问题在越来越精细的控制分辨率水平上的引导搜索，其动态学习的参数需要仔细调整。我们通过两种特定的策略实例化了提出的 m-lev 自适应 ES 框架，即经典的精英主义单子 (1+1)-ES 和非精英主义的多子随机化 我们引入了一个带有自动化方案的框架，以促进优化问题在越来越精细的控制分辨率水平上的引导搜索，其动态学习的参数需要仔细调整。我们通过两种特定的策略实例化了提出的 m-lev 自适应 ES 框架，即经典的精英主义单子 (1+1)-ES 和非精英主义的多子随机化 我们引入了一个带有自动化方案的框架，以促进优化问题在越来越精细的控制分辨率水平上的引导搜索，其动态学习的参数需要仔细调整。我们通过两种特定的策略实例化了提出的 m-lev 自适应 ES 框架，即经典的精英主义单子 (1+1)-ES 和非精英主义的多子随机化\((\mu_W,\lambda )\) -sep-CMA-ES。我们首先通过对 QC 系统进行基于模拟的优化来证明该方法适用于迄今为止被认为过于复杂而无法解决的问题。我们还针对基本实验 QC 系统目标提出的方法提出了实验室概念验证。