Multi-level evolution strategies for high-resolution black-box control

Ofer M. Shir, Xi Xing, Herschel Rabitz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 (μW, λ) -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.

Original languageEnglish (US)
Pages (from-to)1021-1055
Number of pages35
JournalJournal of Heuristics
Issue number6
StatePublished - Dec 2021

All Science Journal Classification (ASJC) codes

  • Software
  • Information Systems
  • Computer Networks and Communications
  • Control and Optimization
  • Management Science and Operations Research
  • Artificial Intelligence


  • Black-box global optimization
  • Derivative-free search heuristics
  • Experimental optimization
  • Multi-resolution
  • Quantum coherent control
  • Scalability
  • Simulation-based optimization


Dive into the research topics of 'Multi-level evolution strategies for high-resolution black-box control'. Together they form a unique fingerprint.

Cite this