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Evolutionary algorithm (EA) is a generic term for optimization algorithms inspired by biological optimization processes in the natural world. Although EAs are widely applied to complex real‐world problems because they do not require mathematical expression of target problems, theoretical design methods of EAs have not been established. To solve this issue, this paper proposes an approach of designing EAs within an algorithm framework in which mathematical characteristics are derived, and it also presents a concrete framework for that purpose. The presented framework, Regulated Evolution Strategies (RES) provides a stability analysis result that contributes to designing algorithms with expected behavior. The RES framework has a high degree of freedom in designing algorithms, so that it is possible to incorporate various contrivances such as local improvement of samples and reduction of constraint violations in RES‐based algorithms while maintaining the stability analysis result. Numerical experiments prove that the RES framework has a capability for designing high‐performance EAs. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]