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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]

In this paper, we analyze the properties of the superior solution set search (SSSS) problem and point out the structural similarities between it and the multiobjective optimization problem. Based on the analyzed properties, we propose a new Firefly algorithm (FA) based on superior relations, which can search for the superior solution set by using the user's quantitative desire level as a search strategy. By introducing the distance of the problem space into the moving mechanism, FA makes it possible to search for multiple local optimal solutions by dividing the solution set into multiple groups. By analyzing this property of FA, we clarify the affinity between FA and the SSSS problem. We subsequently analyze the SSSS problem and FA, and discuss their properties together in a similar problem setting. We propose an FA based on superior relations as a new optimization technique for the superior solution set problem based on these analyses. Numerical experiments are then conducted using the SSSS problem and demonstrate the usefulness of the proposed method by comparing the performance of the proposed method with the conventional FA. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]