An Emperor Penguin Optimizer with Intelligent Modular Arithmetic-Driven Multi-Population Partitioning

Abstract

Metaheuristic optimization algorithms are essential for solving complex and high-dimensional problems, yet their performance is often constrained by premature convergence and insufficient population diversity. Although the Emperor Penguin Optimizer (EPO) has demonstrated promising results, its single-population structure and static search behavior limit robustness and scalability. To overcome these drawbacks, this paper proposes a Multi-Population Emperor Penguin Optimizer with Joint Opposite Selection (MLPEPO-JOS), an adaptive multi-population optimization framework that introduces a process innovation in how population coordination, diversity preservation, and opposition learning are integrated. The proposed approach integrates three complementary mechanisms: an adaptive multi-population regulation strategy driven by real-time fitness improvement trends, an intelligent modular arithmetic-based division scheme that ensures balanced population partitioning under arbitrary population sizes, and a Joint Opposite Selection (JOS) mechanism that combines Selective Leading Opposition and Dynamic Opposition to enhance exploration-exploitation balance. MLPEPO-JOS is evaluated on 41 benchmark functions from the IEEE CEC2017 and CEC2022 suites, achieving the best mean ranking and competitive performance in terms of accuracy, robustness, and convergence behavior. Statistical analyses indicate significant improvements over many of the evaluated competitors, although the significance varies across individual comparisons.