What question did this study set out to answer?

The research aims to address premature convergence and population stagnation in metaheuristic optimization algorithms.

July 12, 2026Open Access

Multi-Strategy Improved Aquila Optimizer with Adaptive Exploration and Individual-Level Stagnation Control: A Bio-Inspired Hybrid Metaheuristic and Its Engineering Applications

OAOluwatayomi Rereloluwa AdegboyeUniversity of Mediterranean Karpasia HKHüseyin KusetoğullarıBlekinge Institute of Technology AFAfi Kekeli FedaEuropean University of Lefke

Key Points

The research aims to address premature convergence and population stagnation in metaheuristic optimization algorithms.
Developed the Stagnation-Aware Aquila Optimizer (SAAO) incorporating adaptive exploration probability and individual-level stagnation counters.
Evaluated SAAO against nine state-of-the-art algorithms on CEC2015 and CEC2022 benchmarks.
Applied SAAO to classical engineering design problems and a real-world anomaly prediction task.
SAAO achieved the best Friedman mean rank on CEC2015 and CEC2022 benchmarks, demonstrating superior performance.
In the anomaly prediction task, SAAO-optimized classifier reached 98.23% accuracy, outperforming baseline models.
Statistical analysis confirmed significant advantages of SAAO over most competitor algorithms.

Abstract

Metaheuristic algorithms remain a widely used class of solvers for solving complex, non-convex optimization problems where gradient information is unavailable, yet two failure modes continue to limit their practical reach: premature convergence caused by inadequate exploration diversity in late iterations and population stagnation that persists even when individual agents are nominally assigned to the exploration phase. This paper proposes the Stagnation-Aware Aquila Optimizer (SAAO), a hybrid algorithm that addresses both failure modes by embedding three targeted mechanisms into the Aquila Optimizer (AO) framework: (i) an adaptive exploration probability that responds to global fitness-improvement history; (ii) individual-level stagnation counters that force exploration re-entry for any agent that fails to improve for more than 30 consecutive iterations, regardless of the global phase schedule; and (iii) a diversity-maintenance module that reinitializes completely stagnant agents via random sampling or opposition-based learning. The biological repertoire of search operators is simultaneously enriched by incorporating four physics-grounded operators from the Animated Oat Optimization (AOO) algorithm centroid-guided dispersal, elite-guided dispersal, hygroscopic rolling, and spring ejection, alongside the original AO operators, yielding six complementary update rules partitioned equally between exploration and exploitation. The SAAO was evaluated against nine state-of-the-art algorithms on the CEC2015 benchmark and CEC2022 under identical experimental settings. The SAAO achieved the best Friedman mean rank on both suites and delivered competitive or superior performance against the nine baselines, with Wilcoxon rank-sum tests confirming statistically significant advantages over most competitors. On three classical engineering design problems, the SAAO achieved competitive outcomes. In a real-world equipment anomaly prediction task, an SAAO-optimized ensemble classifier attained 98.23% accuracy, surpassing the compared baseline models. These results establish SAAO as a robust and computationally tractable optimizer for both benchmark and applied settings.

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