<p>This study proposes the Adaptive Quantum Beetle Swarm Optimization (AQBSO), a novel metaheuristic algorithm that integrates quantum-inspired probabilistic exploration with adaptive control mechanisms and beetle antenna-based directional search. The main contributions of this work are threefold: (i) a Gaussian quantum sampling mechanism that enhances global exploration, (ii) an adaptive step-size and antenna-length strategy that dynamically balances exploration and exploitation, and (iii) a hybrid update rule combining stochastic perturbation with gradient-based refinement to improve convergence accuracy. The performance of AQBSO was extensively evaluated on six classical benchmark functions (Michalewicz, Levy, Schwefel, Griewank, Ackley, and Cross-in-Tray) across multiple dimensions (10, 20, 30, and 60), as well as on constrained engineering problems and real-world applications. Experimental results demonstrate that AQBSO consistently achieves superior accuracy and stability compared to fourteen state-of-the-art algorithms, including PSO, GA, WOA, SMA, CSMA, and QBSO. Quantitatively, AQBSO achieved an average value of -4.26 (± 2.13 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\times\)</EquationSource> </InlineEquation> 10<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(^{-1}\)</EquationSource> </InlineEquation>) on the Michalewicz function (10D), outperforming QBSO (-4.02 ± 0.53) and PSO (-1.44 ± 0.63). On the Levy and Griewank functions, AQBSO reached the exact global optimum with near-zero variance, indicating highly stable convergence, whereas competing methods exhibited residual errors or higher dispersion. For the Schwefel function, AQBSO achieved 4.18 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\times\)</EquationSource> </InlineEquation> 10<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(^{2}\)</EquationSource> </InlineEquation> (± 2.57), significantly improving over BASBS (5.64 <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\times\)</EquationSource> </InlineEquation> 10<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(^{2}\)</EquationSource> </InlineEquation>) and PSO (9.41 <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\times\)</EquationSource> </InlineEquation> 10<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(^{2}\)</EquationSource> </InlineEquation>), demonstrating superior global exploration capability. On the Ackley function, AQBSO obtained 5.48 <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\times\)</EquationSource> </InlineEquation> 10<InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(^{-5}\)</EquationSource> </InlineEquation> (± 3.38 <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\times\)</EquationSource> </InlineEquation> 10<InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(^{-7}\)</EquationSource> </InlineEquation>), outperforming SMA and DO by up to two orders of magnitude. In the highly multimodal Cross-in-Tray function, AQBSO achieved -2.06 (± 1.05 <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(\times\)</EquationSource> </InlineEquation> 10<InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(^{-1}\)</EquationSource> </InlineEquation>), reaching values very close to the global optimum with lower variability than competing methods. Statistical validation using Wilcoxon rank-sum, Friedman, and Nemenyi tests confirms that the improvements are statistically significant (<InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(p < 0.05\)</EquationSource> </InlineEquation>), with AQBSO consistently ranked in the first position across all benchmark scenarios. These results demonstrate that AQBSO provides a robust, precise, and scalable optimization framework, particularly effective in high-dimensional and multimodal search spaces, outperforming both classical and recent bio-inspired optimization methods.</p>

Development of an AQBSO (Adaptive Quantum-Based Swarm Optimization) meta-heuristic with adaptive mechanisms and quantum exploration for solving optimization problems

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2026年6月17日

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Fernando Rodrigues Trindade Ferreira,
Loena Marins do Couto

摘要

This study proposes the Adaptive Quantum Beetle Swarm Optimization (AQBSO), a novel metaheuristic algorithm that integrates quantum-inspired probabilistic exploration with adaptive control mechanisms and beetle antenna-based directional search. The main contributions of this work are threefold: (i) a Gaussian quantum sampling mechanism that enhances global exploration, (ii) an adaptive step-size and antenna-length strategy that dynamically balances exploration and exploitation, and (iii) a hybrid update rule combining stochastic perturbation with gradient-based refinement to improve convergence accuracy. The performance of AQBSO was extensively evaluated on six classical benchmark functions (Michalewicz, Levy, Schwefel, Griewank, Ackley, and Cross-in-Tray) across multiple dimensions (10, 20, 30, and 60), as well as on constrained engineering problems and real-world applications. Experimental results demonstrate that AQBSO consistently achieves superior accuracy and stability compared to fourteen state-of-the-art algorithms, including PSO, GA, WOA, SMA, CSMA, and QBSO. Quantitatively, AQBSO achieved an average value of -4.26 (± 2.13 \(\times\) 10 \(^{-1}\) ) on the Michalewicz function (10D), outperforming QBSO (-4.02 ± 0.53) and PSO (-1.44 ± 0.63). On the Levy and Griewank functions, AQBSO reached the exact global optimum with near-zero variance, indicating highly stable convergence, whereas competing methods exhibited residual errors or higher dispersion. For the Schwefel function, AQBSO achieved 4.18 \(\times\) 10 \(^{2}\) (± 2.57), significantly improving over BASBS (5.64 \(\times\) 10 \(^{2}\) ) and PSO (9.41 \(\times\) 10 \(^{2}\) ), demonstrating superior global exploration capability. On the Ackley function, AQBSO obtained 5.48 \(\times\) 10 \(^{-5}\) (± 3.38 \(\times\) 10 \(^{-7}\) ), outperforming SMA and DO by up to two orders of magnitude. In the highly multimodal Cross-in-Tray function, AQBSO achieved -2.06 (± 1.05 \(\times\) 10 \(^{-1}\) ), reaching values very close to the global optimum with lower variability than competing methods. Statistical validation using Wilcoxon rank-sum, Friedman, and Nemenyi tests confirms that the improvements are statistically significant ( \(p < 0.05\) ), with AQBSO consistently ranked in the first position across all benchmark scenarios. These results demonstrate that AQBSO provides a robust, precise, and scalable optimization framework, particularly effective in high-dimensional and multimodal search spaces, outperforming both classical and recent bio-inspired optimization methods.