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<p>This paper proposes a novel hybrid metaheuristic algorithm that combines the Quasi-Oppositional-Chaotic Symbiotic Organisms Search (QOCSOS) with the Bald Eagle Search (BES), termed the Chaotic Quasi-Oppositional Hybrid (CQOBES) algorithm. The proposed CQOBES integrates the core search mechanisms of both algorithms, deploying quasi-oppositional learning (QOL) in the population initialization and the logistic chaotic map for optimized diversity. The robustness of the proposed hybrid CQOBES has been evaluated against the algorithms cited to minimize the total error (TE) of fractional-order low-pass Butterworth filters (FOLPBF). Additional error indices, such as MARME and MAME, are also investigated. Furthermore, the hybrid algorithm is applied to high-pass and band-pass Butterworth filters, validating its broad applicability. Relative to reported techniques such as EFADE, EPSO, HCLPSO, CoDE, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>oDE, and the standard BES, the proposed QOCSOS-BES hybrid demonstrates excellence across multiple metrics, including the minimization of error performances, solution quality, convergence profile, algorithmic precision, and computational complexity. Parameter sensitivity analysis is implemented to calculate the optimal control values of CQOBES for different-order FOLPBFs. Magnitude and phase-response behavior, Nyquist plots, and pole-zero plots also justify the proposed hybrid algorithm’s stability and accuracy. Statistical analysis of TE in terms of best, worst, mean, and standard deviation is compared with reported approaches and depicted using a box plot and ANOVA plots to justify our algorithm’s suitability.</p>

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Accurate Design of Digital Fractional-Order Butterworth Filters Using a Novel Chaotic Quasi-Oppositional Bald Eagle Search Algorithm

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • Souvik Dey,
  • Provas Kumar Roy,
  • Angsuman Sarkar

摘要

This paper proposes a novel hybrid metaheuristic algorithm that combines the Quasi-Oppositional-Chaotic Symbiotic Organisms Search (QOCSOS) with the Bald Eagle Search (BES), termed the Chaotic Quasi-Oppositional Hybrid (CQOBES) algorithm. The proposed CQOBES integrates the core search mechanisms of both algorithms, deploying quasi-oppositional learning (QOL) in the population initialization and the logistic chaotic map for optimized diversity. The robustness of the proposed hybrid CQOBES has been evaluated against the algorithms cited to minimize the total error (TE) of fractional-order low-pass Butterworth filters (FOLPBF). Additional error indices, such as MARME and MAME, are also investigated. Furthermore, the hybrid algorithm is applied to high-pass and band-pass Butterworth filters, validating its broad applicability. Relative to reported techniques such as EFADE, EPSO, HCLPSO, CoDE, \(C^2\) C 2 oDE, and the standard BES, the proposed QOCSOS-BES hybrid demonstrates excellence across multiple metrics, including the minimization of error performances, solution quality, convergence profile, algorithmic precision, and computational complexity. Parameter sensitivity analysis is implemented to calculate the optimal control values of CQOBES for different-order FOLPBFs. Magnitude and phase-response behavior, Nyquist plots, and pole-zero plots also justify the proposed hybrid algorithm’s stability and accuracy. Statistical analysis of TE in terms of best, worst, mean, and standard deviation is compared with reported approaches and depicted using a box plot and ANOVA plots to justify our algorithm’s suitability.