<p>The Salp Swarm Algorithm (SSA) is a well-established swarm intelligence metaheuristic whose performance is fundamentally constrained by two structural deficiencies: a passive follower update in which each salp averages only with its immediate predecessor, causing slow propagation of global-best information and insufficient directed exploitation; and a complete absence of stagnation detection or diversity-recovery, leaving the swarm permanently trapped once population diversity collapses. This paper proposes two philosophically distinct and structurally complementary variants that directly target each deficiency. Weighted Follower Guidance (SSA-WFG) replaces the standard uniform follower update with a rank-based, socially aware rule: front-rank followers receive a strong attraction toward the global best solution, accelerating exploitation, while rear-rank followers retain conservative movement as a diversity reservoir – a heterogeneous structure absent from the original SSA. Dynamic Swarm Restructuring (SSA-DSR) augments the standard SSA with an event-triggered stagnation-recovery mechanism the original algorithm entirely lacks: when a stagnation counter exceeds a threshold, the lowest-fitness salps are re-initialized to random positions while elite solutions are preserved, injecting targeted diversity precisely when standard dynamics have failed. Both modifications preserve the <InlineEquation ID="IEq1"><EquationSource Format="TEX">$\mathcal {O}(L \cdot N \cdot d)$</EquationSource><EquationSource Format="MATHML"><math><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mi>L</mi><mo>·</mo><mi>N</mi><mo>·</mo><mi>d</mi><mo stretchy="false">)</mo></mrow></math></EquationSource></InlineEquation> time complexity of the original SSA. Evaluated on 23 classical benchmark functions and the CEC 2020 suite, SSA-WFG achieves the best Friedman rank on classical landscapes (Wilcoxon <InlineEquation ID="IEq2"><EquationSource Format="TEX">$p < 0.05$</EquationSource><EquationSource Format="MATHML"><math><mrow><mi>p</mi><mo><</mo><mn>0.05</mn></mrow></math></EquationSource></InlineEquation>), while SSA-DSR attains the highest average rank on 9 of 10 CEC 2020 functions, confirming complementary, landscape-dependent superiority over standard SSA. On the PRO-ACT Amyotrophic Lateral Sclerosis (ALS) progression dataset, both variants reduce MLP mean squared error by approximately 71.5% relative to standard SSA, with run-to-run standard deviations two to three orders of magnitude smaller. Following wrapper-based feature selection, SSA-DSR exhibits exceptional biomarker reproducibility (<InlineEquation ID="IEq3"><EquationSource Format="TEX">$\textrm{std} \approx 1.1$</EquationSource><EquationSource Format="MATHML"><math><mrow><mtext>std</mtext><mo>≈</mo><mn>1.1</mn></mrow></math></EquationSource></InlineEquation> features vs. 6.7 for standard SSA across 21 independent runs). The proposed dual-strategy framework provides a principled and efficient methodology for metaheuristic optimization on high-dimensional, noisy real-world problems where gradient-based methods and unmodified SSA are inadequate.</p>

Evaluating dual-strategy salp swarm optimization on synthetic benchmarks and ALS disease progression

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2026年5月20日

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Mahmoud Hammad,
Sofian Kassaymeh,
Sharif Makhadmeh,
Mohammed Al-Betar

摘要

The Salp Swarm Algorithm (SSA) is a well-established swarm intelligence metaheuristic whose performance is fundamentally constrained by two structural deficiencies: a passive follower update in which each salp averages only with its immediate predecessor, causing slow propagation of global-best information and insufficient directed exploitation; and a complete absence of stagnation detection or diversity-recovery, leaving the swarm permanently trapped once population diversity collapses. This paper proposes two philosophically distinct and structurally complementary variants that directly target each deficiency. Weighted Follower Guidance (SSA-WFG) replaces the standard uniform follower update with a rank-based, socially aware rule: front-rank followers receive a strong attraction toward the global best solution, accelerating exploitation, while rear-rank followers retain conservative movement as a diversity reservoir – a heterogeneous structure absent from the original SSA. Dynamic Swarm Restructuring (SSA-DSR) augments the standard SSA with an event-triggered stagnation-recovery mechanism the original algorithm entirely lacks: when a stagnation counter exceeds a threshold, the lowest-fitness salps are re-initialized to random positions while elite solutions are preserved, injecting targeted diversity precisely when standard dynamics have failed. Both modifications preserve the $\mathcal {O}(L \cdot N \cdot d)$ $O (L \cdot N \cdot d)$ time complexity of the original SSA. Evaluated on 23 classical benchmark functions and the CEC 2020 suite, SSA-WFG achieves the best Friedman rank on classical landscapes (Wilcoxon $p < 0.05$ $p < 0.05$ ), while SSA-DSR attains the highest average rank on 9 of 10 CEC 2020 functions, confirming complementary, landscape-dependent superiority over standard SSA. On the PRO-ACT Amyotrophic Lateral Sclerosis (ALS) progression dataset, both variants reduce MLP mean squared error by approximately 71.5% relative to standard SSA, with run-to-run standard deviations two to three orders of magnitude smaller. Following wrapper-based feature selection, SSA-DSR exhibits exceptional biomarker reproducibility ($\textrm{std} \approx 1.1$ $std \approx 1.1$ features vs. 6.7 for standard SSA across 21 independent runs). The proposed dual-strategy framework provides a principled and efficient methodology for metaheuristic optimization on high-dimensional, noisy real-world problems where gradient-based methods and unmodified SSA are inadequate.