article · Algorithms
The dimension-tiered gaining-sharing knowledge algorithm, known as DT-GSK, configures its optimisation mechanisms according to problem dimensionality. Unlike existing variants that use a single operating setup, it deploys an adaptive scaffold across all problem dimensions and introduces a deterministic final refinement step for problems with fifty or more dimensions. In benchmark evaluations against six related algorithms across five standard benchmark suites, DT-GSK achieved top aggregate ranks on the CEC2013 and CEC2017 suites. However, statistically significant advantages over the leading baseline occurred primarily at lower dimensions, and it lagged behind existing variants on suites restricted to twenty or fewer dimensions where its dimension-dependent features remain inactive. Controlled tests also revealed that an experimental memory mechanism provided no standalone advantage over standard coordinate axes.
Optimisation algorithms are essential for solving complex mathematical and computational problems efficiently. Understanding how algorithm configurations should change across different problem scales helps researchers refine algorithmic design. This work identifies specific conditions where dimension-dependent tuning succeeds, while also providing negative results that clarify which complex components fail to deliver practical performance improvements.
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Published gaining-sharing knowledge (GSK) variants adapt scalar parameters and donor/selection policy to a single operating point. Dimension-Tiered GSK (DT-GSK) selects its configuration by dimension: an adaptive scaffold serves every tier, a deterministic, budget-exact final refinement runs once at D≥50, with the GSK vector-update equations retained; an exploratory interaction-structure memory supplies the refinement’s basis. Against six GSK-family baselines re-executed on five CEC suites under one budget-fair paired protocol, DT-GSK attains the best descriptive family-rank aggregate on CEC2017 (2.48) and CEC2013 (2.80), though Holm-corrected tests separate it from eGSK on either suite only at D=10; it is second behind eGSK at CEC2017 D=30 and on CEC2011 (Holm-significant loss). On AGSK’s strongest suite, the CEC2020 competition in which it was the runner-up, DT-GSK places fourth; the family panel corroborates AGSK’s published strength in this low-dimensional boundary regime, where every dimension-gated DT-GSK subsystem is inactive (D≤20). On CEC2013LSGO the comparison is family-internal: tied-first descriptive rank; paired tests do not separate DT-GSK from AGSK. Suite roles: CEC2017 selection-exposed; CEC2011/CEC2013 corroborative; CEC2020 pre-registered confirmatory; CEC2013LSGO post hoc. Direct isolations find no standalone benefit from that memory; coordinate axes outperform its basis: controlled negative results. All findings are scoped to the GSK-family panel.
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DOI: 10.3390/a19090769
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