On the Structural and Statistical Flaws of the Exponential-Trigonometric Optimizer

Abstract

The proliferation of metaphor-based metaheuristics has often been accompanied by issues of symbolic inflation, benchmarking opacity, and statistical misuse. This study presents a diagnostic critique of the recently proposed Exponential Trigonometric Optimizer (ETO), exposing fundamental flaws in its algorithmic structure and the statistical reporting of its performance. Through a stripped mathematical reconstruction, we identify inert symbolic constructs, ill-defined recurrence schedules, and ineffective update mechanisms that collectively undermine the algorithm's purported balance and effectiveness. A principled benchmarking comparison against nine established metaheuristics on the CEC 2017 and 2021 suites reveals that ETO's performance claims are inflated. While it demonstrates mid-tier competitiveness, it consistently fails against top-tier algorithms, especially under high-dimensional and shift-rotated landscapes. Our statistical framework, employing rank-based non-parametric tests and effect size diagnostics, quantifies these limitations and highlights ETO's structural fragility and lack of scalability. The paper concludes by advocating for a reformist framework in metaheuristic research, emphasizing symbolic hygiene, operator attribution, and statistical transparency to mitigate misleading narratives and foster a more robust and reproducible optimization literature.