Sensitivity Analysis of the Transformation Using a Parameterized CEC 2017 Benchmark

Abstract

CEC 2017 applies bias, shift and rotation simultaneously, obscuring their individual effects on algorithm behavior. We introduce a parameterized implementation controlling them independently while preserving the original functions and transformation data. It diagnoses hybrid Marine Predators Algorithm (hMPA), whose predicted-candidate mechanism relies on numerical objective values and coordinate-wise reconstruction. Deep Statistical Comparison (DSC) and extended DSC (eDSC) are adapted from algorithm-level comparison to configuration-level diagnosis. To our knowledge, this is the first exhaustive DSC and eDSC analysis of all eight bias-shift-rotation configurations of a parameterized CEC 2017 benchmark. We examine all 56 three-configuration subsets and comparisons with the untransformed control, using 29 functions, dimensions 10, 30, 50 and 100, 30 independent runs and a fixed budget of 10,000 objective-function evaluations per dimension. DSC and eDSC show statistically significant configuration differences at every dimension, but rankings vary across functions, precluding a consistent ordering. Most individual effect-size confidence intervals include zero. Among those excluding zero, comparisons favor MPA more often at dimension 10 and hMPA at dimensions 50 and 100. Shift generally worsens objective-value outcomes. Isolated rotation causes no systematic deterioration; isolated bias barely changes final-solution distributions. Combined shift and rotation differ most consistently from the control. Convergence plots show function- and dimension-dependent separation, plateaus and late improvement. Numerical findings are limited to hMPA, but the framework can be extended to other continuous optimizers and adapted to related CEC benchmarks, including CEC 2024 and CEC 2025.