Table 1.
Structural comparison of the proposed Felis Catus Optimization (FCO) algorithm with 17 competitor metaheuristic methods across seven design criteria. Checkmarks (✓) indicate the presence of a feature in the algorithm, while crosses (✗) denote its absence.
Table 2.
Summary taxonomy of metaheuristic algorithms by primary inspiration and mechanistic domain. Sixteen algorithms are categorized by their dominant source of inspiration: animal/behavioral, physical-process, evolutionary/mathematical, or hybrid and by their underlying search mechanism. This classification illustrates how metaphoric origin guides exploration–exploitation balance and population dynamics.
Fig 1.
Positions of explorers and exploits in continuous space.
Fig 2.
Visualization of exploration and exploitation mechanisms in FCO algorithm.
Fig 3.
Schematic representation of noise-driven rejuvenation and reallocation in FCO.
Environmental Noise Injection (ENI) introduces mild random perturbations to agent positions to maintain population diversity, while the Random Rejuvenation (RJ) mechanism replaces aging agents with newly initialized ones within the search bounds, serving as a continuous alternative to discrete renewal events.
Fig 4.
Pseudo code of the FCO algorithm.
Table 3.
Average runtime (seconds) of 18 metaheuristic algorithms on CEC 2005 and CEC 2017.
Table 4.
Unimodal benchmark functions.
Table 5.
Multimodal benchmark functions.
Table 6.
Fixed dimension multimodal benchmark functions.
Fig 5.
2 D versions of unimodal benchmark functions.
Fig 6.
2 D version of multimodal benchmark functions.
Fig 7.
2 D version of fixed-dimension multimodal benchmark functions.
Table 7.
Specifications and features of CEC 2017 benchmark Test Functions.
Table 8.
Default algorithmic parameters and control policies of felis catus optimization (FCO v2, MATLAB R2019a).
Table 9.
Mean values (± standard deviation) of 18 metaheuristic algorithms on 17 CEC 2005 benchmark test functions (F1–F17). Lower values indicate better performance for minimization.
Table 10.
Friedman mean ranks of 18 metaheuristic algorithms over 17 CEC 2005 benchmark functions (F1–F17).
Table 11.
Results of the Holm sequential procedure for pairwise comparisons against the proposed Felis Catus Optimization (FCO) algorithm on the CEC 2005 benchmark suite (p – values and adjusted α levels).
Fig 8.
Critical Difference (CD) diagram based on Friedman mean ranks for 18 algorithms on the CEC 2005 benchmark set (α = 0.05, Nemenyi test).
Smaller ranks correspond to better performance. The red dashed line indicates the critical threshold CD = 4.104 algorithms within this distance are not statistically different.
Fig 9.
Representative convergence profiles of the Felis Catus Optimization (FCO) algorithm over selected CEC 2005 functions.
Table 12.
Summarizes the statistical results (Mean ± Std) of all 30 functions and 18 algorithms. Lower mean values correspond to better solution quality. The values follow scientific notation (E-format) for numerical consistency.
Table 13.
Results of the Friedman test and average ranks of 18 algorithms on 30 CEC 2017 benchmark functions (χ² = 361.47, df = 17, p = 2.02 × 10 ⁻ ⁶⁶). Lower ranks denote better overall performance.
Table 14.
Holm post-hoc comparison of Felis Catus Optimization (FCO) algorithm versus competing metaheuristics on the CEC 2017 benchmark functions under the minimization criterion.
Fig 10.
Critical Difference (CD) diagram based on Friedman mean ranks for 18 algorithms on the CEC 2017 benchmark set (α = 0.05, Nemenyi test).
Fig 11.
Representative convergence profiles of the Felis Catus Optimization (FCO) algorithm on selected CEC 2017 functions (F1: Unimodal, F20: Hybrid, F26: Composition).
Fig 12.
Schematic representation of the compression/tension spring design optimization problem.
(a) Three-dimensional view of a helical spring subjected to axial load P between two rigid plates. (b) Geometrical configuration and design variables: mean coil diameter (D), wire diameter (d), number of active coils (N), and free length. (c) Feasible design space defined by inequality constraints (g ≤ 0), the shaded region indicates the combinations of (D, d, N) that satisfy shear stress and deflection limits under the applied load P.
Table 15.
Comparison of results for tension/compression spring design problem.
Table 16.
Post-hoc wilcoxon test results against FCO.
Fig 13.
Schematic representation of the welded beam design optimization problem.
(a) Three-dimensional view of the beam welded to a fixed support. (b) Geometrical configuration showing the design variables: weld thickness (h), weld length (l), beam height (t), and beam width (b). (c) Feasible design region defined by the inequality constraints (g ≤ 0), where the shaded area denotes the combination of variables satisfying all stress, deflection, and geometry limits.
Table 17.
Design variables for the welded beam optimization problem.
Table 18.
Comparison results of the welded beam design problem.
Table 19.
Holm’s post-hoc test results with FCO as control algorithm.
Table 20.
Variable of pressure vessel design problem.
Fig 14.
Schematic illustration of the Pressure Vessel Design Problem.
(a) Three-dimensional CAD view of the cylindrical vessel with two hemispherical heads supported on saddle bases. (b) Technical section A–A showing the four design variables: shell thickness (), head thickness (
), inner radius (R), and cylindrical length (L). (c) Feasible design region based on the nonlinear constraint boundaries (g ≤ 0).
Table 21.
Statistical comparison of eighteen metaheuristic algorithms applied to the Pressure Vessel Design Problem.
Table 22.
Post-hoc wilcoxon test results against FCO.