An Analysis of Bezier Curve-Based Optimization Integrated with Diversity-Adaptive Balance, Reflective Repair, and Stagnation Recovery

Bezier curve-based optimization (BCO) provides a population-based search framework that generates candidate solutions along linear, quadratic, and cubic Bezier paths defined by control points. This paper presents IBCO, an improved BCO configuration that integrates three established controls: dimension- and bound-gated diversity feedback, reflective boundary repair, and stagnation-triggered differential or elite-guided perturbation. The contribution is an auditable integration and activation design, not a claim that these operators are individually new. Existing records comprise 30 runs on 26 classical instances, 29 evaluated CEC2017 functions (F1 and F3–F30; F2 excluded), 24 CEC2022 instances, 5 constrained engineering problems, and 26 high-dimensional classical instances. The CEC2017, CEC2022, and engineering profiles used fixed per-run realized evaluation counts within each documented profile; this does not imply identical candidate-evaluation sequences within every run. Classical and high-dimensional IBCO runs used 9030–9144 evaluations, versus 9030 for Original BCO; therefore, those profiles do not establish fixed-evaluation superiority. A retrospective, problem-blocked reanalysis of existing runs rejected the omnibus null of equal treatments in all seven comparison and ablation profiles at α=0.05 (largest p=0.0220), but IBCO’s advantage over Original BCO did not exceed profile-level Nemenyi critical differences. Among 24 classical rank-1 results, only 4 were unique first places. Ablation records identify reflective repair as the most stable component but do not establish synergy among the complete configuration combining diversity feedback, reflective boundary repair, and stagnation-triggered perturbation. IBCO is therefore interpreted as a competitive, incremental BCO configuration relative to the implemented historical baselines, not as a scale-invariant, evaluation-efficient, or universally dominant optimizer.