A Preliminary Numerical Investigation of Global Extrema Attainment Using the Constrained Adaptive Model-Based Exploration Optimiser (CAMEO)

Optimisation algorithms play an important role in the solution of nonlinear engineering design problems, particularly where objective functions exhibit complex, nonconvex, and potentially multimodal behaviour. Classical gradient-based methods, including the Method of Moving Asymptotes (MMA) and Sequential Quadratic Programming (SQP), are widely recognised for their computational efficiency and rapid local convergence; however, their performance may be sensitive to the presence of local extrema. In contrast, metaheuristic approaches such as Particle Swarm Optimisation (PSO) generally provide enhanced global exploration capabilities, albeit often at significantly greater computational expense. This study presents a preliminary investigation of a hybrid optimisation framework termed the Constrained Adaptive Model-based Exploration Optimiser (CAMEO). The proposed approach combines bounded stochastic exploration with constrained local refinement in an attempt to improve robustness within multimodal optimisation landscapes whilst retaining the efficiency associated with deterministic optimisation methods. The performance of the proposed framework was examined using a series of benchmark optimisation problems and compared against MMA, SQP, and PSO. The numerical results indicate that CAMEO is capable of attaining solutions closer to the global optimum in several test cases, whilst maintaining stable convergence characteristics.