arXiv:2607.16876v1 Announce Type: new Abstract: Constrained Optimization Problems are crucial in fields such as engineering, economics, and robotics, where high-dimensional search spaces and complex objectives and constraints are common. Numerical optimization methods, including Feasible Direction, Interior Point, and Sequential Quadratic Programming, have shown strong performance in finding feasible local optima, but require accurate analytical gradients and effective initialization, which can be challenging in real-world settings. Evolutionary Algorithms, on the other hand, offer gradient-free search and robustness to noisy landscapes, managing to detect global optima more often than numerical methods, but they often suffer from high computational costs and slow convergence. In this work, we propose a Hybrid Augmented Lagrangian (HyAL) method that integrates the AL framework's constraint-handling strengths with the exploratory power of population-based search. Our approach employs ev...