Constrained Optimization using an Evolutionary - Augmented Lagrangian approach

Abstract

Constraint Optimization is crucial to fields such as engineering, economics, and robotics, where high-dimensional search spaces and complex constraints are common. Numerical optimization methods, like Interior Point and Sequential Quadratic Programming, achieve strong performance but rely on accurate gradients and good initialization, which are difficult to obtain. Evolutionary Algorithms (EAs) provide gradient-free search and robustness to complex landscapes, but suffer from high computational cost and slow convergence. In this work, we propose a Hybrid Augmented Lagrangian (HyAL) method that combines the constraint-handling capabilities of the AL framework with the exploratory power of population-based search. Evolutionary techniques are used to solve subproblems within the AL iterations, enhancing exploration and enabling escape from local optima. We evaluate four population-based methods within this framework and compare them against a state-of-the-art solver. Results demonstrate that HyAL effectively solves constrained optimization problems, including high-dimensional cases where population-based methods struggle.