Hybrid Augmented Lagrangian Method for General Constrained Optimization via Evolutionary Algorithms
Neural and Evolutionary Computing
Summary
The authors created a new method called Hybrid Augmented Lagrangian (HyAL) to solve problems where there are many rules (constraints) and complex goals. They combined evolutionary algorithms, which explore many solutions without needing detailed math, with a traditional method that handles constraints well. Their tests showed HyAL finds better solutions than methods that only use evolution or standard numerical techniques, especially in tricky, high-dimensional problems with many local traps. They also checked how different evolutionary methods affect results within their framework. Overall, their approach balances exploration and constraint handling better than existing methods.
Authors
Lampros Printzios, Konstantinos Chatzilygeroudis
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 evolutionary techniques to solve subproblems within the AL iterations, promoting exploration and aiding in the escape from local optima. We conduct extensive experiments on benchmark optimization problems, comparing our method against state-of-the-art optimizers, including IPOPT and CMA-ES, and a standalone evolutionary optimization baseline (with constraint enforcement via penalties). In addition, we evaluate four population-based methods integrated within the AL framework to study the effect of different evolutionary solvers. Our results show that HyAL consistently produces high-quality solutions across the benchmark suite. It outperforms purely evolutionary approaches and scales more effectively to high-dimensional constrained problems, where evolutionary-only methods often struggle. HyAL also surpasses state-of-the-art numerical optimization algorithms on complex landscapes containing numerous local minima and saddle points.