AI 中文总结
研究一般约束优化问题，提出混合增广拉格朗日（HyAL）方法，结合增广拉格朗日框架与进化算法优势，解决迭代子问题。实验表明该方法在基准测试中表现出色，优于纯进化方法和先进数值算法，能有效处理高维约束问题。
AI 中文摘要
约束优化问题在工程、经济和机器人等领域至关重要，其搜索空间高维且目标与约束复杂。数值优化方法虽能找到可行局部最优解，但需精确解析梯度和有效初始化，在实际场景中颇具挑战。进化算法可无梯度搜索且抗噪声，但计算成本高、收敛慢。本文提出混合增广拉格朗日（HyAL）方法，将增广拉格朗日框架的约束处理优势与基于种群搜索的探索能力相结合。通过进化技术解决增广拉格朗日迭代中的子问题，促进探索并助于逃离局部最优。在基准优化问题上进行大量实验，与包括IPOPT和CMA - ES在内的先进优化器及独立进化优化基线比较。结果表明，HyAL在基准测试中始终能产生高质量解，优于纯进化方法，在高维约束问题上扩展性更好，在复杂景观上也超越了先进数值优化算法。
英文摘要
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.
Comments16 pages, 5 figures
