Decoupling Numerical and Structural Parameters: An Empirical Study on Adaptive Genetic Algorithms via Deep Reinforcement Learning for the Large-Scale TSP

While deep Reinforcement Learning (deep-RL) has been increasingly applied to parameter control in evolutionary algorithms, rigorous theoretical analysis of parameter control remains largely restricted to single-parameter settings, owing to the difficulty of deriving effective, interpretable multi-parameter policies amenable to formal study. We demonstrate how deep-RL can be leveraged to overcome this barrier, using the (1+($λ$,$λ$))-genetic algorithm optimizing OneMax, one of the few problems where a super-constant speedup of dynamic control has been formally proven, as a representative case study. We first show that standard approaches struggle to converge in this multi-parameter setting, and introduce algorithm-agnostic enhancements targeting action-space decomposition, reward shifting, and long-horizon discounting. With these in place, we compare common deep-RL methods and find that Double Deep Q-Networks uniquely avoid the policy collapse observed in Proximal Policy Optimization, yielding trajectories suitable for downstream analysis. Crucially, we move beyond the ``black-box'' nature of neural networks by distilling the learned behaviors into a transparent, symbolic control policy. This resulting policy does not only offer interpretability for future theoretical analysis but also yields exceptional performance, consistently outperforming existing baselines across a wide range of problem sizes.

Solving high-dimensional structural model updating problems requires an algorithm capable of navigating complex, non-convex landscapes with correlated parameters. Existing hybrid evolutionary algorithms typically rely on static architectures or fixed switching rules, resulting in disjointed search phases. To address this, this study proposes a Deep Reinforcement Learning-governed dynamic DE-CMAES Orchestration (DRL-DCO) algorithm, in which a Deep Deterministic Policy Gradient (DDPG)-based actor-critic agent continuously governs the evolutionary process as a single, unified system rather than a mechanical concatenation of algorithms. Guided by a progression-aware state representation and a diversity-informed reward, the agent fluidly reallocates computational resources between the differencevector-based exploration of Differential Evolution (DE) and the covariance-guided exploitation of CMA-ES, while jointly regulating population size, elite preservation, and a restart mechanism to escape local optima. This allows DRL-DCO to autonomously transition between exploration-dominant, exploitation-dominant, and mixed-strategy regimes across generations. Beyond the training phase, the trained actor can operate in a supervision-free inference mode, where the internalized policy autonomously orchestrates DE and CMA-ES control from observed search states through forward inference alone, without critic evaluation or weight updates, enabling faster deployment while retaining full effectiveness. Validated on high-dimensional single-objective optimization benchmarks and the IASC-ASCE structural health monitoring benchmark, DRL-DCO achieves superior convergence accuracy and robustness compared to state-of-the-art adaptive and hybrid evolutionary algorithms, as well as single-operator DRL-governed baselines.

Adaptive Large Neighborhood Search (ALNS) is a prominent metaheuristic and a widely adopted approach for production and logistics optimization. However, it has long relied on hand-crafted components built on expert experience, which makes development slow and costly to adapt to new problems. This paper proposes a closed-loop, large-language-model-driven evolutionary framework that decouples ALNS and automatically rebuilds all of its components. We break ALNS into seven key modules: destroy, repair, operator selection, weight update, initial solution construction, acceptance rule, and destroy-rate control, and evolve each module through a dedicated task. By incorporating the Multi-dimensional Archive of Phenotypic Elites mechanism, the framework maintains a multi-dimensional elite archive to simultaneously drive the evolution of solution quality and strategic diversity. In addition, we design multiple mechanisms, including parallel and sequential multi-module evolution as well as single-expert-driven and multi-expert-driven evolution, to systematically evaluate the impact of different evolutionary paradigms on algorithm generation performance. Evaluations on Traveling Salesman Problem and Capacitated Vehicle Routing Problem benchmarks demonstrate that evolved algorithms consistently outperform optimized classic ALNS baselines under both fixed-iteration and fixed-time limits. The framework also shows a degree of generalizability and cross-problem transferability. Code analysis also uncovers several counterintuitive yet meaningful design patterns that emerged naturally during evolution, offering practical and theoretical insights for future ALNS design. Finally, comparisons across multiple language models highlight clear differences in their ability to support evolutionary algorithm design, helping guide model selection for real-world engineering use.