Multi-Objective Mobile Damped Wave Algorithm (MOMDWA): A Novel Approach For Quantum System Control

In this paper, we introduce a novel multi-objective optimization algorithm, the Multi-Objective Mobile Damped Wave Algorithm (MOMDWA), specifically designed to address complex quantum control problems. Our approach extends the capabilities of the original Mobile Damped Wave Algorithm (MDWA) by incorporating multiple objectives, enabling a more comprehensive optimization process. We applied MOMDWA to three quantum control scenarios, focusing on optimizing the balance between control fidelity, energy consumption, and control smoothness. The results demonstrate that MOMDWA significantly enhances quantum control efficiency and robustness, achieving high fidelity while minimizing energy use and ensuring smooth control pulses. This advancement offers a valuable tool for quantum computing and other domains requiring precise, multi-objective control.

Graph Neural Networks Are Evolutionary Algorithms

In this paper, we reveal the intrinsic duality between graph neural networks (GNNs) and evolutionary algorithms (EAs), bridging two traditionally distinct fields. Building on this insight, we propose Graph Neural Evolution (GNE), a novel evolutionary algorithm that models individuals as nodes in a graph and leverages designed frequency-domain filters to balance global exploration and local exploitation. Through the use of these filters, GNE aggregates high-frequency (diversity-enhancing) and low-frequency (stability-promoting) information, transforming EAs into interpretable and tunable mechanisms in the frequency domain. Extensive experiments on benchmark functions demonstrate that GNE consistently outperforms state-of-the-art algorithms such as GA, DE, CMA-ES, SDAES, and RL-SHADE, excelling in complex landscapes, optimal solution shifts, and noisy environments. Its robustness, adaptability, and superior convergence highlight its practical and theoretical value. Beyond optimization, GNE establishes a conceptual and mathematical foundation linking EAs and GNNs, offering new perspectives for both fields. Its framework encourages the development of task-adaptive filters and hybrid approaches for EAs, while its insights can inspire advances in GNNs, such as improved global information propagation and mitigation of oversmoothing. GNE's versatility extends to solving challenges in machine learning, including hyperparameter tuning and neural architecture search, as well as real-world applications in engineering and operations research. By uniting the dynamics of EAs with the structural insights of GNNs, this work provides a foundation for interdisciplinary innovation, paving the way for scalable and interpretable solutions to complex optimization problems.