Evolutionary multiobjective optimization (EMO) has made significant strides over the past two decades. However, as problem scales and complexities increase, traditional EMO algorithms face substantial performance limitations due to insufficient parallelism and scalability. While most work has focused on algorithm design to address these challenges, little attention has been given to hardware acceleration, thereby leaving a clear gap between EMO algorithms and advanced computing devices, such as GPUs. To bridge the gap, we propose to parallelize EMO algorithms on GPUs via the tensorization methodology. By employing tensorization, the data structures and operations of EMO algorithms are transformed into concise tensor representations, which seamlessly enables automatic utilization of GPU computing. We demonstrate the effectiveness of our approach by applying it to three representative EMO algorithms: NSGA-III, MOEA/D, and HypE. To comprehensively assess our methodology, we introduce a multiobjective robot control benchmark using a GPU-accelerated physics engine. Our experiments show that the tensorized EMO algorithms achieve speedups of up to 1113x compared to their CPU-based counterparts, while maintaining solution quality and effectively scaling population sizes to hundreds of thousands. Furthermore, the tensorized EMO algorithms efficiently tackle complex multiobjective robot control tasks, producing high-quality solutions with diverse behaviors. Source codes are available at https://github.com/EMI-Group/evomo.

翻译：进化多目标优化在过去二十年中取得了显著进展。然而，随着问题规模和复杂性的增加，传统EMO算法因并行性和可扩展性不足而面临显著的性能限制。尽管大多数工作集中于通过算法设计来应对这些挑战，但对硬件加速的关注甚少，从而在EMO算法与先进计算设备（如GPU）之间留下了明显的鸿沟。为弥合这一鸿沟，我们提出通过张量化方法在GPU上并行化EMO算法。通过采用张量化，EMO算法的数据结构和操作被转换为简洁的张量表示，从而无缝实现GPU计算的自动利用。我们通过将该方法应用于三种代表性EMO算法——NSGA-III、MOEA/D和HypE——来证明其有效性。为全面评估我们的方法，我们引入了一个使用GPU加速物理引擎的多目标机器人控制基准测试。实验表明，张量化EMO算法相较于其基于CPU的版本实现了高达1113倍的加速，同时保持了求解质量，并能将种群规模有效扩展至数十万。此外，张量化EMO算法高效处理了复杂的多目标机器人控制任务，生成了具有多样化行为的高质量解。源代码可在 https://github.com/EMI-Group/evomo 获取。