Real-world applications involve various discrete optimization problems. Designing a specialized optimizer for each of these problems is challenging, typically requiring significant domain knowledge and human efforts. Hence, developing general-purpose optimizers as an off-the-shelf tool for a wide range of problems has been a long-standing research target. This article introduces MEGO, a novel general-purpose neural optimizer trained through a fully data-driven learning-to-optimize (L2O) approach. MEGO consists of a mixture-of-experts trained on experiences from solving training problems and can be viewed as a foundation model for optimization problems with binary decision variables. When presented with a problem to solve, MEGO actively selects relevant expert models to generate high-quality solutions. MEGO can be used as a standalone sample-efficient optimizer or in conjunction with existing search methods as an initial solution generator. The generality of MEGO is validated across six problem classes, including three classic problem classes and three problem classes arising from real-world applications in compilers, network analysis, and 3D reconstruction. Trained solely on classic problem classes, MEGO performs very well on all six problem classes, significantly surpassing widely used general-purpose optimizers in both solution quality and efficiency. In some cases, MEGO even surpasses specialized state-of-the-art optimizers. Additionally, MEGO provides a similarity measure between problems, yielding a new perspective for problem classification. In the pursuit of general-purpose optimizers through L2O, MEGO represents an initial yet significant step forward.

翻译：现实应用涉及多种离散优化问题。为每个问题设计专门的优化器具有挑战性，通常需要大量领域知识和人力投入。因此，开发可作为现成工具适用于广泛问题的通用优化器，一直是长期的研究目标。本文介绍MEGO，一种通过完全数据驱动的学习优化方法训练的新型通用神经优化器。MEGO包含一个基于解决训练问题经验训练的专家混合模型，可被视为处理二元决策变量优化问题的基础模型。当面对待解决问题时，MEGO主动选择相关专家模型以生成高质量解。MEGO可作为独立的样本高效优化器使用，或与现有搜索方法结合作为初始解生成器。MEGO的通用性在六个问题类别上得到验证，包括三个经典问题类别以及源自编译器、网络分析和三维重建实际应用的三个问题类别。仅基于经典问题类别训练的MEGO在所有六个问题类别上均表现优异，在解质量和效率方面显著超越广泛使用的通用优化器。在某些情况下，MEGO甚至超越了专门的先进优化器。此外，MEGO提供了问题间的相似性度量，为问题分类提供了新视角。在通过学习优化方法追求通用优化器的进程中，MEGO代表了初步但意义重大的进展。