In computer science, there exist a large number of optimization problems defined on graphs, that is to find a best node state configuration or a network structure, such that the designed objective function is optimized under some constraints. However, these problems are notorious for their hardness to solve, because most of them are NP-hard or NP-complete. Although traditional general methods such as simulated annealing (SA), genetic algorithms (GA), and so forth have been devised to these hard problems, their accuracy and time consumption are not satisfying in practice. In this work, we proposed a simple, fast, and general algorithm framework based on advanced automatic differentiation technique empowered by deep learning frameworks. By introducing Gumbel-softmax technique, we can optimize the objective function directly by gradient descent algorithm regardless of the discrete nature of variables. We also introduce evolution strategy to parallel version of our algorithm. We test our algorithm on four representative optimization problems on graph including modularity optimization from network science, Sherrington–Kirkpatrick (SK) model from statistical physics, maximum independent set (MIS) and minimum vertex cover (MVC) problem from combinatorial optimization on graph, and Influence Maximization problem from computational social science. High-quality solutions can be obtained with much less time-consuming compared to the traditional approaches.

中文翻译：

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基于Gumbel-softmax的优化：用于图上优化问题的简单通用框架

在计算机科学中，存在图上定义的大量优化问题，即找到最佳的节点状态配置或网络结构，从而在某些约束下优化设计的目标函数。但是，这些问题因其难以解决而臭名昭著，因为它们大多数是NP硬的或NP完全的。尽管针对这些难题设计了传统的通用方法，例如模拟退火（SA），遗传算法（GA）等，但它们的准确性和时间消耗在实践中并不令人满意。在这项工作中，我们提出了一种简单，快速且通用的算法框架，该框架基于深度学习框架支持的高级自动微分技术。通过引入Gumbel-softmax技术，无论变量的离散性质如何，我们都可以通过梯度下降算法直接优化目标函数。我们还将进化策略引入算法的并行版本。我们在图上的四个代表性优化问题上测试了我们的算法，包括网络科学的模块化优化，统计物理学的Sherrington-Kirkpatrick（SK）模型，图组合优化的最大独立集（MIS）和最小顶点覆盖（MVC）问题，以及从计算社会科学影响最大化问题。与传统方法相比，可以以更少的时间获得高质量的解决方案。我们在图上的四个代表性优化问题上测试了我们的算法，包括网络科学的模块化优化，统计物理学的Sherrington-Kirkpatrick（SK）模型，图组合优化的最大独立集（MIS）和最小顶点覆盖（MVC）问题，以及从计算社会科学影响最大化问题。与传统方法相比，可以以更少的时间获得高质量的解决方案。我们在图上的四个代表性优化问题上测试了我们的算法，包括网络科学的模块化优化，统计物理学的Sherrington-Kirkpatrick（SK）模型，图组合优化的最大独立集（MIS）和最小顶点覆盖（MVC）问题，以及从计算社会科学影响最大化问题。与传统方法相比，可以以更少的时间获得高质量的解决方案。