Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and might lead to a suboptimal solution to the original problem. In addition, the intermediate solutions, often ignored by classic homotopy optimization, could be useful for many real-world applications. In this work, we propose a novel model-based approach to learn the whole continuation path for homotopy optimization, which contains infinite intermediate solutions for any surrogate subproblems. Rather than the classic unidirectional easy-to-hard optimization, our method can simultaneously optimize the original problem and all surrogate subproblems in a collaborative manner. The proposed model also supports real-time generation of any intermediate solution, which could be desirable for many applications. Experimental studies on different problems show that our proposed method can significantly improve the performance of homotopy optimization and provide extra helpful information to support better decision-making.

翻译：同伦优化是一种传统方法，通过求解一系列由易到难的代理子问题来处理复杂优化问题。然而，该方法对连续进度表的设计非常敏感，并可能导致原问题求解陷入次优解。此外，经典同伦优化中常被忽略的中间解，对许多实际应用可能具有价值。本文提出了一种新颖的基于模型的方法，用于学习同伦优化的完整连续路径，其中包含任意代理子问题的无限个中间解。与经典的单向由易到难优化不同，我们的方法能够以协作方式同时优化原问题及所有代理子问题。所提出的模型还支持实时生成任意中间解，这在许多应用中具有重要价值。在不同问题上的实验研究表明，我们的方法能显著提升同伦优化的性能，并额外提供有助于决策的支持信息。