This paper presents a new two-phase method for solving convex mixed-integer nonlinear programming (MINLP) problems, called Decomposition-based Outer Approximation Algorithm (DECOA). In the first phase, a sequence of linear integer relaxed sub-problems (LP phase) is solved in order to rapidly generate a good linear relaxation of the original MINLP problem. In the second phase, the algorithm solves a sequence of mixed integer linear programming sub-problems (MIP phase). In both phases the outer approximation is improved iteratively by adding new supporting hyperplanes by solving many easier sub-problems in parallel. DECOA is implemented as a part of Decogo (Decomposition-based Global Optimizer), a parallel decomposition-based MINLP solver implemented in Python and Pyomo. Preliminary numerical results based on 70 convex MINLP instances up to 2700 variables show that due to the generated cuts in the LP phase, on average only 2–3 MIP problems have to be solved in the MIP phase.

本文提出了一种新的两阶段方法，用于解决凸混合整数非线性规划（MINLP）问题，称为基于分解的外部近似算法（DECOA）。在第一阶段，解决了一系列线性整数松弛子问题（LP阶段），以便快速生成原始MINLP问题的良好线性松弛。在第二阶段，该算法求解一系列混合整数线性规划子问题（MIP阶段）。在这两个阶段中，通过并行解决许多更简单的子问题，通过添加新的支持超平面来迭代地改善外部逼近。DECOA是作为Decogo（基于分解的全局优化器）的一部分实现的，Decogo是用Python和Pyomo实现的基于并行分解的MINLP求解器。