Towards Multi-tree Methods for Large-Scale Global Optimization

Abstract

© 2020, Springer Nature Switzerland AG. In this paper, we present a new multi-tree approach for solving large scale Global Optimization Problems (GOP), called DECOA (Decomposition-based Outer Approximation). DECOA is based on decomposing a GOP into sub-problems, which are coupled by linear constraints. It computes a solution by alternately solving sub- and master-problems using Branch-and-Bound (BB). Since DECOA does not use a single (global) BB-tree, it is called a multi-tree algorithm. After formulating a GOP as a block-separable MINLP, we describe how piecewise linear Outer Approximations (OA) can be computed by reformulating nonconvex functions as a Difference of Convex functions. This is followed by a description of the main- and sub-algorithms of DECOA, including a decomposition-based heuristic for finding solution candidates. Finally, we present preliminary results with MINLPs and conclusions.