# Homotopy Continuation Enhanced Branch and Bound Algorithms for Strongly Nonconvex Mixed-Integer Nonlinear Programming Problems

arXiv: https://arxiv.org/abs/2109.07379 · HTML: https://mlsanity.com/paper/2109.07379/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2021.

## Built on by (most cited first, 1 of 1)

- [Mixed-Integer Optimal Control via Reinforcement Learning: A Case Study on Hybrid Electric Vehicle Energy Management](https://mlsanity.com/paper/2305.01461/) (2023)

## Abstract (arXiv)

Large-scale strongly nonlinear and nonconvex mixed-integer nonlinear programming (MINLP) models frequently appear in optimisation-based process synthesis, integration, intensification, and process control. However, they are usually difficult to solve by existing algorithms within an acceptable time. In this work, we propose two robust homotopy continuation enhanced branch and bound (HCBB) algorithms (denoted as HCBB-FP and HCBB-RB) where the homotopy continuation method is employed to gradually approach the optimum of the NLP subproblem at a node from the solution at its parent node. A variable step length is adapted to effectively balance feasibility and computational efficiency. The computational results from solving four existing process synthesis problems demonstrate that the proposed HCBB algorithms can find the same optimal solution from different initial points, while the existing MINLP algorithms fail or find much worse solutions. In addition, HCBB-RB is superior to HCBB-FP due to the much lower computational effort required for the same locally optimal solution.