Homotopy continuation enhanced branch and bound algorithms for strongly nonconvex <scp>mixed‐integer</scp> nonlinear optimization

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