Homotopy Continuation Enhanced Branch and Bound Algorithms for Strongly Nonconvex Mixed‐Integer Nonlinear Optimisation

A feasible path-based branch and bound algorithm for strongly nonconvex MINLP problems

In this paper, a feasible path-based branch and bound (B&B) algorithm is proposed to solve mixed-integer nonlinear programming problems with highly nonconvex nature through integration of the previously proposed hybrid feasible-path optimisation algorithm and the branch and bound method. The main advantage of this novel algorithm is that our previously proposed hybrid steady-state and time-relaxation-based optimisation algorithm is employed to solve a nonlinear programming (NLP) subproblem at each node during B&B. The solution from a parent node in B&B is used to initialize the NLP subproblems at the child nodes to improve computational efficiency. This approach allows circumventing complex initialisation procedure and overcoming difficulties in convergence of process simulation. The capability of the proposed algorithm is illustrated by several process synthesis and intensification problems using rigorous models.