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Process synthesis using rigorous unit operation models is highly desirable to identify the most efficient pathway for sustainable production of fuels and value-added chemicals. However, it often leads to a large-scale strongly nonlinear and nonconvex mixed integer nonlinear programming (MINLP) model. 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 optimal solution 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 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 lower computational effort required for the same locally optimal solution.
In this paper, we have developed a parallel branch and bound algorithm which computes the maximal structured singular value $mu$ without tightly bounding $mu$ for each frequency and thus significantly reduce the computational complexity.
The talent scheduling problem is a simplified version of the real-world film shooting problem, which aims to determine a shooting sequence so as to minimize the total cost of the actors involved. In this article, we first formulate the problem as an
Quasi branch and bound is a recently introduced generalization of branch and bound, where lower bounds are replaced by a relaxed notion of quasi-lower bounds, required to be lower bounds only for sub-cubes containing a minimizer. This paper is devote
We propose a new algorithm for numerical path tracking in polynomial homotopy continuation. The algorithm is `robust in the sense that it is designed to prevent path jumping and in many cases, it can be used in (only) double precision arithmetic. It
Electronic phased-array radars offer new possibilities for radar search pattern optimization by using bi-dimensional beam-forming and beam-steering. Radar search pattern optimization can be approximated as a set cover problem and solved using integer