scholarly journals Homotopy Continuation Enhanced Branch and Bound Algorithms for Process Synthesis Using Rigorous Unit Operation Models

2021 ◽  
Author(s):  
Yingjie Ma ◽  
Jie Li
Keyword(s):  
Branch And Bound ◽  
Large Scale ◽  
Continuation Method ◽  
Optimal Solution ◽  
Value Added ◽  
Mixed Integer ◽  
Process Synthesis ◽  
Homotopy Continuation ◽  
Unit Operation ◽  
Homotopy Continuation Method

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.

scholarly journals Research on HC-LSSVM Model for Soft Soil Settlement Prediction Based on Homotopy Continuation Method

2021 ◽  
Vol 11 (22) ◽  
pp. 10666
Author(s):  
Guangjun Cui ◽  
Shenghua Xiong ◽  
Cuiying Zhou ◽  
Zhen Liu
Keyword(s):  
Soft Soil ◽  
Continuation Method ◽  
Engineering Application ◽  
Optimal Solution ◽  
Least Square ◽  
Support Vector ◽  
Model Parameters ◽  
Homotopy Continuation ◽  
Homotopy Continuation Method ◽  
Soil Settlement

Prediction of soft soil settlement is an important research topic in the field of civil engineering, and the least square support vector machine is one of the commonly used prediction methods at present. Nonetheless, the existing LSSVM models have problems of low search efficiency in the search process and lack of global optimal solution in the search results. In order to solve this problem, based on the leave-one-out cross-validation method, the homotopy continuation method was used to optimize the LSSVM model parameters, and then the HC-LSSVM model was constructed with the goal of minimizing the sum of squares of the prediction error of the full sample retention one. Finally, the rationality and correctness of the model are verified by engineering application. The results show that the HC-LSSVM model constructed in this study can accurately predict the settlement of soft ground, which is superior to the common LSSVM model and solves the problem that the parameters of LSSVM model cannot be solved optimally. The research results provide a new method for prediction of soft soil settlement.

scholarly journals New collocation path-following approach for the optimal shape parameter using Kernel method

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Zouhair Saffah ◽  
Abdelaziz Timesli ◽  
Hassane Lahmam ◽  
Abderrahim Azouani ◽  
Mohamed Amdi
Keyword(s):  
Shape Parameter ◽  
Kernel Method ◽  
Continuation Method ◽  
Path Following ◽  
High Order ◽  
Homotopy Continuation ◽  
Homotopy Continuation Method ◽  
Optimal Value ◽  
Rbf Kernel ◽  
Order Algorithm

AbstractThe goal of this work is to develop a numerical method combining Radial Basic Functions (RBF) kernel and a high order algorithm based on Taylor series and homotopy continuation method. The local RBF approximation applied in strong form allows us to overcome the difficulties of numerical integration and to treat problems of large deformations. Furthermore, the high order algorithm enables to transform the nonlinear problem to a set of linear problems. Determining the optimal value of the shape parameter in RBF kernel is still an outstanding research topic. This optimal value depends on density and distribution of points and the considered problem for e.g. boundary value problems, integral equations, delay-differential equations etc. These have been extensively attempts in literature which end up choosing this optimal value by tests and error or some other ad-hoc means. Our contribution in this paper is to suggest a new strategy using radial basis functions kernel with an automatic reasonable choice of the shape parameter in the nonlinear case which depends on the accuracy and stability of the results. The computational experiments tested on some examples in structural analysis are performed and the comparison with respect to the state of art algorithms from the literature is given.

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