An interval sequential linear programming for nonlinear robust optimization problems
•An interval sequential linear programming for nonlinear robust optimization is proposed.•An approximate possibility sensitivity is proposed to efficiently obtain the partial derivatives of the constraints.•A novel iterative mechanism is established to improve the convergence rate.•Two numerical exa...
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| Vydáno v: | Applied Mathematical Modelling Ročník 107; s. 256 - 274 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
Elsevier Inc
01.07.2022
Elsevier BV |
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| ISSN: | 0307-904X, 1088-8691, 0307-904X |
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| Abstract | •An interval sequential linear programming for nonlinear robust optimization is proposed.•An approximate possibility sensitivity is proposed to efficiently obtain the partial derivatives of the constraints.•A novel iterative mechanism is established to improve the convergence rate.•Two numerical examples and two practical engineering problems are applied to verify the accuracy and efficiency.
In this paper, interval sequential linear programming (ISLP) is proposed to solve nonlinear robust optimization (RO). The main idea of the programming is to transform the uncertain optimization into several possibility-sensitivity analyses and deterministic linear optimization problems that are sequentially solved. At each cycle, a possibility-sensitivity analysis method is proposed to obtain the approximate partial derivatives of the uncertain constraints at the current design point, based on which a deterministic linear optimization model is constructed and the design point is updated by solving the linear optimization. Moreover, an iterative mechanism is created to adaptively update the design space and improve the convergence rate. Finally, two numerical examples and two practical engineering problems are applied to verify the accuracy and efficiency of the proposed method. |
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| AbstractList | •An interval sequential linear programming for nonlinear robust optimization is proposed.•An approximate possibility sensitivity is proposed to efficiently obtain the partial derivatives of the constraints.•A novel iterative mechanism is established to improve the convergence rate.•Two numerical examples and two practical engineering problems are applied to verify the accuracy and efficiency.
In this paper, interval sequential linear programming (ISLP) is proposed to solve nonlinear robust optimization (RO). The main idea of the programming is to transform the uncertain optimization into several possibility-sensitivity analyses and deterministic linear optimization problems that are sequentially solved. At each cycle, a possibility-sensitivity analysis method is proposed to obtain the approximate partial derivatives of the uncertain constraints at the current design point, based on which a deterministic linear optimization model is constructed and the design point is updated by solving the linear optimization. Moreover, an iterative mechanism is created to adaptively update the design space and improve the convergence rate. Finally, two numerical examples and two practical engineering problems are applied to verify the accuracy and efficiency of the proposed method. In this paper, interval sequential linear programming (ISLP) is proposed to solve nonlinear robust optimization (RO). The main idea of the programming is to transform the uncertain optimization into several possibility-sensitivity analyses and deterministic linear optimization problems that are sequentially solved. At each cycle, a possibility-sensitivity analysis method is proposed to obtain the approximate partial derivatives of the uncertain constraints at the current design point, based on which a deterministic linear optimization model is constructed and the design point is updated by solving the linear optimization. Moreover, an iterative mechanism is created to adaptively update the design space and improve the convergence rate. Finally, two numerical examples and two practical engineering problems are applied to verify the accuracy and efficiency of the proposed method. |
| Author | Fu, Chunming Liu, Haibo Tang, Jiachang Mi, Chengji |
| Author_xml | – sequence: 1 givenname: Jiachang surname: Tang fullname: Tang, Jiachang organization: Department of Mechanical Engineering, Hunan University of Technology, Zhuzhou City, 412007, PR China – sequence: 2 givenname: Chunming surname: Fu fullname: Fu, Chunming organization: College of Mechanical Engineering, University of South China, Hengyang City, 421001, PR China – sequence: 3 givenname: Chengji surname: Mi fullname: Mi, Chengji email: michengji_86@126.com organization: Department of Mechanical Engineering, Hunan University of Technology, Zhuzhou City, 412007, PR China – sequence: 4 givenname: Haibo surname: Liu fullname: Liu, Haibo organization: Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment, Hunan University of Science and Technology, Xiangtan City, 411201, PR China |
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| Keywords | Interval uncertainty Robust optimization Sensitivity analysis Sequential linear programming Reliability-based possibility degree of interval (RPDI) |
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| Snippet | •An interval sequential linear programming for nonlinear robust optimization is proposed.•An approximate possibility sensitivity is proposed to efficiently... In this paper, interval sequential linear programming (ISLP) is proposed to solve nonlinear robust optimization (RO). The main idea of the programming is to... |
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| SubjectTerms | Interval uncertainty Iterative methods Linear programming Optimization models Reliability-based possibility degree of interval (RPDI) Robust optimization Robustness (mathematics) Sensitivity analysis Sequential linear programming |
| Title | An interval sequential linear programming for nonlinear robust optimization problems |
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