For the purpose of dealing with uncertainty factors in engineering optimization problems, this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation. The method anal...For the purpose of dealing with uncertainty factors in engineering optimization problems, this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation. The method analyzes the effect of uncertain factors to objective and constraints functions, and then the maximal variations to a solution are calculated. In order to guarantee robust feasibility the maximal variations of constraints are added to original constraints as penalty term; the maximal variation of objective function is taken as a robust index to a solution; linear physical programming is used to adjust the values of quality characteristic and quality variation, and then a bi-level mathematical robust optimal model is constructed. The method does not require presumed probability distribution of uncertain factors or continuous and differentiable of objective and constraints functions. To demonstrate the proposed method, the design of the two-bar structure acted by concentrated load is presented. In the example the robustness of the normal stress, feasibility of the total volume and the buckling stress are studied. The robust optimal design results show that in the condition of maintaining feasibility robustness, the proposed approach can obtain a robust solution which the designer is satisfied with the value of objective function and its variation.展开更多
In this paper, the problem of program performance scheduling with accepting strategy is studied. Considering the uncertainty of actual situation, the duration of a program is expressed as a bounded interval. Firstly, ...In this paper, the problem of program performance scheduling with accepting strategy is studied. Considering the uncertainty of actual situation, the duration of a program is expressed as a bounded interval. Firstly, we decide which programs are accepted. Secondly, the risk preference coefficient of the decision maker is introduced. Thirdly, the min-max robust optimization model of the uncertain program show scheduling is built to minimize the performance cost and determine the sequence of these programs. Based on the above model, an effective algorithm for the original problem is proposed. The computational experiment shows that the performance’s cost (revenue) will increase (decrease) with decision maker’s risk aversion.展开更多
The Dantzig/Wolfe linear programming decomposition algorithm has had important economicinterpretations as well as a widespread impact on solving large scale linear programming problem.Inthis paper we consider a simila...The Dantzig/Wolfe linear programming decomposition algorithm has had important economicinterpretations as well as a widespread impact on solving large scale linear programming problem.Inthis paper we consider a similar underlying structure,where however there is only one couplinginequality or equation.With this simplification,we demonstrate how to achieve an equitable partitionof the overall coupling resource to individual subproblem constraints through a simple iterationprocedure which appears to be very efficient.展开更多
基于鲁棒优化理论的机组组合问题存在解的保守性较大,计算过程复杂等缺点。该文基于改进轻鲁棒模型,建立了新型的风–火电机组组合新模型,并推导出其混合整数线性规划(mixed integer linear programming,MILP)对应式。该模型通过弃风变...基于鲁棒优化理论的机组组合问题存在解的保守性较大,计算过程复杂等缺点。该文基于改进轻鲁棒模型,建立了新型的风–火电机组组合新模型,并推导出其混合整数线性规划(mixed integer linear programming,MILP)对应式。该模型通过弃风变量实现了风电出力调度,并通过设备的防止过度过载和连续过载约束,实现了对设备短时过载能力的安全利用,改善了保守性;所推得的MILP对应式为一个线性确定性优化问题,可以直接求解,不会像其他方法那样因对偶变换产生非线性项而不易求解,所以计算效率明显提高。该文的算例证明了文中所提的ILR-UC模型及其MILP对应式的有效性。展开更多
基金supported by Program for New Century Excellent Talents in University, Ministry of Education of China (Grant No. NCET- 05-0285 )
文摘For the purpose of dealing with uncertainty factors in engineering optimization problems, this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation. The method analyzes the effect of uncertain factors to objective and constraints functions, and then the maximal variations to a solution are calculated. In order to guarantee robust feasibility the maximal variations of constraints are added to original constraints as penalty term; the maximal variation of objective function is taken as a robust index to a solution; linear physical programming is used to adjust the values of quality characteristic and quality variation, and then a bi-level mathematical robust optimal model is constructed. The method does not require presumed probability distribution of uncertain factors or continuous and differentiable of objective and constraints functions. To demonstrate the proposed method, the design of the two-bar structure acted by concentrated load is presented. In the example the robustness of the normal stress, feasibility of the total volume and the buckling stress are studied. The robust optimal design results show that in the condition of maintaining feasibility robustness, the proposed approach can obtain a robust solution which the designer is satisfied with the value of objective function and its variation.
文摘In this paper, the problem of program performance scheduling with accepting strategy is studied. Considering the uncertainty of actual situation, the duration of a program is expressed as a bounded interval. Firstly, we decide which programs are accepted. Secondly, the risk preference coefficient of the decision maker is introduced. Thirdly, the min-max robust optimization model of the uncertain program show scheduling is built to minimize the performance cost and determine the sequence of these programs. Based on the above model, an effective algorithm for the original problem is proposed. The computational experiment shows that the performance’s cost (revenue) will increase (decrease) with decision maker’s risk aversion.
文摘The Dantzig/Wolfe linear programming decomposition algorithm has had important economicinterpretations as well as a widespread impact on solving large scale linear programming problem.Inthis paper we consider a similar underlying structure,where however there is only one couplinginequality or equation.With this simplification,we demonstrate how to achieve an equitable partitionof the overall coupling resource to individual subproblem constraints through a simple iterationprocedure which appears to be very efficient.
文摘基于鲁棒优化理论的机组组合问题存在解的保守性较大,计算过程复杂等缺点。该文基于改进轻鲁棒模型,建立了新型的风–火电机组组合新模型,并推导出其混合整数线性规划(mixed integer linear programming,MILP)对应式。该模型通过弃风变量实现了风电出力调度,并通过设备的防止过度过载和连续过载约束,实现了对设备短时过载能力的安全利用,改善了保守性;所推得的MILP对应式为一个线性确定性优化问题,可以直接求解,不会像其他方法那样因对偶变换产生非线性项而不易求解,所以计算效率明显提高。该文的算例证明了文中所提的ILR-UC模型及其MILP对应式的有效性。
