A new methodology for the general multiparametric mixed-integer linear programming (MILP) problems
A new methodology for the general multiparametric mixed-integer linear programming (MILP) problems
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DOI：
10.1021/ie070148s
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发表时间：
2007-07-18
影响因子：
4.2
通讯作者：
Ierapetritou, Marianthi G.
中科院分区：
文献类型：
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作者：
Li, Zukui;Ierapetritou, Marianthi G.
针对多参数混合整数线性规划(MpMILP)问题，提出了一种同时具有左(LHS)、右(RHS)和目标函数系数不确定的多参数混合整数线性规划问题的通用算法。该算法是基于一般的多参数线性规划(MpLP)算法，该算法是利用标准线性规划(LP)问题的最优性条件导出的。拟议框架的目的是提出一个通用框架，以解决过程工程问题中的不同不确定性。此外，本文还讨论了将LHS不确定性作为连续变量系数包含在优化模型中的特殊问题的解，指出由于目标函数和非凸临界区的非线性，恢复大规模问题的严格解所需的计算复杂性很高。通过几个算例说明了该方法的有效性和适用性。
In this paper, a general algorithm is developed to address the multiparametric mixed-integer linear programming (mpMILP) problem with uncertain parameters in the left-hand side (LHS), right-hand side (RHS), and objective function coefficients simultaneously. The algorithm is based on a general multiparametric linear programming (mpLP) algorithm, which is derived using the optimality conditions of standard linear programming (LP) problem. The intent of the proposed framework is to propose a general framework to address different uncertainties in the process engineering problems. In addition, the paper also discusses the solution of the special problem where LHS uncertainty is included in the optimization model as a coefficient of continuous variable, and it notes the high computational complexity needed to retrieve the rigorous solution of large-scale problems, because of the nonlinearities of the objective function and nonconvex critical regions. Several numerical examples are presented to illustrate the effectiveness and applicability of the proposed method.