A new nonlinear interval programming method for uncertain problems with dependent interval variables
A new nonlinear interval programming method for uncertain problems with dependent interval variables
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DOI：
10.1016/j.ejor.2014.03.029
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发表时间：
2014-10
期刊：
影响因子：
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通讯作者：
C. Jiang;Zhiguo Zhang;Q. F. Zhang;Xue Han;H. Xie;J. Liu
中科院分区：
文献类型：
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作者：
C. Jiang;Zhiguo Zhang;Q. F. Zhang;Xue Han;H. Xie;J. Liu
本文提出了一种新的非线性区间规划方法，可用于处理区间变量之间存在依赖关系的不确定优化问题。不确定域采用多维平行六面体区间模型建模。该模型描述了单变量的不确定性使用的边际区间和区间变量之间的依赖程度使用相关角和相关系数。基于区间的序关系和区间的可能度，将不确定性优化问题转化为确定性双层嵌套优化问题。然后引入仿射坐标将多维平行六面体区间模型的不确定域转化为标准区间不确定域。一个高效的迭代算法，制定了一个有效的解决方案的多层排料优化问题后转换。通过三个算例验证了该方法的有效性。
This paper proposes a new nonlinear interval programming method that can be used to handle uncertain optimization problems when there are dependencies among the interval variables. The uncertain domain is modeled using a multidimensional parallelepiped interval model. The model depicts single-variable uncertainty using a marginal interval and depicts the degree of dependencies among the interval variables using correlation angles and correlation coefficients. Based on the order relation of interval and the possibility degree of interval, the uncertain optimization problem is converted to a deterministic two-layer nesting optimization problem. The affine coordinate is then introduced to convert the uncertain domain of a multidimensional parallelepiped interval model to a standard interval uncertain domain. A highly efficient iterative algorithm is formulated to generate an efficient solution for the multi-layer nesting optimization problem after the conversion. Three computational examples are given to verify the effectiveness of the proposed method.