Ren Aihong, Wang Yuping, Xue Xingsi
Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721013 China.
School of Computer Science and Technology, Xidian University, Xi'an, 710071 China.
J Inequal Appl. 2017;2017(1):112. doi: 10.1186/s13660-017-1384-1. Epub 2017 May 15.
This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers. In order to keep as much uncertainty of the original constraint region as possible, the original problem is first converted into an interval bilevel programming problem with interval coefficients in both objective functions only through normal variation of interval number and chance-constrained programming. With the consideration of different preferences of different decision makers, the concept of the preference level that the interval objective function is preferred to a target interval is defined based on the preference-based index. Then a preference-based deterministic bilevel programming problem is constructed in terms of the preference level and the order relation [Formula: see text]. Furthermore, the concept of a preference -optimal solution is given. Subsequently, the constructed deterministic nonlinear bilevel problem is solved with the help of estimation of distribution algorithm. Finally, several numerical examples are provided to demonstrate the effectiveness of the proposed approach.
本文提出了一种新的方法来求解区间双层线性规划问题，其中目标函数和约束条件的所有系数都被视为区间数。为了尽可能保留原始约束区域的不确定性，首先通过区间数的正态变化和机会约束规划，仅将原始问题转化为目标函数中具有区间系数的区间双层规划问题。考虑到不同决策者的不同偏好，基于偏好指数定义了区间目标函数优于目标区间的偏好水平概念。然后根据偏好水平和序关系[公式：见原文]构建了基于偏好的确定性双层规划问题。此外，给出了偏好最优解的概念。随后，借助分布估计算法求解构建的确定性非线性双层问题。最后，提供了几个数值例子来证明所提方法的有效性。
