This study investigates a novel interval linear programming based on probabilistic dominance. Firstly, the definition of interval linear programming is briefly reviewed. Then a new interval linear programming model is presented based on probabilistic dominance. The probabilistic dominance index treats the intervals as uniformly distributed variables and the interval inequality relation is further defined by probability. To deal with non-linearity in probabilistic dominance index, sequential quadratic programming is used to solve the problem and the performance measure approach is proposed to overcome the convergence difficulties. The determination and sensitivity analysis of the target performance measure are discussed to assess the sequential quadratic programming algorithm. Meanwhile, the extension of the proposed method to fuzzy interval linear programming is discussed. Furthermore, the proposed method is applied to the design of the plane truss structure with interval parameters. Finally, the effectiveness and rationality of the developed method are demonstrated by two mathematical examples and one interval parametric plane truss structure optimization example.

本研究研究了一种基于概率优势的新型区间线性规划。首先，简要回顾了区间线性规划的定义。然后提出了一种基于概率优势的区间线性规划模型。概率优势指数将区间视为均匀分布的变量，区间不等式关系进一步由概率定义。针对概率优势指数的非线性问题，采用序列二次规划求解，并提出性能度量方法来克服收敛困难。讨论了目标性能度量的确定和敏感性分析，以评估顺序二次规划算法。同时，讨论了该方法对模糊区间线性规划的推广。此外，将该方法应用于带区间参数的平面桁架结构设计。最后通过两个数学算例和一个区间参数平面桁架结构优化算例证明了所开发方法的有效性和合理性。