区间多目标线性优化的功效系数求解方法

针对工程领域中普遍存在的具有不确定参数的多目标优化问题,提出了一种基于功效系数的区间优化模型及求解方法.通过引入增补变量,将含有区间参数的目标函数化为参数确定的形式.建立以功效系数为基础的评价函数,将原多目标优化问题转化为单目标优化问题,然后分别在区间约束条件的最好情况和最差情况下求解,得到设计变量的最优解区间和目标函数的最优值区间.通过工程算例,与传统概率方法的优化结果相比较,验证了所提出优化模型及方法的有效性.

Efficiency coefficient method to solve interval multi-objective linear optimization problems

Based on the efficiency coefficients, a new interval model and its correlative method for solving multi-objective optimization problems with uncertain parameters in the engineering field were proposed. A group of supplementary variables were introduced to transform the interval objective functions into the forms with deterministic parameters. In terms of the evaluation function deduced from efficiency coefficients, the original multi-objective optimization problem was converted into one with a single objective function. The simplified model was solved respectively under the best case and worst case of the interval constraints, and then the ranges of optimal solution and optimal values were easily obtained. Two numerical examples were given to demonstrate the effectiveness of proposed model and algorithm by comparing their results with probabilistic method.