灰色二层多目标线性规划问题及其解法

针对二层多目标线性规划问题,结合灰色系统的特性,提出了一般灰色二层多目标线性规划问题,并给出了模型的相关定义和定理.针对漂移型灰色二层多目标线性规划问题,提出一种具有全局收敛性质的求解算法.首先通过线性加权模理想点法把多目标转化为单目标;然后当可行域为非空紧集时,利用库恩塔克条件把双层转化为单层,再利用粒子群算法搜索单目标单层线性规划即可得到原问题的解;最后通过算例表明了该算法的有效性.

Problem of grey bilevel multi-objective linear programming and its algorithm

Based on the bilevel multi-objective linear programming and the characteristic of grey system, the general gray bilevel multi-objective linear programming problem with its relevant definition and theorem are given. A globally convergent algorithm is given to solve the drifting grey bilevel multi-objective linear programming problem. Firstly, multi-objective programming is transformed into single programming by using linear plus power ideal point algorithm. Then, the grey bilevel linear programming can be transformed into a grey linear programming problem by its Kuhn-Tucker condition when the feasible domain is nonempty compact aggregate. So these problems can be solved by using the particle swarm optimization algorithm to obtain the solution of the gray bilevel multi-objective linear programming problem. Finally, an example shows the effectiveness of the proposed algorithm.