鲁棒多目标线性规划模型及混合遗传算法

摘要

Aiming at solving the uncertain multi-objective linear programming (MOLP) with the coefficients under the ellipsoidal disturbance in objective functions and constrain conditions,this paper proposed a robust MOLP problem under the ellipsoidal disturbance.Based on the assumption that all objective functions needed to acquire the robust solutions,it proposed the theorem and proof.Therefore,converted the original uncertain MOLP to the deterministic MOLP constrained with second-order cone.Then,it designed the mixed strategy algorithm,in which the overall process was multi-objective genetic algorithm and calculated the local optimization by SOCP software Sedumi,to obtain the robust solution set.A numerical example demonstrates the effectiveness of the algorithm.%针对目标函数系数和约束条件系数均在椭球扰动集下的不确定多目标线性规划,提出了椭球扰动集下的鲁棒多目标线性规划问题.基于每个目标均需获得鲁棒解的假设下给出了定理及证明,以此把原问题转换为具有二阶锥约束的确定性多目标优化问题.设计了一种混合策略求解算法,整体流程采用多目标遗传算法,局部采用SOCP优化软件Sedumi进行计算,从而获得不确定多目标线性规划的鲁棒解集,并通过数值算例验证了该算法的有效性.