CAJ | 학술논문

针对一类上层为线性规划、下层为线性分式规划的区间系数双层规划问题，提出了一种基于系数取值区间搜索的遗传算法。首先，对下层目标系数进行个体编码，使得对每一编码个体，原问题被转化为确定的双层规划问题；其次，利用分式规划的最优性条件求解得到确定性问题；最后，算法通过不断进化下层目标系数找到最好最优解和最差最优解。数值仿真结果表明，该算法是可行并有效的。
침대일류상층위선성규화、하층위선성분식규화적구간계수쌍층규화문제，제출료일충기우계수취치구간수색적유전산법。수선，대하층목표계수진행개체편마，사득대매일편마개체，원문제피전화위학정적쌍층규화문제；기차，이용분식규화적최우성조건구해득도학정성문제；최후，산법통과불단진화하층목표계수조도최호최우해화최차최우해。수치방진결과표명，해산법시가행병유효적。
For a class of bilevel programming problems with interval coefficients, in which the upper-level problem is linear, whereas the lower-level problem is a linear fractional program, a genetic algorithm was presented by taking the coefficient intervals as the searching space. Firstly, individuals could be gotten by encoding the lower-level objective coefficients such that the original problem could be transformed into certain bilevel programs for each encoded individual; in addition, the optimality results were used to solve these certain problems; finally, the best and the worst solutions could be obtained by evolving the coefficients of the lower level objective. The simulation results show that the proposed algorithm is feasible and efficient.