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一类带区间系数的分式双层规划问题的遗传算法A Genetic Algorithm for a Class of Fractional Bilevel Programming Problems with Interval Coefficients
区间系数, 分式双层规划, 遗传算法, 最优性条件, 最优解Interval Coefficients, Fractional Bilevel Programming, Genetic Algorithm, Optimality Condition, Optimal Solutions
《Advances in Applied Mathematics》, Vol.4 No.1, 2015-02-27
针对上层为区间系数分式规划、下层为线性规划的一类双层规划问题，提出了一种基于四个适应度评估函数的遗传算法。首先，利用上层系数区间的上下端点将原问题转化成四个系数确定的分式双层规划问题；其次，利用四个确定问题的特征和线性规划的最优性条件设计了一个基于四个目标函数评估的遗传算法，通过该算法获得原问题的最好最优解和最差最优解。最后，数值仿真结果表明，该算法是可行有效的。For a class of bilevel programming problems, in which the upper-level problem is an interval coef-ficients fractional program, whereas the lower-level problem is linear, a genetic algorithm based on four fitness functions is presented. Firstly, four certain programs can be gotten by taking up-per-lower bounds of the coefficient intervals of the upper level objective. In addition, using the characteristics of the four problems and the optimality conditions of linear programming, a genetic algorithm which takes four objective functions as evaluation is designed, and the best and the worst optimal solutions can be obtained by using the proposed algorithm. Finally, the simulation results show that the proposed algorithm is feasible and efficient.