Optimizing a function over the efficient set of a multiojective problem plays an important role in many fields of application. This problem arises whenever the decision maker wants to select the efficient solution that optimizes his utility function. Several methods are proposed in literature to deal with the problem of optimizing a linear function over the efficient set of a multiobjective integer linear program MOILFP. However, in many real-world problems, the objective functions or the utility function are nonlinear. In this paper, we propose an exact method to optimize a quadratic function over the efficient set of a multiobjective integer linear fractional program MOILFP. The proposed method solves a sequence of quadratic integer problems. Where, at each iteration, the search domain is reduced s6uccessively, by introducing cuts, to eliminate dominated solutions. We conducted a computational experiment, by solving randomly generated instances, to analyze the performance of the proposed method.

在多目标问题的有效集合上优化函数在许多应用领域中发挥着重要作用。每当决策者想要选择优化其效用函数的有效解决方案时，就会出现这个问题。文献中提出了几种方法来处理在多目标整数线性程序MOILFP的有效集合上优化线性函数的问题。然而，在许多实际问题中，目标函数或效用函数是非线性的。在本文中，我们提出了一种精确的方法来优化多目标整数线性分数程序MOILFP的有效集合上的二次函数. 所提出的方法解决了一系列二次整数问题。其中，在每次迭代中，通过引入切割，搜索域逐渐减少 s6，以消除主导解决方案。我们通过求解随机生成的实例进行了计算实验，以分析所提出方法的性能。