Optimizing a linear function over the efficient set of a multiple objective integer quadratic program

In this paper, we investigate the optimization of a function over the efficient set of a Multiple Objective Integer Quadratic Program (MOIQP). The method described employs a branch-and-cut approach to address the problem. At every node within the search tree, a profound cut is derived by considering the ascending trends of the criteria. This cut enables the removal of branches where the associated sub-problems don’t contain efficient solutions. The proposed methodology is illustrated in an example. Extensive numerical experiments are conducted to demonstrate the method’s effectiveness against state-of-the-art methods.