OPTIMIZING A LINEAR FRACTIONAL FUNCTION OVER AN INTEGER EFFICIENT SET

Over recent decades, significant advancements have been made in optimization over the efficient set. This paper introduces a novel exact algorithm designed to optimize a linear fractional objective function over the integer efficient set of a multi-objective linear programming problem (MOILP). Without enumerating all efficient solutions, our method employs a selection strategy to iteratively improve the primary objective while progressively refining the feasible region and excluding dominated points. By exploring edge connections within the truncated feasible space, the proposed algorithm ensures convergence to the global optimal value in a finite number of iterations. A numerical example demonstrates the algorithm’s effectiveness and practical application. This approach addresses critical challenges in multiobjective integer programming, particularly the nonconvexity of the efficient set and the absence of explicit feasible set descriptions.