2024/02/02 by Bencheikh, Ali, Moulai, Mustapha, Badaoui, Ilies
#90C10 #90C20 #90C29 #90C32 #90C57 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2402.01310
In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a preference function to optimize over the efficient set of a multi-objective problem. The algorithm employs a branch-and-cut approach, which involves: (1) exploring the solution space using a branch-and-bound strategy in the decision space, and (2) eliminating inefficient solutions using a cutting plane technique with efficient cuts constructed from the non-increasing directions of objective functions. Additionally, integral tests are incorporated to further ensure the efficiency of the obtained solutions.We present a comprehensive example, accompanied by a step-by-step resolution, to demonstrate the functioning of the algorithm.