Quadratic optimization over a discrete pareto set of a multi-objective linear fractional program

ABSTRACT

In the present paper, an exact algorithm is proposed for maximizing a quadratic function over the efficient set of a multi-objective integer linear fractional programming problem. This method uses a branch and bound search in the decision space and a cutting plane which will significantly shorten the search. A sequence of quadratic programs are solved, the feasible region is iteratively partitioned with two branching constraints or reduced using a cutting plane. We establish theoretical results which prove the effectiveness of this exact method. For illustration, a numerical example and some computational experiments are reported.

Keywords:

• Multi-objective optimization
• global optimization
• integer fractional programming
• quadratic programming

AMS CLASSIFICATIONS:

• 90C29
• 90C32
• 90C26
• 90C10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Authors work was supported by Direction Générale de la Recherche Scientifique et du Développement Technologique (DGRSDT) Grant ID: C0656104.