Search

The multi-objective integer programming problem often occurs in multi-criteria decision-making situations, where the decision variables are integers. In the present paper, we have discussed an algorithm for finding all efficient solutions of a multi-objective integer quadratic programming problem. The proposed algorithm is based on the aspect that efficient solutions of a multi-objective integer quadratic programming problem can be obtained by enumerating ranked solutions of an integer quadratic programming problem. For determining ranked solutions of an integer quadratic programming problem, we have constructed a related integer linear programming problem and from ranked solutions of this integer linear programming problem, ranked solutions of the original integer quadratic programming problem are generated. Theoretically, we have shown that the developed method generates the set of all efficient solutions in a finite number of steps, and numerically we have elaborated the working of our algorithm and compared our results with existing algorithms. Further, we have analyzed that the developed method is efficient for solving a multi-objective integer quadratic programming problem with a large number of constraints, variables and objectives. [ABSTRACT FROM AUTHOR]

The problem of optimizing a linear plus linear fractional function is an important field of search, it is a difficult problem since the linear plus linear fractional function doesn't possess any convexity propriety. In this paper, we propose a method that generates the set of the efficient solutions of multiobjective integer linear plus linear fractional programming problem. Our method consists in Branch-and-Bound exploration combined with cutting plane technique that allows to remove from search inefficient solutions. The cutting plane technique takes into account the inefficiency of a solution in another problem that implies the inefficiency of that solution in our problem and uses this link to reduce the exploration's domain. [ABSTRACT FROM AUTHOR]

In this note we have discussed that a simplex like algorithm to solve a indefinite quadratic fractional programming problem proposed by Mekhilef et al. (Ann Oper Res, 2019. https://doi.org/10.1007/s10479-019-03178-2) fails to find its optimal solution and so it may not generate the actual set of efficient points of the corresponding multi-objective integer indefinite quadratic fractional programs. A counter example in support of this argument is also given. [ABSTRACT FROM AUTHOR]

In this article, a new exact method is proposed to solve a problem, say (ILFP)E, of maximizing a linear fractional function over the integer efficient set of multi-objective integer linear programming problem (MOILP). The method is developed through the branch and cut technique and the continuous linear fractional programming, to come up with an integer optimal solution for problem (ILFP)E without having to explicitly list all efficient solutions of problem (MOILP). The branching process is strengthened by an efficient cut as well as an efficiency test so that a large number of non-efficient feasible solutions can be avoided. Illustrative example and an experimental study are reported to show the merit of this new approach. [ABSTRACT FROM AUTHOR]