Using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems

An interactive reference point approach for multiobjective mixed-integer programming using branch-and-bound

We propose an interactive reference point approach for multiple objective (mixed) integer linear programming problems that exploits the use of branch-and-bound techniques for solving the scalarizing programs. At each dialogue phase, the decision maker must specify a criterion reference point or just choose an objective function he/she wants to improve in respect to the previous ecient (nondomi...

On Linear Programming, Integer Programming and Cutting Planes

Solving multiobjective linear programming problems using ball center of polytopes

Here‎, ‎we aim to develop a new algorithm for solving a multiobjective linear programming problem‎. ‎The algorithm is to obtain a solution which approximately meets the decision maker's preferences‎. ‎It is proved that the proposed algorithm always converges to a weak efficient solution and at times converges to an efficient solution‎. ‎Numerical examples and a simulation study are used to illu...

Cutting Planes for Mixed Integer Programming

The purpose of this paper is to present an overview of families of cutting planes for mixed integer programming problems. We examine the families of disjunctive inequalities, split cuts, mixed integer rounding inequalities, mixed integer Gomory cuts, intersection cuts, lift-and-project cuts, and reduceand-split cuts. In practice, mixed integer Gomory cuts are very useful in obtaining solutions ...

Interactive Fuzzy Decision Making for Hierarchical Multiobjective Linear Programming Problems Using Reference Membership Intervals

In this paper, we focus on hierarchical multiobjective linear programming problems where multiple decision makers in a hierarchical organization have their own multiple objective linear functions together with common linear constraints, and propose an interactive decision making method to obtain a satisfactory solution which reflects not only the hierarchical relationships between multiple deci...