in this paper we investigate multi-objective integer linear programming (moilp) problems with unbounded feasible region and introduce recession direction for moilp problems. then we present necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of moilp problems. finally we present some examples with unbounded feasible region and fi...

this paper uses the l1−norm and the concept of the non-dominated vector, topropose a method to find a well-dispersed subset of non-dominated (wdsnd) vectorsof a multi-objective mixed integer linear programming (momilp) problem.the proposed method generalizes the proposed approach by tohidi and razavyan[tohidi g., s. razavyan (2014), determining a well-dispersed subset of non-dominatedvectors of...

generally, an engineering design problem has multiple objective functions. some of these problems can be formulated as multiobjective geometric programming models. on the other hand,often in the real world, coefficients of the objective functions are not known precisely. coefficients may be interpreted as fuzzy numbers, which lead to a multiobjective geometric programming with fuzzy parameters....

In the present paper a bi-objective integer linear programming problem (BILP) is discussed. The main effort in this work to effectively implement ?-constraint method produce complete set of non dominated points. convergence algorithm has been established theoretically. Further comparative study some existing also made.

Abstract In this article we introduce robustness measures in the context of multi-objective integer linear programming problems. The proposed are line with concept decision robustness, which considers uncertainty respect to implementation a specific solution. An efficient solution is considered be robust if many solutions its neighborhood as well. This rather new area research differs from conc...