Multi-Criteria Integer Programming Problems

Abstract

Multi-criteria optimization is concerned with mathematical optimizationlproblems having more than one objective function to be optimized simultaneously. In this thesis we have reviewed two different papers based on multi-criteria optimization. In second chapter we have studied a bicriteria integer linear programming problem, where we aim generating all the efficient solutions of a multicriteria optimization problem. An algorithm discussed in this chapter makes use of a scalarization technique, where the bicriteria optimization problem is converted into a single criteria optimization by treating one of the objective function as constraint. In third chapter we obtain optimal integer solution of linear fractional problem over the efficient set of multi-objective integer linear problem. An iterative algorithm is discussed which by making use of efficiency test at each stage of an optimal solution of a constrained integer programming problem is obtained, finds an integer efficient solution of the given problem.