Enhancement of the Improved Recursive Method for Multi-objective Integer Programming Problem

In this paper, we developed a new algorithm to find the set of a non-dominated points for a multi-objective integer programming problem. The algorithm is an enhancement on the improved recursive method where the authors have used a lexicographic method for analysis. In this approach a sum of two objectives is considered as one weighted sum objective for each iteration. Computational results show that the proposed approach outperforms the currently available results obtained by the improved recursive method with respect to CPU time and the number of integer problems solved to identify all non-dominated points. Many problems such as assignment, knapsack and travelling salesman have been investigated on different sized problems. The benefit of this approach becomes more visible with the increase in the number of objective functions.