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

Masar Al-Rabeeah, Ali Al-Hasani, Santosh Kumar, Andrew Eberhard
2020 Journal of Physics, Conference Series  
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
more » ... y 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. This paper develops an exact method for the multi-objective integer programming (MOIP) problem by reformulating the improved recursive method (IRM) [16] which becomes faster than the IRM especially when the number of objective functions is large for a given problem. In a multi-objective linear programming problem, the objective functions are linear and the variables are continuous, therefore, the non-dominated set contains only supported non-dominated points [5] . In the case of multi-objective integer programming and multi-objective mixed integer
doi:10.1088/1742-6596/1490/1/012061 fatcat:og6cu52firbaxcq5kuzmulufhe