Improved solution to the non-domination level update problem

In this paper, we present two approaches for non-domination level update problem. The first one is a space efficient non-domination level update (SENLU) approach. The second one is a binary search tree based efficient non-domination level update (BST-ENLU) approach which uses the basic property of binary search tree. Although the space complexity of BST-ENLU approach is higher than SENLU approach in case of insertion, but in terms of number of dominance comparisons, BST-ENLU approach can outperform SENLU approach. Thus, these two approaches are complementary to each other. The comparative results show that in case where all the solutions are in different fronts, the maximum number of dominance comparisons using BST-ENLU approach is very less than ENLU approach. A tree based approach is introduced to identify the correct position of the solution to be deleted efficiently. Also a theoretical upper bound to the maximum number of dominance comparisons is obtained for both the proposed approaches in case of both insertion and deletion operations.