Fig. 3.

Comparison between the proposed modified and the original ε-constraint methods. We have used ‘*’ to indicate the objective vector and ‘o’ to specify the solution vector. Solutions given by (a) the ε-constraint method and (b) the proposed modified ε-constraint approach on the first example, and (c) the ε-constraint method and (d) the modified ε-constraint approach on the second example. Note that the proposed approach identifies the Pareto-frontier, while the original algorithm identifies weakly Pareto-solutions, since the solution vectors go beyond the Pareto-frontier.