A study of the weighting method for a certain type of multicriteria optimization problem

The study is concerned with a certain type of multicriteria optimization problem for which some objective functions are also retained as design constraints. It is shown that if at least one of the criteria-defined constraints becomes active at the Pareto optimum point, there exists then an interval in which all combinations of weightings are ineffective and useless to attain a new Pareto optimum solution. To perform the effective discretization of weightings, an analytical approach is presented to find the lower and upper bounds of the ineffective interval. Illustrative examples show this method.