A min-max method with adaptive weightings for uniformly spaced Pareto optimum points

This work aims at obtaining uniformly spaced Pareto optimum points in the objective space when multicriteria optimization problems are solved. An original adaptive scheme is proposed to update automatically weighting coefficients involved in the min-max method. By means of a novel bilevel approach, it is shown that with the calculation of the tangent and normal directions of the Pareto curve, Pareto optimum points can be obtained sequentially with a uniformly spaced distribution. Meanwhile, the distance between two adjacent Pareto optimum points is controllable depending upon the prescribed step length along the tangent direction. To validate the method, numerical bicriteria examples are solved to show its effectiveness.