Adaptive weighted aggregation: A multiobjective function optimization framework taking account of spread and evenness of approximate solutions

The multi-starting descent method is a promising approach to unimodal multiobjective function optimization problems because of its precision of obtained solutions. Descent methods can be classified into two categories; the multiobjective descent method directly using the Jacobian matrix of objective functions and the scalarized descent method using the gradient of a scalarized objective function. In the multiobjective descent method and the scalarized descent method, a convergent point depends on an initial solution and a weight vector, respectively. However, it is difficult to choose appropriate initial solutions or weight vectors for obtaining widely and evenly distributed solutions. In order to remedy the problems of the conventional methods, we propose a multi-starting scalarized descent method named AWA that employs the Chebyshev norm method as a scalarization method and an adaptive scheme of weight vectors for the scalarization method. We show the effectiveness of the proposed method through some experiments.