A Population Based Incremental Learning Algorithm for the Multiobjective Portfolio

Multiobjective optimization problem Portfolio is a hard–decision–making problem in investment management. With respect to how to obtain the multiobjective candidate decisive solutions for Portfolio, a multiobjective optimization method M– PBIL (Multiobjective Population Based Incremental Learning) to Portfolio is proposed. Different from the traditional evolutionary algorithms which generate individuals based on the recombination of the current ones, M–PBIL follows the strategy of PBIL to generate individuals based on probability model and researches three key technologies in solving multiobjective optimization problems. First, for the multiobjective optimization problem in continuous space, a real number–based coding scheme is proposed, which can overcome the defects of binary coding such as code redundancy and probability conflict. In the second place, a variable probability model for the gene bit is designed so as to realize the dynamic partition for the intervals of decision variables. Next, a dominance and representativeness– based assessment mechanic is employed for the selection of non– dominated solutions of multiobjective optimization problem. The performances of the M–PBIL are evaluated by convergence and distribution and compared with the representative NSGAII on benchmark data. The experimental results show that M–PBIL outperforms NSGAII in convergence and distribution. Keywords—portfolio; multiobjective optimization algorithm; evolutionary algorithm