An enhanced distributed differential evolution algorithm for portfolio optimization problems.

The population structure of differential evolution (DE) algorithm cannot maintain the diversity of the population to the greatest extent and help the population avoid to fall into the local optima in time. In this paper, a co-evolutionary multi-swarm adaptive differential evolution algorithm, namely ECMADE is proposed to solve the premature convergence and search stagnation. First of all, in terms of population structure, based on the parallel distributed framework, ECMADE randomly and evenly divides the population into exploration subpopulation, development subpopulation, and auxiliary subpopulation, and introduces an adaptive information exchange mechanism so that subpopulations can escape local optima in time. Then, a multi-operator parallel search strategy is proposed to keep population diversity and meet the optimization needs of different problems. Finally, an adaptive adjustment mechanism of control parameters is developed, through recent elite parameter archive and weight distribution to fully mine successful parameter information, and generate control parameters with a high success rate for the current evolutionary stage. In order to prove the effectiveness of the ECMADE, 10 test functions and portfolio optimization problem are selected in here. The experiment results show that the ECMADE can effectively solve these test functions, the accuracy and efficiency is superior to those of two classical DE algorithms. The actual application results show that the ECMADE can significantly improve the ability of portfolio to resist extreme losses, which proves the effectiveness and feasibility of the ECMADE once again. The ECMADE has better optimization performance by comparing with some well-known algorithms in term of the solution quality, robustness and space distribution. It provides a new algorithm for solving complex optimization problems.