Multi-objective Evolutionary Algorithm Based On Reference Point Adaptation And Its Application

Based on the two algorithms,NSGA-? and A-NSGA-?,this paper proposes a new multi-objective evolutionary algorithm AR-NSGA-? based on adaptive adjustment of reference points.In this algorithm,we put more emphasis on the guiding role of the original uniform reference point,and for the sake of diversity,after selecting the individuals according to the reference point,we use the furthest element addition mechanism to maximize the population diversity.In order to further enhance the convergence of the algorithm,we introduce a penalty-based intersection distance(PBI distance)to measure the distance from the individual to the reference point.During the adaptive adjustment of the reference points,the reference points are newly added according to the degree of congestion of the reference points,and in order to avoid the reference point set being too dense,it is deleted according to a preset threshold.In addition,we are also improving the offspring generated by mating through a new measure of congestion and a way to gradually increase the probability of the neighbor solution as a matching parent in the mating selection process.After numerical experiments on benchmark problems,such as the WFG test set and the DTLZ test set,this paper confirms the algorithm is significantly better than other five widely used algorithms(NSGA-?,NSGA-?,A-NSGA-?,MOEA / D,and AR-MOEA).We apply this algorithm to the mean-variance-third-moment portfolio model,and also consider constraints in practical transactions such as cardinality constraints,pre-allocation constraints,boundary constraints,and integer transaction constraints.This paper conducted an empirical analysis on the S & P 500 constituent stock data set from January 2017 to October 2018,and compared the effects of the NSGA-? and AR-NSGA-? algorithms.The experimental results show that AR-NSGA-? is better than NSGA-?.In addition,this paper generates actual investment strategies based on the individuals obtained on the approximate Pareto effective frontier,which also have corresponding investment effects compared with the S&P 500 index over the same period.