Multi-objective Evolutionary Algorithm Based On DEA Model And Its Application Of Portfolio Optimization

Multi-objective optimization problem has always been a hot topic,but there are many disadvantages existed in applying the traditional methods.For examples,the traditional algorithm has a stringent requirement in the constraints of the problem.It is also difficult for the traditional algorithm to deal with large-scale,multi-modal and other complex issues because of the complexity.As one of the classical intelligent optimization algorithms,genetic algorithm performs excellent when it deals with large sacale multi-objective problems.It does not require priory information of the objective function,and does not require the objective function to be differentiable or continuous.Furthermore,it supports parallel operations.That's why the genetic algorithm is widely used in financial mathematics,combinatorial optimization,shop scheduling and other applications.In this thesis,two hybrid algorithms are presented.One is the multi-objective genetic algorithm based on the FDH model,namely FDH-MOGA.The algorithm evaluates the performance of individuals of populations and making choice according to the efficiencies and crowding distances,which can improve the local searching ability.At the same time,the partition strategy is used to enlarge the searching regions and improve the diversity of the solutions.Several test functions and portfolio optimization models are used to compare the performance of FDH-MOGA and non-dominated sorting genetic algorithm(NSGA-?).The results show that the FDH-MOGA algorithm performs better than NSGA-?.Besides,a modified multi objective evolutionary algorithm based on decomposition using DEA is presented,namely,DEA-MOEA/D.Current multiobjective evolutionary algorithms treat a MOP as a whole.While MOEA/D decomposes a MOP into a number of scalar optimization subproblems and optimizes them simultaneously.Each subproblem is optimized by using information from its several neighboring subproblems.According to the characteristics of MOEA/D,the initial solutions are generated by DEA and the crossover operator of the parent uses the difference operator.The same test functions and portfolio optimization models are used to compare the performance of DEA-MOEA/D and MOEA/D.The results show that the DEA-MOEA/D algorithm performs better than NSGA-II.Comparing the four algorithms in the test function,a conclusion can be drawn that the DEA-MOEA/D performs best.The performances of FDH-MOGA,MOEA/D and NSGA II have minor differences.FDH-MOGA is better than the other two algorithms.However,FDH-MOGA performes the best in dealing with discontinuities,followed by NSGA ? and DEA-MOEA/D,while MOEA/D was relatively poor.