Interactive Evolutionary Multi-objective Optimization Method For Portfolio Based On Integrated Cost Control

With the increase of disposable income and the gradual marketization of the financial industry,investors pay more and more attention to how to allocate limited assets optimally through the way of portfolio in order to achieve the maximum profits and the minimum risks.Therefore,portfolio is a typical problem associated with the optimization of multi-objective.However,investors just need to find out one of the many investment options which exactly fits their preferences.Thus It's very important to introduce information of investor preference when dealing with portfolio problems.At present,the main ways to solve the portfolio problem is the interactive evolutionary multi-objective optimization method(IEMO),which includes evolutionary algorithm,preference feedback and preference model.At present,IEMO still has the problem of high interaction cost,which mainly comes from three aspects.Firstly,there is a problem about loud noise in the preference feedback as a result of the limited rationality of investors,which is the root reason of interaction cost.Secondly,because the IEMO is designed with the fixed interaction step,some interaction times from imagery parameters are wasted.Thirdly,due to the lack of diversity of solutions in the process of evolution,evolutionary algorithms need more interaction times and evolutionary algebra to obtain new satisfactory solutions of investor when investors' preferences change dramatically.In view of the reasons of the interaction cost mentioned above,this paper proposes three control strategies.The first is the prior control strategy.That is the control strategy before it happens,which control the question and the answer of the preference feedback phase in order to solve the problem associated with root reason of the interaction cost.In terms of the question,this paper designs a method called selecting and comparing through dichotomy which can reduce the cognitive burden of investors by being asked questions from easy to difficult.In terms of answers,in order to help investors answer those increasingly difficult questions,this paper use the combination of main and auxiliary factors to expand the spatial difference of interactive samples,so as to help investors make more accurate choices.The second is the control strategy in the process of events.According to the imagery parameters of interaction cost,the judgment condition is designed in the process of interaction,in other words,whether the error rate of the preference model is lower than the given threshold.The unnecessary number of interactions in the process of interaction can be reduced and the waste of interaction can be avoided through the judgment for error rate.The third is the control strategy after the event.In order to solve the problem of lack of diversity of solutions in the process of evolution,a diversity archiver is designed for evolutionary algorithms.After a drastic change in investor preference,the solution in the archive is merged with the solution in the current population and the population is reorganized.In this way,the diversity of evolutionary solutions can be increased,the phenomenon of early convergence of the algorithm can be avoided and the interaction cost can be reduced.In addition,this paper tests the effectiveness of three control strategies: the control before the event,the control during the event and the control after the event.Through experimental verification of investors with different risk aversion types and different levels of rationality,it is shown that the the control before the event based on the method of selecting and comparing through dichotomy and the combination of main and auxiliary factors can control the appearance of noise in the feedback from the source and reduce the interaction cost.The control during the event based on error rate of model can reduce the unnecessary number of interactions in the intermediate phase.The control after the event based on the external archiver improves the diversity of solutions in the evolutionary algorithm.And that speeds up the response speed of the algorithm to the drastic adjustment of preferences.The three strategies further reduce the interaction cost while ensuring the satisfaction of investors.Then they can help investors find more satisfactory investment combination more quickly.