Research On Complex Dynamic Multi-Objective Optimization Based On Evolutionary Algorithm

Dynamic multi-objective optimization problems exist widely in real life,including not only multiple conflicting objectives,but also uncertain dynamic factors such as time-varying decision variables,environmental parameters,objective functions,etc.When traditional evolutionary algorithms solve dynamic multi-objective problems,they would face problems such as the population can not converge in time after the environment changes,and the population diversity is difficult to guarantee.If traditional evolutionary algorithms are directly applied to solve dynamic multi-objective optimization problems,the optimal solutions of the new problem would be difficult to meet.Therefore,targeted dynamic response mechanism is needed.Aiming at dynamic multi-objective optimization problems,this paper explores effective environmental change detection and response strategies,and carries out relevant research from the following aspects.Aiming at the low prediction accuracy of traditional dynamic multi-objective optimization,a dynamic multi-objective optimization algorithm based on feature information prediction is proposed.When the environment changes,the feature information from the objective space at the current time and the optimization function at the new time are selected.Then,the prediction model of joint distribution adaptation is established,and the mapping function before and after the environment change is determined.Thus,the distribution of the solution set after the environment change could be identified.The feature information of decision space at next time is obtained using the interior point method.Based on the population boundary formed by the feature information,new individuals are randomly generated to improve the population diversity and the accuracy of population prediction.The performance of the proposed method is verified by comparing it with the four classical algorithms on eight test functions.The simulation results show that the proposed method can quickly track the population front in a dynamic environment with rapidly changing environments.For dynamic multi-objective optimization problems with complex front features,a dynamic multi-objective optimization algorithm based on multiregional co-evolutionary is proposed.The algorithm mainy includes two parts: multiregional prediction strategy and multiregional diversity maintenance mechanism.When detecting environmental changes,the number of subregions is adaptively determined according to the severity of environmental changes,which enhances the adaptability of subregions to dynamic problems.The difference model is built based on the historical center points in different subregions,which could judge the moving trend of the optimal solutions,estimate the position of the center points at the new time,and generate new individuals that adapt to the front.Secondly,new individuals are randomly generated in the subregions that may exist at the new time of the predicted optimal solutions to promote population diversity.These two sets of solutions constitute the initial population in the new environment.The proposed method is tested on 11 test functions.The simulation results show that the proposed algorithm can quickly track the changes of the complex front and effectively predict the location of the optimal solutions.Targeting at solving the complex dynamic multi-objective optimization problem can not accurately predict the front with multiple convex-concave knee points due to the lack of accurate detection mechanism for the degree of environmental change,a dynamic multi-objective optimization algorithm with double-space environmental change detection and response strategy is proposed.When environmental changes are detected,the severity of the changes in the objective space and the decision space can be judged respectively through the recognition of concave-convex knee points and statistical methods.For the changes of the objective space in different degrees,the population evolution is guided adaptively by judging the population change trend,which is driven by the shape information of the population front.With regard to the changes in the decision space to different degrees,a prediction model is constructed through long-term and short-term self-learning under the guidance of population variable information to generate new individuals that are more adaptable to the new environment.Simulation experiments on 10 test functions show that the proposed algorithm can effectively detect the change intensity of the objective space and the decision space,and accurately predict the dynamic problems with multiple convex-concave knee points front features.Aiming at the problem that convergence and diversity are difficult to balance in the dynamic multi-objective optimization problem with variable number of objectives,a dynamic multi-objective optimization algorithm based on decision space information driven is proposed.When the number of objectives of the problem changes,according to the increase or decrease of the number of objectives,select excellent representative individuals that adapt to the change of the objective space,learn their manifolds through self-organizing mapping,guide the population to generate new optimal solutions,and promote population convergence.At the same time,according to the contribution of different decision variables in individuals,they are classified according to convergence and diversity,and targeted evolution operations are taken for different types of variables to improve population diversity.The proposed algorithm is applied to 13 test functions for comparative analysis.The simulation results show that the proposed method can effectively balance the convergence and diversity of the problem with changing the number of objectives.Targeting at solving the dynamic multi-objective optimization problem with simultaneous changes in the number of objectives and time-varying objective functions,a dynamic multi-objective optimization algorithm based on multi spatial information joint guidance is proposed.When the environment changes,first of all,according to the decision space information at different times,the mapping relationship at different times is established through the geodesic flow kernel method,and the initial individual of the new environment is generated based on the historical solution set and spatial information.Thus,the optimal soutions could be accurately identified.Secondly,representative individuals with good diversity are selected from the objective space,and new solutions are obtained by sampling on multiple dimensions near the decision space of these individuals to improve population diversity.The simulation results of 15 test functions with time-varying objective functions and the number of objectives show that the proposed algorithm outperforms the comparison algorithm in the test problems where the number of objectives and the number of time-varying objective functions exist simultaneously.