Research And Application On High-dimensional Multi-objective Visualization Technology

The varied objectives of high-dimensional multi-objective optimization often conflict with each other,which any improvement in one objective may lead to the degradation of the performance of other multiple objectives.Then the complexity and difficulty analyzing the Pareto optimal solution sets of high-dimensional multi-objective is added with increasing dimension of objectives,which bring great difficulties to the analysis and decision of Pareto optimal solution sets.The visualization of high-dimensional multi-objective by applying numerous techniques of computer graphics,image processing,etc.,which can display the Pareto optimal solution sets of high-dimensional in the form of images or graphs on computer screen,which the decision makers can carry on analyzing and making final choice depending on the actual situations,significantly reduces the complexity and difficulty for analyzing and deciding optimal solution sets,and has peculiar advantages in the analysis of high-dimensional Pareto optimal solution sets.However,almost all of current visualization technology of high-dimensional multi-objective still suffers from those problems,such as lack of preference information,unable to show the property of all objectives,lack of exhibition of overall performance for solution sets,on-unique localization,slow visual discrimination,etc.,and has no means of satisfying the demands of high-dimensional multi-objective optimization problems.Therefore,to devote to seek efficacious analysis methods for the Pareto optimal solution sets of high-dimensional is of great value.In view of the drawbacks of current visualization technology of high-dimensional multi-objective,this thesis is devoted to thoroughly research on analysis demands of the Pareto optimal solution sets of high-dimensional multi-objective.According to the applied demands of different sides,three visualization techniques of high-dimensional multi-objective is proposed to significantly enhance the visualization effects of high-dimensional multi-objective.Moreover,according to varied features of practical problems,the proposed techniques mentioned above are respectively applied to analyze the performance indexes of amphibious transformable robot and comprehensively evaluate the power quality,and have achieved better effect.The effectiveness and advancement of the proposed visualization techniques when they analyze high-dimensional Pareto optimal solution sets have been verified.Meanwhile,the application field of current visualization technology of high-dimensional multi-objective is expanded.This thesis main contents of which can be summarized as follows:Firstly,in order to solve the problems of current visualization techniques of high-dimensional multi-objective which cannot give consideration to convergence,distribution and extension,when the Pareto optimal solution sets is displayed,a high-dimension multi-objective visualization technique based on single-objective fitting is proposed.In this visualization technique,after sorting the function values of each objective of standard Pareto frontier,the function values of varied objectives are drawn in sub-diagram to obtain a truly growth curve.Furthermore,the Pareto solution set,which the markers are hunt on the Pareto frontier according to Euclidean distance,is drawn in sub-diagram.Ultimately,the Pareto solution set is entirely displayed by joining the same solution in each sub-diagram.The proposed method,which displays clearly various indexes of overall performance of all solution sets and further helps observe the evolution level and the actual optimization status of solution sets,can provide the theory basis for further research on high-dimensional multi-objective optimization problems.Secondly,the n-dimensional graphical visualization technique is improved from extracting the characteristic solution and joining the decision preference information two respects,and a new n-dimensional graphical visualization technique based on the characteristic solution extraction and the decision preference information is proposed.On the basis of the feature of multi-objective optimization problems,a new method in the light of decision error,which can extract the characteristic solutions and reduce the redundant solutions,is designed to reduce the pressure of visual distinction of diagram.Furthermore,in order to improve the lack of decision preference information when the information of various objectives is shared,three objective-sharing mechanisms based on preference weight factor,fluctuation analysis of performance of objectives and regional scoring system are designed.Additionally,sort all characteristic solutions by proposed objective-sharing mechanism.After that,according to sorting information mentioned above,the Pareto optimal solutions in varied sub-diagram are drawn.Not only can this proposed n-dimensional graphical visualization technique effectively prune the redundant solutions of decision,but also can entirely display data information.Meanwhile,the decision preference of selecting options for decision-makers is reflected directly.Thirdly,in order to solve the problems of being difficult for current visualization techniques to combine with interactive operation,which lack in the display of specific performance of Pareto optimal solution set and distinction of mapping interrelation between entire data and specific data,a new visualization technique of high-dimension multi-objective of rotation basis based on interactive decision making is proposed.In this method,the quality of each objective in Pareto optimal solutions is reflected on the rotation angle of the basis vector.After that,the basis vector after rotation is stacked successively based on the basic point of the drawing as the initial position and the Pareto optimal solutions by an independent path are mapped to a polygonal line on the plane of two-dimensional space.Ultimately,draw polygonal lines in graph in form of interactive operation.This proposed visualization technology mentioned above involve various information such as comprehensive performance of the Pareto optimal solutions,fluctuation performance of objectives and distinguish the display form of the whole data and the specific data of the Pareto optimal solutions.Furthermore,the proposed drawing mode of interactive polygonal lines can reduce visual distinction pressure for observers to some extent.Fourthly,the proposed n-dimensional graphical visualization technique and the visualization technique of rotation basis are respectively applied to physical problems on analyzing the performance indexes of amphibious transformable robot and comprehensively evaluating the power quality and acceptable as well.Therefore,not only can the proposed visualization techniques improve the search efficiency of data information of objectives for decision-makers and the analysis method of objective data,but also can deepen the comprehension of implication information of entire solution set for decision-makers.Additionally,the effectiveness and advancement of the proposed visualization techniques in practical applications are further verified,and meanwhile the application field of current visualization technology of high-dimensional multi-objective has been expanded.