Study On Visualization Of Many-objective Optimization

Multi-objective Optimization Problems(MOPs), a kind of optimization problems,commonly exist in the real world. If the number of objectives is more than3, they arecalled many-objective optimization problems. The increasing number of objectives willnot only bring great challenges to many-objective optimization algorithms but alsomake it difficult to visualize the high-dimensional front obtained by many-objectiveoptimization algorithms, which may influences user’s decisions. Thus, research on thevisualization of many-objective optimization has important academic interests andvaluable applications. In this dissertation, the main issues involving MOPs and thevisualization technologies are discussed, and the visualization of many-objectiveoptimization is studied intensively. The main contents are as follows:①The current research on many-objective optimization are reviewed. Then afurther introduction to the related concepts, challenges and research direction about themany-objective optimization is given. Moreover, the data analysis method and thevisualization tools about visualization technologies are elaborated.②A kind of method about the visualization of many-objective optimization basedon Principal Component Analysis (PCA) is presented. The method combines thefeatures of dimensionality reduction and non-dimensionality reduction techniques ofdata analysis. That is to say, the method adopts the PCA to obtain the features of data,and then use the features to reorganize the data. The method does not need to reduce thedimension and miss any information, which ensures that it can fully use the features andkeep the integrity of data. The experimental results show that the method can offersatisfactory visual effects and help user make effective decisions.③A kind of method about the visualization of many-objective optimization basedon the similarity ordering is proposed and two sorting strategies, minimizing the sum ofsimilarity(MSS) and user’s preference(UP), are present. The method takes heatmap asvisualization tools and use similarity to measure the relation between data withoutconsidering data redundancy. The method firstly adopts the strategy of MSS to sort theobjectives and use Hierarchical Cluster Analysis to order the rows of the data. However,the strategy of MSS suffers from the large calculation and complexity. UP is anothersorting strategy, which orders the objectives and data rows simultaneously by means ofuser’s preference. The strategy of UP has less calculation and low complexity. The experimental results show that the strategy of minimizing the sum of similarity hasbetter performance in terms of visual effect and making decision, while the strategybased on preference has an advantage over the computational complexity and userparticipation.④A new multi-objective optimization platform is designed and implemented. Thesystem has user-friendly interface, excellent architecture and reasonable programinterface design, rich functionality, and is easy to use. The system includes manymainstream multi-objective optimization algorithms and test functions, and it can beeasily extensible.