高维多目标进化计算及可视化研究

Many objective optimization problems are widely seen in the evolutionary community and real-world application. However, the performance of most existing algorithms seriously degrades when the number of objectives is larger than three. The recent research results cannot efficaciously resolve the problem of inability of dominance or non-dominance based optimization methods to converge to the Pareto frontier, the problem of the prohibitively high computational complexity, the difficulty of maintaining good diversity, the difficulty for human users or decision makers to clearly understand the relationship between objectives and articulate preferences, the grand challenge of the visualization of the solutions, the problem of incapable of accurately assessing and comparing the quality of solution sets. Therefore it is of great theoretical and practical importance to efficiently solve above series key problems. This project aims to resolve these key problems, the research contents include effective and efficient individual comparing criterions, efficient reproduction operators dedicated to many objectives, preference articulation and modeling, preference knowledge formation methods and its evolving mechanism, performance indicators, new visualization techniques, correlation and importance analysis methods for different objectives, test problems involving more than three objectives, theoretical analysis of convergence, and its applications in complicated image processing and analysis. Cultural algorithm with cellular structure will be used to produce, correct and update the knowledge of preference information. Neighborhood culture extraction method and culture fusion and diffusion mechanism will be set up to evolve the preference knowledge in order to get better preference information and to guide to evolving direction for many objective optimization. A novel individual assessing method will be built based on individual group measure. An additional optimization module having three objectives will be inserted into the evolutionary procedure, it try to find an optimal sub-group which is superior to any other sub-group according to the group measure based on hyper-volume, individual distribution and degree of convergence. Therefore the individuals in this optimal sup-group will be superior to those not belonging to this optimal sup-group. The high dimensional optimal attraction theorem will be built to analyze the characteristics of objective functions, so as to estimate difficulty degree of optimizing each objective. The difficulty degree can be used to select suitable evolutionary strategies and evolutionary parameters and to keep the population diversity. Also the problem of serious attenuation of evolving selection pressure caused by remarkable proportion increase of non-dominated individuals can be resolved effectively..A novel method of analyzing correlation and significance between different objectives will be established based on co-occurrence matrix of many objectives. The co-occurrence matrix, which is similar to gray co-occurrence matrix used in image processing, aims to find the minimum dimension which the original objectives can be reduced with the constraint of reserving statistically valid information of all the objective functions. A new visualization method will be proposed preserving Pareto dominance relationship, retaining shape and location of the Pareto front, and maintaining distribution of individuals. It maps individuals from a high-dimensional objective space into a 2-D circle area. Each objective original point is equally distributed on the circle according to its correlation, significance, then the position of each individual is decided by minimizing the total weighed distance between this position to each individual original point, specially the distance is weighed by each objective fitness. And this mapping method can also be used to easily evaluate performance of different optimization algorithms.

在工程实践中经常需要解决4个以上目标数的高维多目标优化问题，目前的研究成果还不能有效解决高维多目标下进化个体间优劣比较困难造成的算法性能急剧下降甚至失效的问题，还不能有效解决计算复杂度剧增、难以保持群体多样性、决策者难以理解偏好与目标之间关系、解集可视化困难、难以评价算法性能等系列关键问题，它们成为当前进化计算理论研究和高维多目标工程优化领域急需解决的问题。本项目将研究如何有效解决这些关键问题，拟建立基于群体测度的非Pareto个体评价方法的高维多目标进化新算法，包括基于元胞自动机结构的文化进化思想下的偏好信息知识提取与进化机制、基于最优吸引子理论的高维多目标进化过程的群体多样性保持方法、基于高维多目标适应度共生矩阵的多目标相关性和重要性分析方法、基于类圆映射的高维多目标可视方法和算法评价方法，由此构建能够有效解决高维多目标优化问题的进化算法理论与框架，并将之应用到复杂图像处理与分析中。

在工程实践中经常需要解决4个以上目标数的高维多目标优化问题，目前的研究成果还不能有效解决高维多目标下进化个体间优劣比较困难造成的算法性能急剧下降甚至失效的问题，还不能有效解决计算复杂度剧增、难以保持群体多样性、决策者难以理解偏好与目标之间关系、解集可视化困难、难以评价算法性能等系列关键问题，它们成为当前进化计算理论研究和高维多目标工程优化领域急需解决的问题。. 主要研究内容包括(1)研究了如何建立高维多目标优化问题的偏好信息的知识表示、提取、影响策略，自动调整个体之间相互支配关系，保持高维多目标优化算法的合适选择压力和良好寻优能力。(2)研究了高维多目标解空间内进化个体的评价与排序方法，进化群体子集的非Pareto支配的评价测度。(3)研究了高维多目标之间的相关性和重要性分析方法，并将之应用在了高维多目标可视化和对算法的评价中。(4)研究了高维多目标解空间的可视化方法，建立了将高维多目标个体映射到两维坐标系下圆弧内的类圆映射规则。(5)研究了如何对高维多目标进化过程进行评价的方法和相关的收敛性问题。(6)图像处理中的多特征融合多目标优化、光流匹配计算中的多目标优化、人脸表情识别及掌纹优化识别。. 重要结果、关键数据及其科学意义包括：针对目前高维多目标进化算法由于维数增加导致的进化个体间的优劣关系难以确定，致使进化过程中缺乏选择压力收敛性能降低的关键问题，提出了一种基于概率准则的适应度计算方法并将其应用于粒子群优化器中。针对多目标优化问题中进化算法重组算子搜索效率低，无法产生高质量子代个体引导种群搜索的问题，提出一种基于SOM聚类和自适应算子选择的方法。为了获得鲁棒可靠的Pareto可行区域解集，提出了一种嵌入SOM神经网络模型的双种群协作进化框架。现阶段对多目标问题的决策变量可扩展性方法仅局限于处理低维大规模多目标优化问题的优化。为了填补该方向在进化计算领域的空白，本项目还提出了一种基于决策变量分组优化策略的粒子群优化技术用以解决大规模高维多目标优化问题。以上提出的这些方法其关键数据都好于国际上同类方法，其在图像多特征融合、光流计算的性能也显示了其明显的优越性。