基于进化算法的高维多目标优化问题研究

Evolutionary Algorithms (EAs) have established themselves as effective means for exploring both converged and diversified approximate Pareto-optimal fronts in multi-objective optimization problems (MOPs), which contain two or three conflicting objectives in general. Due to their heuristic characteristics and population-based framework, multi-objective evolutionary algorithms (MOEAs) provide powerful search ability to find the Pareto-optimal fronts in MOPs. However, many real-world problems involve simultaneously optimizing many conflicting objectives (in most cases, at least four), which are commonly referred to as many-objective optimization problems (MaOPs). There are several challenges brought to MOEAs in MaOPs because of the curse of dimensionality. First, Pareto optimality loses the selection pressure during the evolutionary process caused by the increasing number of objectives. Second, MaOP’s extremely large objective space considerably weakens the effect of the evolutionary operator. Third, visualization of Pareto solutions becomes difficult and existing performance metrics cannot provide accurately evaluation for the quality of Pareto fronts. Therefore, the performance of classic MOEAs and visualization methods deteriorate severely in face of MaOPs. Based on analysis of above challenges, we will conduct our research for many-objective optimization using evolutionary algorithms in three aspects. First, analyze the performance of the individual solution and the whole Pareto front, respectively. Second, develop efficient selection strategy for MOEAs. Third, effective visualization approach for Pareto fronts at high-dimensional space is proposed. Research on this project will further develop the theory of MaOPs, design effective MOEAs for MaOPs, and provide efficient visualization method. Meanwhile, our research will improve EAs' search and optimization ability, enhancing EAs' application in more fields.

进化算法作为实现全局最优的搜索启发式算法，已在二或三维的多目标优化问题上取得显著效果。然而，工程和科学领域中多数问题涉及同时优化至少四个互相冲突的目标，此类问题称为高维多目标优化问题。目标维数的增加，不仅导致进化算法的Pareto占优关系不能提供足够的选择压力，而且削弱了进化算子功能。此外，Pareto前沿的可视化和性能评价变得非常困难。因此，传统的进化算法和可视化方法难以适用于高维多目标优化问题。本项目分析以上挑战，旨在探索基于进化算法的高维多目标优化问题，将在以下方面开展研究：1）分析单个个体和整体Pareto前沿的优化性能；2）设计有效选择策略, 开发进化算法；3）提出高维空间中Pareto前沿的可视化方法。本项目的研究，必将有助于进一步奠定基于进化算法的高维多目标优化的理论基础，为高维多目标优化问题提供高效算法和有效可视化方法；同时提高进化算法自身搜索和优化能力，增强其应用性。

工程实践和科学研究中的优化问题，包含多个相互冲突，相互竞争的目标，当目标个数大于等于四时，该问题被称为高维多目标优化问题。本项目面向高维多目标优化和决策难题，在高维多目标进化优化算法和高维空间Pareto前沿可视化方法两方面开展研究，取得了具有一定国际影响力的研究成果。代表性研究成果如下。1）通过实现种群收敛性和多样性提升和平衡，首次提出充分挖掘进化算法基于种群的特性，深度提炼目标空间和决策空间地形特征，全面反映个体解多目标优化性能及其抗扰动的鲁棒性能，从而提升进化算法在实际高维多目标优化问题中的应用能力。2）创新性地从个体性能和种群整体质量两个维度出发，设计收敛性和多样性协同度量方法；在此基础上，提出深入发展进化算法自然选择理论，改进适者生存机制筛选优秀个体，设计外部存储空间插入和删除机制，帮助算法快速适应不确定性环境，进一步增强算法在实际问题中的应用能力。3）突破高维空间大量可行解的存在使得决策者难以筛选符合偏好的最优解的难题，首次提出面向高维多目标决策的高维空间可视化方法，反映各个目标之间的耦合关系、以及最优解对各个目标优化程度的区别。提炼最优解在决策空间和目标空间的邻域信息，计算决策者偏好变化发生时，需要付出的转移代价。在项目实施过程中，项目组在IEEE Transactions 等计算智能领域国际一流期刊和会议上发表论文5 篇，协助培养研究生4 名，项目负责人获吴文俊人工智能科学技术奖自然科学三等奖，参加多个重要国际国内会议，开展深入的学术交流与合作。