基于R2性能指标的昂贵高维多目标优化算法研究

Traditional evolutionary multi-objective optimization algorithms are difficult for solving the expensive many-objective optimization problems. This project proposes an expensive many-objective optimization algorithm based on the R2 performance indicator. Firstly, we design a weight vector generated strategy based on the Coulomb's law. We select and sample the surrogate model after mining the useful data information in the objective space. The proper adaptive weight vector updated method is designed after the secondary selection according to a set of the combined weight vectors. Secondly, a multi-stage selection strategy is proposed to address the disconnected many-objective optimization problems after specifying the age for each subspace. Furthermore, a gene-culture coevolution algorithm is proposed to balance the exploration and exploitation. Finally, the R2 performance indicator based expensive many-objective optimization algorithm will be proposed. The R2 indicator infill criterion is designed to balance the convergence, the diversity and the uncertainty. In addition, the bi-level archive management strategy is formulated to achieve the model management and the model updated procedure. The algorithm is validated on the benchmark test problems. The project will offer the theoretical basis and method reference for the industrial integrated automation system production procedure.

针对常规进化多目标优化算法难以求解昂贵高维多目标优化问题，本项目提出基于R2性能指标的昂贵高维多目标优化算法。首先，借鉴库仑定律设计权值任意给定方法，充分挖掘目标空间的数据信息建立代理模型、采样和选择对权值自适应更新；借鉴微观经济学中柯布道格拉斯生产效用函数构建R2指标。其次，通过对每个子空间设定年龄，提出多阶段选择机制求解不连续高维多目标优化问题。再次，为了综合权衡算法的勘探和开采能力，提出基因文化共演化算法。最后，设计一种综合权衡算法收敛性、多样性和不确定性的R2指标作为填充准则，构建双层档案管理策略完成模型管理和更新过程，提出基于R2性能指标的昂贵高维多目标优化算法，并在测试平台上进行仿真验证，为将算法应用于流程工业综合自动化生产过程提供理论支持和方法参考。

针对常规进化多目标优化算法难以求解昂贵高维多目标优化问题的难题，项目研究了基于性能指标的昂贵高维多目标优化算法。针对高维多目标优化问题、大规模多目标优化问题等，结合R2性能指标和IGD+性能指标，项目提出了一系列融合性能指标的进化高维多目标优化算法来处理此类复杂问题。具体地，在算法设计工作中，本项目重点关注如何将评价指标应用于求解高维多目标优化问题、昂贵高维多目标优化问题和昂贵大规模多目标优化问题。针对R2指标在求解昂贵多目标优化问题时，难以有效进行模型管理的问题，提出了一种基于置信下限的双重选择机制，采用Kriging模型降低计算代价；针对IGD+指标难以求解高维多目标优化问题，提出了两阶段选择机制综合权衡算法的收敛性和多样化性；针对常规径向基网络模型难以预测不确定性信息的问题，提出了反距离加权方法和径向基网络辅助的算法求解昂贵大规模多目标优化问题。.整个项目期间的成果以学术论文为主，完成学术论文13篇，进入实审专利3项，获批软件著作权2项。本项目不仅设计了多个灵活性好、实用性强的基于性能指标的进化多目标优化算法，丰富了进化多目标优化研究领域，推动了复杂工业过程智能控制与优化和智能优化方法与技术的发展，具有广阔的应用前景。