基于群集智能的非凸稀疏优化算法的研究

Sparse optimization, which is the key technology for sparse representation and compressed sensing, is important for many engineering areas. It is an NP hard problem which is non-convex and non-differentiable. Since swarm intelligence does not require that the problem is convex or linear and can solve different types of problems, this project is going to propose novel sparse optimization algorithms based on swarm intelligence. Considering that the sparse optimization problem can be transferred to a large scale multi-objective composite problem of which the solution is sparse, we plan to analyze the influence of the different norm constraints on the performance of the swarm intelligence algorithms to obtain the relationship between the sparsity requirements, the behavior patterns of the swarm and the knowledge of the distribution of the solutions obtained under the L1 norm and L0 norm minimization condition. Employing the comprehensive learning strategy and dynamic neighborhood topology, we will seek for the solutions to the problems existing in the sparse optimization based on swarm intelligence, such as how to search along the Pareto front effectively, how to keep the diversity of the individuals and how to design effective strategies for the large scale multiobjective composite problems. Through this project, efficient novel sparse optimization algorithms based on swarm intelligence will be constructed. A benchmark suite for sparse optimization will also be proposed and the constructed novel sparse optimization algorithms will be improved based on their performance on this benchmark suite. Finally, the algorithms will be applied on the medical signal/image reconstruction problems and the neural networks with sparse linkages. The research involving in this project will provide a novel general tool for sparse optimization related areas.

稀疏优化是稀疏表示和压缩感知理论中的关键技术，在多领域具有重要应用价值。针对稀疏优化本质属于非凸不可微的NP难问题，本项目利用群集智能算法不要求问题满足凸性/线性要求、适应性强的优点，开展群集智能稀疏优化方法的基础理论和新型算法研究。针对问题高维、多目标、混合离散的性质，从解的稀疏特性出发，分析不同范数约束对群集智能优化结果的影响，从而获得稀疏严格性逐步递增对解空间中群体行为的作用规律和L1与L0范数条件下解的相关性信息。结合理解性学习策略和动态拓扑结构，解决群集智能稀疏优化中帕累托前沿搜索、解的多样性保持、高维多目标混合离散优化策略等关键问题，构建快速有效的新型群集智能稀疏优化算法，建立稀疏优化问题的标准测试平台对算法性能进行评估并改进，最终应用算法解决医学信号/图像重构、稀疏连接神经网络等稀疏优化问题。研究结果可为稀疏优化相关领域提供一种新的通用型解决方案。

本项目的目标是利用群集智能算法解决非凸优化问题的优势，针对稀疏优化问题的特性，设计群集智能稀疏优化算法，最终将研究出的优化算法应用于实际优化问题。围绕该目标，本项目首先对稀疏优化理论进行研究，分析了稀疏优化问题的特点；针对该类问题的特点，设计了多目标群集智能稀疏优化算法；并将所设计的算法成功应用于稀疏人脸表情识别，核磁共振图像稀疏重构等实际问题，取得了一些有意义的研究成果。此外，本项目成员组织了稀疏优化算法竞赛，构建了稀疏优化标准测试平台。.本项目执行期间共发表学术论文44篇，其中期刊论文30篇，会议论文14篇。其中SCI收录17篇，EI收录13篇。获得授权发明专利2项，授权软件著作权5项，项目组在国际会议上做口头报告11次。