融合动态感知与双向搜索的精英群引导PID搜索算法及其应用

Elite Group-Guided PID Search Algorithm Integrating Dynamic Perception and Bidirectional Search and Its Application

  • 摘要: 针对增量PID搜索算法(PSA)全局搜索能力较差、易陷入局部最优值的问题,提出了一种融合动态感知与双向搜索的精英群引导PID搜索算法(DPSA)。DPSA的改进策略包括:首先,设计了一种动态正弦因子控制的精英群引导机制,该机制吸取优质个体的信息,增强了算法的全局信息获取能力。其次,融入基于适应度景观动态感知的奖惩因子 \varepsilon ,使算法可以自适应平衡探索和开发行为,增强了算法对不同问题的适应能力。最后,设计了一种基于余弦相似度的劣势子群双向搜索策略,减少无用个体数量的同时,为算法提供了跳出局部最优解和精细搜索的机会。通过在CEC2017基准测试函数上进行仿真实验,DPSA在100维的CEC2017测试集中的平均适应度优胜率为79.31%。此外,进行了Friedman检验、Wilcoxon秩和检验及算法稳定性分析,实验结果表明:DPSA在收敛速度和精度上均显著提升,且相较于其他优化算法,具有更优的寻优效果和更高的稳定性。另外,将算法应用于19个实际工程问题和3维无线传感器网络(WSN)节点覆盖问题中,进一步验证了DPSA的优越性和实用性。

     

    Abstract: To solve the problem that the incremental PID search algorithm (PSA) suffers from poor global search ability and is prone to falling into local optima, we propose an elite group-guided PID search algorithm with dynamic perception and bidirectional search (DPSA). The proposed algorithm introduces three key improvements. Firstly, it incorporates a dynamic sine factor-controlled elite group-guided mechanism that extracts information from high-quality individuals, enhancing global search capability. Secondly, it integrate a fitness landscape-aware dynamic perception-based reward and penalty factor \varepsilon to adaptively balance between exploration and exploitation, which improves its adaptability to different optimization problems. Finally, it employs a bidirectional search strategy for weak subgroups based on cosine similarity to reduce the number of ineffective individuals while enhancing the algorithm’s ability to escape local optima and conduct refined searches. Simulation experiments on the CEC2017 benchmark functions demonstrate that DPSA achieves an average fitness superiority rate of 79.31% in the 100-dimensional CEC2017 test set. Additionally, statistical analyses, including Friedman tests, Wilcoxon rank-sum tests, and stability analysis, show that DPSA significantly improves both convergence speed and accuracy, outperforming other optimization algorithms in solution quality and stability. Furthermore, its application to 19 real-world engineering problems and the node coverage problem in 3D wireless sensor networks (WSN) further validates its effectiveness and applicability.

     

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