融合模式搜索的蝗虫优化算法及其应用

Integration of pattern search into the grasshopper optimization algorithm and its applications

在智能优化算法应用于复杂优化问题的求解过程中,平衡开发和探索以获得最优解具有重要意义。因此针对传统蝗虫优化算法在处理一些较为复杂的优化问题时出现的收敛精度低、搜索能力弱且容易陷入局部最优等缺陷,提出一种融合模式搜索的蝗虫优化算法。首先引入Sine混沌映射初始化蝗虫个体种群位置,减少个体重叠概率以增强种群迭代初期的多样性;其次利用模式搜索法,对种群目前找到的最优目标展开局部搜索,提高算法的收敛速度与寻优精度;同时为了避免算法后期陷入局部最优,引入了基于凸透镜成像的反向学习策略。实验部分通过对改进的蝗虫算法进行消融实验,验证了Sine混沌映射、模式搜索、反向学习每个策略的独立有效性。并用两组测试函数进行仿真实验,采用Wilcoxon秩和检验、Friedman检验的方法进行结果分析。实验结果均表明了融合模式搜索法改进的蝗虫算法在收敛速度与寻优精度上得到明显提高。最后,将其应用于移动机器人路径规划,测试结果进一步验证了改进算法的有效性。

In the process of applying intelligent optimization algorithms to solve complex optimization problems,balancing exploration and exploitation is of great significance in order to obtain optimal solutions.Therefore,this paper proposes a grasshopper optimization algorithm that integrates pattern search to address the limitations of traditional grasshopper optimization algorithm,such as low convergence accuracy,weak search capability,and susceptibility to local optima in handling complex optimization problems.First,a Sine chaotic mapping is introduced to initialize the positions of individual grasshopper population,reducing the probability of individual overlap and enhancing the diversity of the population in the early iterations.Second,the pattern search method is employed to perform local search for the currently found optimal targets in the population,thereby improving the convergence speed and optimization accuracy of the algorithm.Additionally,to avoid falling into local optima in the later stages of the algorithm,a reverse learning strategy based on the imaging of convex lenses is introduced.In the experimental section,a series of ablative experiments is conducted on the improved grasshopper algorithm to validate the independent effectiveness of each strategy,including the Sine chaotic mapping,pattern search,and reverse learning.Simulation experiments are performed on two sets of test functions,with the results analyzed using the Wilcoxon rank-sum test and Friedman test.Experimental results consistently demonstrate that the fusion mode search strategy improved grasshopper algorithm exhibits significant enhancements in both convergence speed and optimization accuracy.Furthermore,the application of the improved algorithm to mobile robot path planning further validates its effectiveness.