摘 要
遗传算法作为一种全局优化搜索方法，在解决复杂优化问题中展现出独特优势，但传统遗传算法存在早熟收敛、局部最优等问题。为此，本研究聚焦于变异概率调整机制的改进，旨在通过动态调整变异概率提升遗传算法的寻优能力和鲁棒性。研究基于对现有遗传算法中变异操作相关理论的深入剖析，提出一种自适应变异概率调整策略，该策略根据种群多样性指标和进化代数动态改变变异概率，以平衡算法的探索与开发能力。实验选取多个经典测试函数进行验证，结果表明改进后的遗传算法在求解精度、收敛速度方面较传统算法有显著提升，尤其在处理高维复杂优化问题时表现出色。此外，新方法有效避免了早熟收敛现象，增强了算法跳出局部最优的能力。本研究创新性地将种群多样性与进化进程相结合来调整变异概率，为遗传算法的性能优化提供了新的思路和方法，对推动遗传算法在更多领域尤其是复杂系统优化中的应用具有重要意义。
关键词：遗传算法 变异概率调整 种群多样性
Abstract
Genetic algorithms, as a global optimization search method, have demonstrated unique advantages in solving complex optimization problems; however, traditional genetic algorithms suffer from issues such as premature convergence and falling into local optima. To address these challenges, this study focuses on improving the mutation probability adjustment mechanism to enhance the optimization capability and robustness of genetic algorithms through dynamic adjustment of mutation probability. Based on an in-depth analysis of the theories related to mutation operations in existing genetic algorithms, an adaptive mutation probability adjustment strategy is proposed. This strategy dynamically alters the mutation probability according to population diversity indicators and the number of evolutionary generations, thereby balancing the exploration and exploitation capabilities of the algorithm. Multiple classical test functions were selected for experimental validation, and the results show that the improved genetic algorithm significantly enhances solution accuracy and convergence speed compared to traditional algorithms, particularly excelling in high-dimensional complex optimization problems. Moreover, the new method effectively avoids premature convergence and strengthens the algorithm's ability to escape local optima. Innovatively combining population diversity with the evolutionary process to adjust mutation probability, this study provides new insights and methods for optimizing the performance of genetic algorithms, which is significant for promoting their application in more fields, especially in the optimization of complex systems.
Keyword:Genetic Algorithm Mutation Probability Adjustment Population Diversity
目 录
1绪论 1
1.1研究背景与意义 1
1.2国内外研究现状 1
1.3研究方法概述 2
2变异概率对遗传算法的影响 2
2.1变异概率的基本概念 2
2.2不同变异概率下的算法表现 3
2.3变异概率与收敛速度的关系 3
3变异概率调整策略的研究 4
3.1常见调整策略分析 4
3.2自适应调整机制设计 5
3.3动态调整策略的实现 5
4改进算法的应用与验证 6
4.1应用场景选择 6
4.2实验设计与结果分析 6
4.3改进效果评估 7
结论 8
参考文献 9
致谢 10
