摘 要
遗传算法作为一种全局优化搜索技术，广泛应用于复杂问题求解中，其中交叉算子作为遗传算法的核心操作之一，对算法性能有着重要影响。为提升遗传算法的搜索效率与求解质量，本研究聚焦于交叉算子的优化设计与实验分析。通过深入剖析现有交叉算子在不同应用场景下的局限性，提出了一种基于自适应机制的新型交叉算子设计方案，该方案能够根据种群多样性动态调整交叉概率及交叉方式，从而有效平衡算法的探索与开发能力。采用多种经典测试函数和实际工程优化问题进行对比实验，结果表明所提出的自适应交叉算子在收敛速度、解的质量以及鲁棒性方面均优于传统固定参数交叉算子。特别是在处理高维复杂优化问题时，新方法展现出更强的全局搜索能力和更高的求解精度。本研究不仅为遗传算法交叉算子的设计提供了新的思路，还为相关领域复杂优化问题的有效求解奠定了理论基础，具有重要的学术价值和应用前景。
关键词：遗传算法 交叉算子 自适应机制
Abstract
Genetic algorithms, as a global optimization search technique, are widely applied in solving complex problems, where the crossover operator, as one of the core operations, significantly influences algorithm performance. To enhance the search efficiency and solution quality of genetic algorithms, this study focuses on the optimization design and experimental analysis of crossover operators. By thoroughly analyzing the limitations of existing crossover operators in various application scenarios, an adaptive mechanism-based novel crossover operator design is proposed. This scheme dynamically adjusts the crossover probability and method based on population diversity, effectively balancing the exploration and exploitation capabilities of the algorithm. Comparative experiments using multiple classical test functions and real-world engineering optimization problems demonstrate that the proposed adaptive crossover operator outperforms traditional fixed-parameter crossover operators in terms of convergence speed, solution quality, and robustness. Notably, when dealing with high-dimensional complex optimization problems, the new method exhibits stronger global search capabilities and higher solution accuracy. This research not only provides new insights into the design of crossover operators for genetic algorithms but also lays a theoretical foundation for effectively solving complex optimization problems in related fields, highlighting significant academic value and application prospects.
Keyword:Genetic Algorithm Crossover Operator Adaptive Mechanism
目 录
1绪论 1
1.1遗传算法与交叉算子概述 1
1.2研究背景与意义 1
1.3国内外研究现状综述 1
1.4本文研究方法与创新点 2
2交叉算子优化设计理论基础 2
2.1遗传算法基本原理 2
2.2传统交叉算子分析 3
2.3交叉算子性能评价指标 3
2.4优化设计的理论依据 4
3交叉算子优化设计方案 4
3.1新型交叉算子构建思路 4
3.2参数选择与调整策略 5
3.3算法流程设计 5
3.4方案可行性分析 6
4实验设计与结果分析 6
4.1实验环境与数据集选择 6
4.2性能对比实验设置 7
4.3实验结果与数据分析 7
4.4结果讨论与方案改进 8
结论 8
参考文献 10
致谢 11
