摘 要
遗传算法作为一种模拟自然选择和遗传机制的优化算法，在众多领域得到广泛应用，种群规模作为遗传算法的重要参数之一，对算法性能有着不可忽视的影响。本研究旨在深入探讨遗传算法中不同种群规模对算法性能的影响，以期为遗传算法在实际应用中的参数设置提供理论依据。研究基于多种经典测试函数构建实验环境，采用控制变量法，设定不同种群规模进行多次独立实验，记录并分析各规模下算法的收敛速度、解的质量等性能指标。结果表明，较小种群规模可能导致算法早熟收敛，难以获得全局最优解；较大种群规模有助于提高解的质量，但会增加计算成本，降低算法效率。通过对比分析发现存在一个较优的种群规模范围，在此范围内可实现算法性能的较好平衡。本研究创新性地引入了适应度分布等新指标来综合评估算法性能，丰富了对种群规模影响算法性能的研究视角，主要贡献在于为合理确定遗传算法的种群规模提供了新的思路与方法，有助于提升遗传算法在解决复杂优化问题时的有效性和可靠性。
关键词：遗传算法 种群规模 算法性能
Abstract
Genetic Algorithm (GA), as an optimization algorithm that simulates natural selection and genetic mechanisms, has been widely applied in various fields. Population size, one of the critical parameters of GA, exerts a significant influence on algorithm performance. This study aims to thoroughly investigate the impact of different population sizes on the performance of genetic algorithms, providing theoretical guidance for parameter settings in practical applications. Based on multiple classical test functions, an experimental environment was constructed, and the control variable method was employed to conduct multiple independent experiments with varying population sizes. The convergence speed and solution quality under each population size were recorded and analyzed. Results indicate that smaller population sizes may lead to premature convergence, making it difficult to obtain global optimal solutions, while larger population sizes can enhance solution quality but increase computational costs and reduce algorithm efficiency. Comparative analysis reveals an optimal range of population sizes within which a better balance of algorithm performance can be achieved. Innovatively, this study introduces new metrics such as fitness distribution to comprehensively evaluate algorithm performance, enriching the research perspective on how population size affects algorithm performance. The primary contribution lies in offering new approaches and methods for reasonably determining the population size of genetic algorithms, thereby enhancing the effectiveness and reliability of GAs in solving complex optimization problems.
Keyword:Genetic Algorithm Population Size Algorithm Performance
目 录
1绪论 1
1.1遗传算法与种群规模研究背景 1
1.2国内外研究现状综述 1
1.3本文研究方法与技术路线 2
2种群规模对收敛速度的影响 2
2.1收敛速度的定义与衡量 2
2.2小规模种群的收敛特性 3
2.3大规模种群的收敛表现 3
3种群规模对解空间探索能力的影响 4
3.1解空间探索的重要性 4
3.2种群规模与多样性维持 5
3.3种群规模对全局搜索能力的影响 5
4种群规模对计算资源消耗的影响 6
4.1计算资源消耗的量化分析 6
4.2不同规模种群的资源占用 7
4.3资源效率与性能平衡探讨 7
结论 8
参考文献 9
致谢 10
