进化算法的随机性成本:交叉可以保存随机位.
1Chair of Algorithms for Intelligent Systems, University of Passau, Passau, Germany car.kneissl@gmail.com.
Evolutionary computation
|January 17, 2025
概括
进化算法使用随机数字进行突变和交叉等操作. 这项研究量化了"随机性成本",发现交叉可以显著降低这一成本,特别是对于像JUMPk这样的函数.
科学领域:
- 计算机科学 计算机科学
- 人工智能的人工智能
- 算法分析 算法分析
背景情况:
- 进化算法 (EAs) 在核心操作中严重依赖随机数生成.
- 电子分析的效率通常与计算资源有关,包括使用的随机数字的质量和数量.
- 量化"随机性成本"对于优化EA性能至关重要.
研究的目的:
- 分析和绑定进化算法中使用的预期随机位数.
- 为了比较只有突变的EA和包含交叉的EA之间的随机性成本.
- 评估交叉对特定基准函数如ONEMAX和JUMPk随机性成本的影响.
主要方法:
- 在突变操作中随机位使用的理论分析 (1位翻转,标准突变).
- 统一交叉的随机性成本的数学推导.
- 一个 (2+1) 基因算法在ONEMAX和JUMPk测试函数上的案例研究分析.
主要成果:
- 基于突变的EA具有与每种突变的log (n) 相关的随机性成本.
- 统一交叉的成本可以高达n,但对于ONEMAX,交叉的总随机性成本只有 Θ(n).
- 对于JUMPk函数来说,交叉导致评估和随机性成本的不对称下降.
结论:
- 交叉运营商可以显著降低进化算法的随机性总体成本.
- 交叉效率的提高,特别是随机性成本,在某些复杂的基准函数上更为明显.
- 结合交叉可以使EA比纯粹基于突变的方法更有效地利用资源.
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