优化莱维航班的飞越长度,并进行重置
Mattia Radice1, Giampaolo Cristadoro2
1<a href="https://ror.org/01bf9rw71">Max Planck Institute for the Physics of Complex Systems</a>, 01187 Dresden, Germany.
Physical review. E
|September 19, 2024
概括
在重尾跳跃的单维搜索中进行随机重置,以确保有限的平均跳跃距离. 这种重置策略可以通过最小化目标之外的距离来优化搜索效率.
科学领域:
- 物理 物理学 物理
- 统计力学 统计力学
- 可能性理论概率理论.
背景情况:
- 研究一维搜索过程与随机重置.
- 检查随机步行与重尾跳跃分布.
- 介绍了跨越长度作为搜索效率指标的概念.
研究的目的:
- 在重尾随机步行中调查随机重置对跨越长度的影响.
- 确定重置是否可以导致有限的平均跳转,与非重置场景不同.
- 通过重置确定优化搜索效率的条件.
主要方法:
- 使用一个离散时间随机步行模型,重置概率.
- 分析了重尾跳跃分布.
- 从理论上计算首次通行时间和跳跃长度.
主要成果:
- 证明当平均跳跃长度有限时,随机重置会诱导有限的平均跳跃长度 (lb(r)).
- 提供了对lb的准确计算.
- 显示重置可以导致非微不足道的优化,最小的跳跃比单个跳跃平均值小.
结论:
- 随机重置是一种可行的策略,用于控制和优化涉及重尾分布的搜索流程.
- 通过重置实现的有限平均杆在非重置场景中比无限的杆提供了显著的优势.
- 进一步的研究可以探索各种搜索动态的最佳重置策略.
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