通过大数的战略定律进行优化
Xiaohong Chen1, Zengjing Chen2, Wayne Yuan Gao3
1Department of Economics, Yale University, New Haven, CT 06511.
概括
本研究介绍了针对全球优化问题的战略蒙特卡洛优化 (SMCO). SMCO算法有效地为复杂的函数找到全局最佳值,超过现有方法.
科学领域:
- 数字分析 数字分析
- 优化理论 优化理论
- 计算数学 计算数学 计算数学
背景情况:
- 多式联运功能的全球优化是各种科学领域的一个具有挑战性的问题.
- 现有的方法经常与高维,非可区分或不连续的客观函数作斗争.
- 开发强大高效的全球优化框架仍然是一个活跃的研究领域.
研究的目的:
- 提出一个新的框架,用于局限域中连续函数的全局优化.
- 为全球优化建立最佳采样策略的理论基础.
- 引入和验证一类战略蒙特卡洛优化 (SMCO) 算法.
主要方法:
- 使用大数的战略定律,建立全球优化与最佳抽样策略形成之间的等价性.
- 提出一类SMCO算法,基于使用客观函数梯度符号 (或第一个差异) 的坐标智能决策.
- 从单个和多个起点分析SMCO算法的收性质.
主要成果:
- 证明SMCO算法从单个开始汇聚到局部优化器和多个开始的全球优化器.
- 广泛的数值研究表明,SMCO在各种,具有挑战性的测试函数,包括高维问题上的稳定性和有效性.
- SMCO 算法优于许多最先进的全球和本地优化方法.
结论:
- 拟议的SMCO框架为全球优化提供了一种强大而通用的方法.
- 在各种复杂的优化场景中,SMCO算法表现出强大的性能和稳定性.
- 这项工作为解决具有挑战性的全球优化任务提供了理论上的基础和实际上有效的工具.
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