单个和多目标进化算法的运行时分析,用于具有正常分布的随机变量的机会受限优化问题
1Optimisation and Logistics, The University of Adelaide, Adelaide, Australia frank.neumann@adelaide.edu.au.
Evolutionary computation
|August 5, 2024
概括
机会受约束优化的进化算法面临着局部最佳. 多目标方法有效地平衡成本和差异,为随机优化问题的不同信心水平提供最佳解决方案.
科学领域:
- 优化优化 优化优化
- 进化计算是一种进化计算.
- 随机系统 随机系统 随机系统
背景情况:
- 机会受约束的优化问题结合了随机元素,需要限制以高概率得到满足.
- 进化算法 (EAs) 在解决这些复杂的优化场景方面取得了成功.
- 应用于机会受约束优化的EA的理论理解,特别是与独立的,正常分布的随机元件,需要进一步发展.
研究的目的:
- 从理论上分析进化算法的性能在机会受约束的优化设置.
- 引入和评估机会受限制的优化问题的多目标公式.
- 为了解决多目标配方中可能存在的众多权衡的计算挑战.
主要方法:
- 在统一的约束条件下分析一个简单的单一目标 (1+1) 进化算法 (EA).
- 开发和应用一个多目标优化公式,交易预期成本和差异.
- 提议和分析改进的凸多目标方法来处理复杂的权衡景观.
- 实验验证使用NP-hard随机最小重量主导集问题的实例.
主要成果:
- 单一目标 (1+1) EA 显示了局限性,导致局部最佳和指数时间复杂性在受限制的场景中.
- 多目标EA公式有效地产生了一系列解决方案,包括所有信任级别的最佳权衡.
- 拟议的凸多目标方法提高了处理复杂的权衡空间的效率.
- 实验结果证实了多目标和改进的凸多目标战略的实际好处.
结论:
- 多目标进化算法方法为解决机会受约束的优化问题提供了强大而有效的方法.
- 这种配方提供了一套全面的解决方案,允许根据所需的信心水平进行选择.
- 该研究推进了对随机优化挑战的进化计算的理论和实践理解.
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