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arXiv 2004.12304cs.NE
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具有时间关联性适应度函数的进化算法分析

Analysis of Evolutionary Algorithms on Fitness Function with Time-linkage Property

Weijie Zheng, Huanhuan Chen, Xin Yao

摘要:

在实际应用中,许多优化问题具有时间关联性,即目标函数值既依赖于当前解,也依赖于历史解。虽然进化算法的严格理论分析在近二十年来得到了迅速发展,但从理论上理解进化算法在时间链接问题上的行为仍然是一个开放的问题。本文采取的第一步,严格分析进化算法的时间链接功能。基于基本的OneMax函数,我们提出了一个时间链接函数,其中最后一个时间步的第一位值被积分,但与当前的第一位具有不同的偏好。我们证明了在概率$1-o(1)$下,随机局部搜索和$(1+1)$ EA都不能找到最优解,而在概率$1-o(1)$下,$(μ+1)$ EA能够找到最优解.

英文摘要:

In real-world applications, many optimization problems have the time-linkage property, that is, the objective function value relies on the current solution as well as the historical solutions. Although the rigorous theoretical analysis on evolutionary algorithms has rapidly developed in recent two decades, it remains an open problem to theoretically understand the behaviors of evolutionary algorithms on time-linkage problems. This paper takes the first step to rigorously analyze evolutionary algorithms for time-linkage functions. Based on the basic OneMax function, we propose a time-linkage function where the first bit value of the last time step is integrated but has a different preference from the current first bit. We prove that with probability $1-o(1)$, randomized local search and $(1+1)$ EA cannot find the optimum, and with probability $1-o(1)$, $(μ+1)$ EA is able to reach the optimum.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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