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A rigorous analysis of the compact genetic algorithm for linear functions

机译:严格的线性函数遗传算法分析

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摘要

Estimation of distribution algorithms (EDAs) solve an optimization problem heuristically by finding a probability distribution focused around its optima. Starting with the uniform distribution, points are sampled with respect to this distribution and the distribution is changed according to the function values of the sampled points. Although there are many successful experiments suggesting the usefulness of EDAs, there are only few rigorous theoretical results apart from convergence results without time bounds. Here we present first rigorous runtime analyses of a simple EDA, the compact genetic algorithm (cGA), for linear pseudo-Boolean functions on n variables. We prove a general lower bound for all functions and a general upper bound for all linear functions. Simple test functions show that not all linear functions are optimized in the same runtime by the cGA.
机译:分布算法(EDA)的估计通过找到围绕其最优值的概率分布来启发式地解决优化问题。从均匀分布开始,针对该分布对点进行采样,然后根据采样点的函数值更改分布。尽管有许多成功的实验表明EDA的有用性,但是除了没有时间限制的收敛结果外,只有很少的严格的理论结果。在这里,我们对n个变量上的线性伪布尔函数进行了简单的EDA(紧凑遗传算法(cGA))的首次严格运行时分析。我们证明了所有函数的一般下界和所有线性函数的一般上限。简单的测试函数表明,并非所有线性函数都由cGA在同一运行时间中进行了优化。

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