Theoretical analysis of evolutionary computation on continuously differentiable functions
Theoretical analysis of evolutionary computation on continuously differentiable functions
复制标题
DOI：
10.1145/1830483.1830742
复制
发表时间：
2010-07
期刊：
影响因子：
--
通讯作者：
Youhei Akimoto;Y. Nagata;I. Ono;S. Kobayashi
中科院分区：
文献类型：
--
作者：
Youhei Akimoto;Y. Nagata;I. Ono;S. Kobayashi
本文从理论上研究了连续可微函数约束极小化问题的一类随机算法的收敛性。我们感兴趣的是不会卡在函数的斜率上，而是仅收敛到局部最优点的算法。收敛到一个既不是函数的驻点也不是边界点的点是收敛性质表现不好的证据。我们研究什么性质是必要的/足够的算法，以避免这种类型的行为，即，算法只收敛到函数的局部最优点需要什么性质。我们还研究了现代EC为基础的随机算法的两个变种，即，CMAES采用秩-μ更新和EDA称为EMNAglobal的参数上的类似条件。通过对两个表面上相似的系统进行比较，发现它们具有明显不同的理论行为。这一结果为我们设计性能良好的优化算法提供了一个洞察。
This paper investigates theoretically the convergence properties of the stochastic algorithms of a class including both CMAESs and EDAs on constrained minimization of continuously differentiable functions. We are interested in algorithms that do not get stuck on a slope of the function, but converge only to local optimal points. Convergence to a point that is neither a stationary point of the function nor a boundary point is evidence that the convergence properties are not well behaved. We investigate what properties are necessary/sufficient for the algorithm to avoid this type of behavior, i.e., what properties are necessary for the algorithm to converge only to local optimal points of the function. We also investigate the analogous conditions on the parameters of two variants of modern EC-based stochastic algorithms, namely, a CMAES employing rank-μ update and an EDA known as EMNAglobal. The comparison between the apparently similar two systems shows that they have significantly different theoretical behaviors. This result presents us with an insight into the way we design well-behaved optimization algorithms.