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arXiv 1105.5540cs.NE
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粒子群优化中有限首中时间与随机收敛性的关系

Finite First Hitting Time versus Stochastic Convergence in Particle Swarm Optimisation

Per Kristian Lehre, Carsten Witt

摘要:

我们重新考虑粒子群优化的随机收敛分析,并指出,以前获得的参数条件并不总是足以保证均方收敛到局部最优。我们表明,停滞实际上可以发生在非平凡的配置在非最佳部分的搜索空间,即使是简单的功能,如球。在这些情况下,基本PSO的收敛特性可能不利于优化的目标,即在合理的时间内找到足够好的解决方案。为了提高算法的优化能力,我们提出了期望首中时间(FHT),即,直到访问到最优值附近的搜索点的时间。结果表明,一个基本的PSO可能有无限的预期FHT,而这里介绍的算法,噪声PSO,有有限的预期FHT的一些功能。

英文摘要:

We reconsider stochastic convergence analyses of particle swarm optimisation, and point out that previously obtained parameter conditions are not always sufficient to guarantee mean square convergence to a local optimum. We show that stagnation can in fact occur for non-trivial configurations in non-optimal parts of the search space, even for simple functions like SPHERE. The convergence properties of the basic PSO may in these situations be detrimental to the goal of optimisation, to discover a sufficiently good solution within reasonable time. To characterise optimisation ability of algorithms, we suggest the expected first hitting time (FHT), i.e., the time until a search point in the vicinity of the optimum is visited. It is shown that a basic PSO may have infinite expected FHT, while an algorithm introduced here, the Noisy PSO, has finite expected FHT on some functions.

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