进化算法中的稳定变异

English | PDF,EPUB | 2018 (2019 Edition) | 175 Pages | ISBN : 3030015475 | 20.42 MB

This book presents a set of theoretical and experimental results that describe the features of the wide family of α-stable distributions (the normal distribution also belongs to this class) and their various applications in the mutation operator of evolutionary algorithms based on real-number representation of the individuals, and, above all, equip these algorithms with features that enrich their effectiveness in solving multi-modal, multi-dimensional global optimization problems. The overall conclusion of the research presented is that the appropriate choice of probabilistic model of the mutation operator for an optimization problem is crucial. Mutation is one of the most important operations in stochastic global optimization algorithms in the n-dimensional real space. It determines the method of search space exploration and exploitation. Most applications of these algorithms employ the normal mutation as a mutation operator. This choice is justified by the central limit theorem but is associated with a set of important limitations. Application of α-stable distributions allows more flexible evolutionary models to be obtained than those with the normal distribution. The book presents theoretical analysis and simulation experiments, which were selected and constructed to expose the most important features of the examined mutation techniques based on α-stable distributions. It allows readers to develop a deeper understanding of evolutionary processes with stable mutations and encourages them to apply these techniques to real-world engineering problems.

这本书介绍了描述α稳定分布（包括正态分布）的特性的理论和实验结果，以及这些分布如何应用于基于实数表示个体的进化算法中性突变算子的各种应用，并且最重要的是为这些算法提供了增强其在解决多模态、高维全局优化问题的有效性的特性。研究的整体结论是，选择一个合适的概率模型来描述优化问题中的变异操作至关重要。变异操作是n维实空间中的随机全局优化算法中最重要的一项操作，它决定了探索和利用搜索空间的方法。这些算法大多数应用时都使用了正态变异作为变异算子。这种选择是由中心极限定理支持的，但也与一系列重要的限制相关联。采用α稳定分布的应用可以获得比基于正态分布的模型更灵活的进化模型。这本书进行了理论分析和仿真实验，以选出并构建出基于α稳定分布的变异技术的关键特性，以便读者能够深入了解具有稳定变异的进化学过程，并鼓励他们在实际工程问题中应用这些技术。

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