拓扑特征对空间结构进化算法动力学的影响
Influence of Topological Features on Spatially-Structured Evolutionary Algorithms Dynamics
摘要：
在过去的几十年里，复杂网络理论显着影响了其他学科的静态和动态方面的建模系统在自然界中观察到的。这项工作的目的是研究网络的拓扑特征对进化算法的动力学的影响，特别是考虑到找到大量的多模态问题的最优解的能力。我们介绍了一种新的空间结构的进化算法，我们将其应用于两个组合问题：ONEMAX和多模态NMAX。考虑三种不同的网络模型，我们调查他们的特点之间的关系，算法的收敛性和它的能力，以找到多个最优（多峰问题）。为了进行更深入的分析，我们研究了引入时变权重的加权图。结果表明，具有大的平均路径长度的网络导致更多的最优解和随之而来的缓慢的探索动力学（即低的首次命中时间）。此外，加权网络的引入表明了在算法执行过程中通过与权值变化相关的参数来调整算法动态特性的可能性。这项工作给出了第一个答案的各种图形拓扑结构的多样性的进化算法的影响，它描述了一个简单但功能强大的算法框架，允许调查ssEAs动态的许多方面。
英文摘要：
In the last decades, complex networks theory significantly influenced other disciplines on the modeling of both static and dynamic aspects of systems observed in nature. This work aims to investigate the effects of networks' topological features on the dynamics of an evolutionary algorithm, considering in particular the ability to find a large number of optima on multi-modal problems. We introduce a novel spatially-structured evolutionary algorithm and we apply it on two combinatorial problems: ONEMAX and the multi-modal NMAX. Considering three different network models we investigate the relationships between their features, algorithm's convergence and its ability to find multiple optima (for the multi-modal problem). In order to perform a deeper analysis we investigate the introduction of weighted graphs with time-varying weights. The results show that networks with a large Average Path Length lead to an higher number of optima and a consequent slow exploration dynamics (i.e. low First Hitting Time). Furthermore, the introduction of weighted networks shows the possibility to tune algorithm's dynamics during its execution with the parameter related with weights' change. This work gives a first answer about the effects of various graph topologies on the diversity of evolutionary algorithms and it describes a simple but powerful algorithmic framework which allows to investigate many aspects of ssEAs dynamics.
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