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arXiv cs/0210030cs.AIcs.MAcs.NE
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基于耦合局部极小的智能协同搜索

Intelligence and Cooperative Search by Coupled Local Minimizers

J. A. K. Suykens, J. Vandewalle, B. De Moor

摘要:

我们展示了如何耦合的局部优化过程可以导致更好的解决方案比多启动局部优化组成的独立运行。这是通过在各个局部最小化器的状态向量之间的同步约束下最小化系综的平均能量成本来实现的。从一个增广的拉格朗日函数,它结合了作为软和硬约束的同步约束,一个网络推导出其中的本地极小交互和交换信息,通过同步约束。从神经网络的角度来看,该阵列可以被认为是一个连续优化的拉格朗日规划网络和细胞神经网络(CNN)。与软状态同步约束相关联的惩罚权重遵循线性规划的解。这表明,系综的能量成本应该最大限度地降低。通过这种方式,成功的局部极小化器可以通过主从动态机制隐式地将其状态强加给其他极小化器,从而形成合作搜索机制。通过应用小世界网络的概念,得到了改善的信息传播的合奏。这项工作表明,在一个跨学科的背景下,信息交换和状态同步的合奏,对进化,集体行为,优化和智能等问题的重要性。

英文摘要:

We show how coupling of local optimization processes can lead to better solutions than multi-start local optimization consisting of independent runs. This is achieved by minimizing the average energy cost of the ensemble, subject to synchronization constraints between the state vectors of the individual local minimizers. From an augmented Lagrangian which incorporates the synchronization constraints both as soft and hard constraints, a network is derived wherein the local minimizers interact and exchange information through the synchronization constraints. From the viewpoint of neural networks, the array can be considered as a Lagrange programming network for continuous optimization and as a cellular neural network (CNN). The penalty weights associated with the soft state synchronization constraints follow from the solution to a linear program. This expresses that the energy cost of the ensemble should maximally decrease. In this way successful local minimizers can implicitly impose their state to the others through a mechanism of master-slave dynamics resulting into a cooperative search mechanism. Improved information spreading within the ensemble is obtained by applying the concept of small-world networks. This work suggests, in an interdisciplinary context, the importance of information exchange and state synchronization within ensembles, towards issues as evolution, collective behaviour, optimality and intelligence.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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