A Collective Neurodynamic Approach to Constrained Global Optimization
A Collective Neurodynamic Approach to Constrained Global Optimization
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DOI：
10.1109/tnnls.2016.2524619
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发表时间：
2017-05
影响因子：
10.4
通讯作者：
Zheng Yan;Jianchao Fan;Jun Wang
中科院分区：
文献类型：
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作者：
Zheng Yan;Jianchao Fan;Jun Wang
全局优化是优化领域一个长期的研究课题，提出了许多具有挑战性的理论和计算问题。本文提出了一种新颖的集体神经动力学方法来解决约束全局优化问题。首先，提出了一种单层循环神经网络（RNN）来搜索所研究的优化问题的Karush-Kuhn-Tucker点。接下来，通过模拟头脑风暴的范式开发了集体神经动力学优化方法。在粒子群优化框架中协同利用多个 RNN 来搜索全局最优解。每个 RNN 都会根据自己的神经动力学进行精确的局部搜索并收敛到候选解。通过交换每个单独网络和整个组的历史信息来重复重置每个神经网络的神经元状态。进行小波变异是为了避免早熟、增加多样性并促进全局收敛。在随机优化的框架中证明，只要使用足够多的神经网络，所提出的集体神经动力学方法就能够以概率 1 计算全局最优解。集体神经动力学优化方法的本质在于其实时解决受限全局优化问题的潜力。通过使用基准优化问题来说明所提出方法的有效性和特征。
Global optimization is a long-lasting research topic in the field of optimization, posting many challenging theoretic and computational issues. This paper presents a novel collective neurodynamic method for solving constrained global optimization problems. At first, a one-layer recurrent neural network (RNN) is presented for searching the Karush–Kuhn–Tucker points of the optimization problem under study. Next, a collective neuroydnamic optimization approach is developed by emulating the paradigm of brainstorming. Multiple RNNs are exploited cooperatively to search for the global optimal solutions in a framework of particle swarm optimization. Each RNN carries out a precise local search and converges to a candidate solution according to its own neurodynamics. The neuronal state of each neural network is repetitively reset by exchanging historical information of each individual network and the entire group. Wavelet mutation is performed to avoid prematurity, add diversity, and promote global convergence. It is proved in the framework of stochastic optimization that the proposed collective neurodynamic approach is capable of computing the global optimal solutions with probability one provided that a sufficiently large number of neural networks are utilized. The essence of the collective neurodynamic optimization approach lies in its potential to solve constrained global optimization problems in real time. The effectiveness and characteristics of the proposed approach are illustrated by using benchmark optimization problems.