IEEE Trans Neural Netw Learn Syst. 2017 May;28(5):1206-1215. doi: 10.1109/TNNLS.2016.2524619. Epub 2016 Apr 1.
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.
全局优化是优化领域中一个长期存在的研究课题，提出了许多具有挑战性的理论和计算问题。本文提出了一种求解约束全局优化问题的新型集体神经动力学方法。首先，提出了一种用于搜索研究优化问题的库恩-塔克点的单层递归神经网络（RNN）。接下来，通过模拟头脑风暴的范例，开发了一种集体神经动力学优化方法。多个 RNN 被利用来协同搜索粒子群优化框架中的全局最优解。每个 RNN 根据其自身的神经动力学进行精确的局部搜索，并收敛到候选解。通过交换每个个体网络和整个群体的历史信息，重复重置每个神经网络的神经元状态。进行小波突变以避免早熟、增加多样性和促进全局收敛。在随机优化框架中证明，只要使用足够数量的神经网络，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它能够实时解决约束全局优化问题。通过使用基准优化问题来说明所提出方法的有效性和特点。
