A collective neurodynamic optimization approach to bound-constrained nonconvex optimization.
This paper presents a novel collective neurodynamic optimization method for solving nonconvex optimization problems with bound constraints. First, it is proved that a one-layer projection neural network has a property that its equilibria are in one-to-one correspondence with the Karush-Kuhn-Tucker points of the constrained optimization problem. Next, a collective neurodynamic optimization approach is developed by utilizing a group of recurrent neural networks in framework of particle swarm optimization by emulating the paradigm of brainstorming. Each recurrent neural network carries out precise constrained local search according to its own neurodynamic equations. By iteratively improving the solution quality of each recurrent neural network using the information of locally best known solution and globally best known solution, the group can obtain the global optimal solution to a nonconvex optimization problem. The advantages of the proposed collective neurodynamic optimization approach over evolutionary approaches lie in its constraint handling ability and real-time computational efficiency. The effectiveness and characteristics of the proposed approach are illustrated by using many multimodal benchmark functions.
Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong. Electronic address: zyan@mae.cuhk.edu.hk.
Zheng
Z
Yan
Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong; School of Control Science and Engineering, Dalian University of Technology, Dalian, Liaoning, China. Electronic address: jwang@mae.cuhk.edu.hk.
Jun
J
Wang
Department of Mathematics, Beijing Information Science and Technology University, Beijing, China. Electronic address: xyliguocheng@sohu.com.
Guocheng
G
Li
D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation / Q000592:standards*; D006126:Group Processes; D016571:Neural Networks, Computer; D011340:Problem Solving
Collective neurodynamic optimization; Nonconvex optimization; Recurrent neural network