A collective neurodynamic optimization approach to bound-constrained nonconvex optimization

• Published in: Neural networks Vol. 55; pp. 20 - 29
• Main Authors: Yan, Zheng, Wang, Jun, Li, Guocheng
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.07.2014; Elsevier
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Biological and medical sciences; Collective neurodynamic optimization; Computer science; control theory; systems; Computer Simulation - standards; Connectionism. Neural networks; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; Group Processes; Neural Networks (Computer); Nonconvex optimization; Problem Solving; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Recurrent neural network; Social interactions. Communication. Group processes; Social psychology; Recurrent neural network; Collective neurodynamic optimization; Nonconvex optimization; Non convex programming; Evolutionary algorithm; Constraint satisfaction; Modeling; Group behavior; Efficiency; Swarm intelligence; Mathematical programming; Constraint handling; Local search; Recurrent neural nets; Local optimum; Neural network; Real time; Particle swarm optimization; Global solution; Social cognition; Neurophysiology; Constrained optimization; Multimodality; Optimal solution; Kuhn Tucker method
• ISSN: 0893-6080; 1879-2782; 1879-2782
• DOI: 10.1016/j.neunet.2014.03.006

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.