A Collaborative Neurodynamic Optimization Approach to Distributed Nash-Equilibrium Seeking in Multicluster Games With...

Area of Science:

• Artificial Intelligence
• Game Theory
• Optimization

Background:

• Distributed optimization problems often involve complex, non-convex functions.
• Finding generalized Nash equilibriums (GNEs) is crucial for analyzing multi-agent systems.
• Existing methods may struggle with scalability and convergence in decentralized settings.

Purpose of the Study:

• To propose a novel collaborative neurodynamic optimization (CNO) method.
• To enable the distributed seeking of GNEs in multicluster games with non-convex functions.
• To demonstrate the method's efficacy using an electricity market price-bidding example.

Main Methods:

• Development of a projection neural network based on an augmented Lagrangian function for local GNE search.
• Proof of convergence for the projection neural network to a local GNE.
• Formulation of a global optimization problem and application of a CNO approach with recurrent neural networks and metaheuristic reinitialization for global search.

Main Results:

• The projection neural network is proven to converge to a local GNE.
• The CNO approach effectively performs scattering searches and state reinitialization.
• The proposed method demonstrates viability in a practical electricity market price-bidding problem.

Conclusions:

• The CNO method offers a robust approach for distributed GNE seeking in challenging game settings.
• The integration of neural networks and metaheuristics enhances search efficiency and quality.
• The approach is validated through a relevant economic application, showing practical applicability.