A new intelligent algorithm for solving generalized Nash equilibrium problem

Abstract

In this paper, the chaotic whale slime mould algorithm (CWSMA) is designed to solve the generalized Nash equilibrium problem (GNEP). First, the GNEP is converted into a non-linear equation system problem using the Karush–Kuhn–Tucker (KKT) condition and the “min” function. Compared to the classical approach, the transformation process does not require the functions to be quadratically differentiable and strongly convex. The CWSMA is proposed by introducing tent mapping, levy flight strategy and the idea of whale optimization algorithm into the slime mould algorithm (SMA), which has the advantages of higher population diversity, faster convergence, less chance of falling into local optimums, and does not depend on the choice of initial points. Furthermore, the convergence analysis of the CWSMA is given by using Markov processes. Finally, several numerical simulation experiments show that the CWSMA is superior to the SMA, the coevolutionary immune quantum particle swarm optimization algorithm, the projection algorithm and the descent algorithm under certain conditions. The CWSMA not only solves the GNEP effectively, but also has better population diversity, global convergence, and off-line performance.