Discrete invasive weed optimization for Nash . . .

... games is a challenging work due to existence of local Nash equilibrium traps. So, devising algorithms that are capable of escaping from local optima and finding global solutions is needed for analysis of nonlinear games. Evolutionary algorithms (EAs) as the popular stochastic global search algorithms can be exploited for this purpose. This paper studies performance of discrete invasive weed optimization (DIWO) for Nash equilibrium search in games with numerous local NEs. Firstly, DIWO is introduced and specialized for optimization in descretized spaces. Efficiency of DIWO for function optimization is evaluated and compared with some other discrete EAs through a number of popular test functions in stochastic optimization literature. Afterwards, it is explained how to characterize NEs as minima of an objective function, and DIWO is used to minimize these functions in two experimental studies. The first problem is a static nonlinear game with multiple local NEs, and the second one is Cournot model of a transmission-constrained electricity market called IEEE30 bus test system. The results show that the proposed algorithm is a promising technique to come up with complex theoretical and practical games