The problem of equilibria detection of a discrete-time Generalized Cournot Dynamic Oligopoly is approached by using a Differential Evolution and a Particle Swarm Optimization algorithm adapted to compute and track the set of generalized Nash equilibria in a dynamic setting. Both challenges of this problem, i.e. to correctly compute the entire set of generalized Nash equilibria of the constrained (generalized) game, and also to cope with the dynamic character of the landscape, are dealt with by using a simple adaptive mechanism. Numerical experiments for settings up to 60 players are performed to illustrate the efficiency of the approach.