  In this paper, a mathematical model is proposed to optimize the production
level of Power Plants (PPs) in collusion and competitive markets and in the
presence of external costs. To evaluate the model, two meta-heuristics, such as
Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), are proposed. A
numerical example is studied to assess the behavior of PPs in the presence of
external costs. According to the computational results, the increment in the
external costs will decrease the production level and profit of all PPs in both
collusion and competitive markets. But the computational results show that the
effect of increment in the external costs on the PPs with high-quality
equipment is less compared to the PPs with poor equipment. Moreover, the
increment in the external costs will force PPs to use greener fuel resources
instead of fossil fuel.

Optimization and Control