Evolutionary Algorithms with Constraint Handling for the Hydroelectric Dispatch Planning

This paper proposes a method to solve the long-term scheduling of the Brazilian hydroelectric power system. The objective is to meet the energy demand by defining the required actions for each individual power plant, whilst respecting boundarie and operational constraints. The mathematical model is formulated as a dynamic, nonlinear, multiobjective, high dimensional and largely constrained optimization problem. We compare two classes of metaheuristics for constrained problems: Differential Evolution (DE) and swarm-based (PSO), using the CEC-2017 constrained optimization competition benchmark. The best performing metaheuristics of each class, evolutionary-based LSHADE44b (a slight variant of LSHADE44, winner of CEC-2017) and swarm-based EPSO-G, are then compared on the hydroelectric power system scheduling problem. We considered 111 power plants for a period of 5 years, with monthly time-step, resulting in 13,320 decision variables with 20,091 constraints, which are optimized for 194 random affluence scenarios. Results show that LSHADE44b outperforms EPSO-G in all scenarios, reducing the constraints violations down to an average of 16. On 45% of the affluence scenarios there were no violations, and the cost steadily decreased, showing convergence after the constraints are satisfied.