This research discusses the application of a mixed-integer-binary small-population-based evolutionary particle swarm optimization to the problem of optimal power flow, where the optimization problem has been formulated taking into account four decision variables simultaneously: active power (continuous), voltage generator (continuous), tap position on transformers (integer) and shunt devices (binary). The constraint handling technique used in the algorithm is based on a strategy to generate and keep the decision variables in feasible space through the heuristic operators. The heuristic operators are applied in the active power stage and the reactive power stage sequentially. Firstly, the heuristic operator for the power balance is computed in order to maintain the power balance constraint through a re-dispatch of the thermal units. Secondly, the heuristic operators for the limit of active power flows and the bus voltage constraint at each generator bus are executed through the sensitivity factors. The advantage of our approach is that the algorithm focuses the search of the decision variables on the feasible solution space, obtaining a better cost in the objective function. Such operators not only improve the quality of the final solutions but also significantly improve the convergence of the search process. The methodology is verified in several electric power systems. 
Modeling a mixed-integer-binary small-population evolutionary particle swarm algorithm for solving the optimal power flow problem in electric power systems