Applications of multi-objective dimension-based firefly algorithm to optimize the power losses, emission, and cost in power systems

In this paper, a new multi-objective dimension-based firefly algorithm (MODFA) is proposed for solving the constrained multi-objective optimal power flow (MOOPF) problem with multiple and contradictory objectives in power systems. In our suggested MODFA algorithm, a constrained Pareto-dominant approach (CPA) is offered for guaranteeing zero violations of various inequality constraints on state variables in the constrained MOOPF problem. In addition to that, the CPA and the dimension-based technology (DT) are federated together to update the information of the non-dominant firefly to speed up the convergence of multiple target search. Crowding distance and non-dominated sorting based on the violation of constraints are also regarded as measures to sustain well-distributed Pareto optimal solution (POS) set. Furthermore, a fuzzy affiliation is utilized to pick the best compromise solution (BCS) from the obtained POS. The IEEE30-bus system, the IEEE57-bus system, and the IEEE118-bus system with nine cases are implemented to validate the performance of the proposed MODFA by considering the active power losses, the emission, and the total fuel cost. The numerous simulation results optimized by the MODFA, which are compared with frequently-used NSGA-III, NSGA-II, and MOPSO algorithm, show the capability of the MODFA for obtaining POS with uniform distribution and high quality. Additionally, three performance metrics are considered to evaluate approximation, distribution, and diversity of POS found by MODFA.