Nature-inspired optimization techniques are useful tools in electrical engineering problems to minimize or maximize an objective function. In this paper, we use the firefly algorithm to improve the optimal solution for the problem of directional overcurrent relays (DOCRs). It is a complex and highly nonlinear constrained optimization problem. In this problem, we have two types of design variables, which are variables for plug settings (PSs) and the time dial settings (TDSs) for each relay in the circuit. The objective function is (...) to minimize the total operating time of all the basic relays to avoid unnecessary delays. We have considered four models in this paper which are IEEE (3-bus, 4-bus, 6-bus, and 8-bus) models. From the numerical results, it is obvious that the firefly algorithm with certain parameter settings performs better than the other state-of-the-art algorithms. (shrink)

Design problems in structural engineering are often modeled as differential equations. These problems are posed as initial or boundary value problems with several possible variations in structural designs. In this paper, we have derived a mathematical model that represents different structures of beam-columns by varying axial load with or without internal forces including bending rigidity. We have also developed a novel solver, the LeNN-NM algorithm, which consists of weighted Legendre polynomials, and a single path following optimizer, the Nelder–Mead algorithm. To (...) evaluate the performance of our solver, we have considered three design problems representing beam-columns. The values of performance indicators, MAD, TIC, NSE, and ENSE, are calculated for a hundred simulations. The outcome of our statistical analysis points to the superiority of the LeNN-NM algorithm. Graphical illustrations are presented to further elaborate on our claims. (shrink)