Firefly algorithm for finding optimal shapes of electromagnetic devices

Many real-world optimization problems have to be treated as multi-objective optimization problems. An approach, well established in recent years, is to find Pareto optimal configurations of the trial variables by detecting nondominated solutions with the help of a suitable vector optimization method. Alternatively, relying on scalar optimization methods (both stochastic or deterministic), a suitable objective function taking all objectives into account simultaneously has to be defined. Depending on the number of trial variables, a scalar objective function of that type will exhibit a considerable number of feasible local solutions besides the global one. Therefore, a useful scalar optimization strategy should be able to end up (with a high probability) in the best of all possible solutions in the given search space and additionally detect as many local solutions as possible. Some population-based stochastic methods are implicitly suited for that task; others can be enhanced to fulfill these requirements. Higher order evolution strategies have successfully been tuned for that kind of problem by introducing cluster sensitive recombination [niching higher order evolution strategy (NES)]. The firefly algorithm (FFA) mimics the behavior of fireflies, which use a kind of flashing light to communicate with other members of their species. Since the intensity of the light of a single firefly diminishes with increasing distance, the FFA is implicitly able to detect local solutions on its way to the best solution for a given scalar objective function. The FFA will be applied to the well-known Rastrigin test function and to a shielding/shunting electromagnetic problem with two and three objectives, respectively, and its results will be compared with the ones obtained with an NES.