Firefly algorithm with division of roles for complex optimal scheduling

A single strategy used in the firefly algorithm (FA) cannot effectively solve the complex optimal scheduling problem. Thus, we propose the FA with division of roles (DRFA). Herein, fireflies are divided into leaders, developers, and followers, while a learning strategy is assigned to each role: the leader chooses the greedy Cauchy mutation; the developer chooses two leaders randomly and uses the elite neighborhood search strategy for local development; the follower randomly selects two excellent particles for global exploration. To improve the efficiency of the fixed step size used in FA, a stepped variable step size strategy is proposed to meet different requirements of the algorithm for the step size at different stages. Role division can balance the development and exploration ability of the algorithm. The use of multiple strategies can greatly improve the versatility of the algorithm for complex optimization problems. The optimal performance of the proposed algorithm has been verified by three sets of test functions and a simulation of optimal scheduling of cascade reservoirs.