A binary cooperative bat algorithm based optimal topology design of leader–follower consensus

Abstract

In this paper, a binary cooperative bat searching algorithm(BCBA) is developed to tackle binary optimization problems. Different from the original bat searching algorithm, a consensus term was added into the velocity equation of the original bat searching algorithm in the cooperative bat searching algorithm(CBA). To develop the binary algorithm, the velocity value is mapped into a probability value between zero and one, and then the position will update to one or zero depending on the comparison between the mapped velocity and a random number. In this paper, four different mapping functions are investigated to determine the best transfer function for the binary CBA. The numerical illustrations are provided to demonstrate the superior performance of BCBA by comparing with the four binary algorithms in the literature. Moreover, the leader–follower consensus problem of multi-agent systems is studied. The condition of the communication topologies of the leader–follower protocol is relaxed so that the different topologies can be used to share different state information. In order to find the trade-off between the convergence rate and communication cost, a binary variable optimal topology design problem is formulated, and then the BCBA is used to tackle the proposed design problem. The numerical evaluation is conducted to show the competitive performance of the BCBA.