A modified ant colony optimization algorithm based on differential evolution for chaotic synchronization

Optimization algorithms inspired by the ants’ foraging behavior have been initially used for solving combinatorial optimization problems. Since the emergence of ant algorithms as an optimization tool, some attempts were also made to use them for tackling continuous optimization problems. In recent years, the investigation of synchronization and control problem for discrete chaotic systems has attracted much attention, and many possible applications. The optimization of a proportional–integral–derivative (PID) controller based on a modified continuous approach of ant colony optimization combined with a differential evolution method (MACO) for synchronization of two identical discrete chaotic systems subject the different initial conditions is presented in this paper. Numerical simulations based on optimized PID control of a nonlinear chaotic model demonstrate the effectiveness and efficiency of MACO approach. Simulation results of the MACO to determine the PID parameters are compared with other metaheuristics including a classical ant colony optimization approach, genetic algorithm and evolution strategy. The proposed approach of PID tuning based on MACO can be generalized to other chaotic systems. 2009 Elsevier Ltd. All rights reserved.