A hybrid method of evolutionary algorithm and simple cell mapping for multi-objective optimization problems

A hybrid method is proposed to take advantages of evolutionary algorithms (EAs) and the simple cell mapping (SCM) for multi-objective optimization problems (MOPs). The hybrid method starts with a random search for Pareto optimal solutions with an EA, and follows up with a neighborhood based search and recovery algorithm using the SCM. The non-dominated sorting genetic algorithm-II (NSGA-II) is used as an example of EAs. It is found that the SCM based search and recovery algorithm can reconstruct the branches of the Pareto set even when only one point in the vicinity of the set is available from the random search by the EA. We have chosen several benchmark MOPs to compare NSGA-II and SCM separately with the EA $$+$$ SCM hybrid method while using the Hausdorff distance as a performance metric, and applied the method to develop multi-objective optimal designs of PID controls for a nonlinear oscillator with time delay. The results show that the EA $$+$$ SCM hybrid method is very promising.