A Novel Linear Time Invariant Systems Order Reduction Approach Based on a Cooperative Multi-objective Genetic Algorithm

Cooperative multi-objective optimization tool is proposed for solving the order reduction problem for linear time invariant systems. Normally, the adequacy of an order reduction problem solution is estimated using two different criteria, but only one of them identifies the model. In this study, it was suggested to identify the parameters using both of the criteria, and since the criteria are complex and multi-extremum there is a need for a powerful optimization algorithm to be used. The proposed approach is based on the cooperation of heterogeneous algorithms implemented in the islands scheme and it has proved its efficiency in solving various multi-objective optimization problems. It allows us to receive a set of lower order models, which are non-dominated solutions for the given criteria and an estimation of the Pareto set. The results of this study are compared to the results of solving the same problems using various approaches and heuristic optimization tools and it is demonstrated that the set of solutions not only outperforms these approaches by the main criterion, but also provides good solutions with another criterion and a combination of them using the same computational resources.