Solving Multi-Objective Optimal Control Problems Using a Hybrid Method of Genetic Algorithm and Simple Cell Mapping

The design of a control system becomes more complex with the advancement of technology, and this requires optimization techniques to be developed. In particular, multi-objective optimal control (MOC) is a method that can be used to achieve a scheme for control system that coordinates several design objectives that can be in conflict with each other. In this study, a new hybrid scheme is presented that is a combination of non-dominated sorting genetic algorithm-II (NSGA-II) and the simple cell mapping (SCM) method. The combined method first starts a random search using the genetic algorithm and then proceeds by using the SCM method for a neighborhood-based search and recovery algorithm. An evaluation of the proposed method’s efficiency and performance was conducted on two benchmark problems and two multi-objective optimal control problems. We utilized two performance indicators (generational distance (GD) and a diversity metric) to assess the convergence to the Pareto front and the diversity of the solution set, respectively. The results demonstrated that the proposed method not only achieved superior efficiency but also produced a more uniform distribution of solutions along the Pareto front compared to the SCM and NSGA-II algorithms.