Multi-objective optimization of active control system using population guidance and modified reference-point-based NSGA-II

The optimization of the active control system is pivotal in achieving an acceptable performance level while minimizing control costs. The optimal location of actuators, efficient control force, and adequate vibration reduction are critical objectives in control system optimization. This study introduces a novel optimization algorithm, the Population-Guided and Modified Reference-Point Based Non-Dominated Sorting Genetic Algorithm-II (PMR-NSGA-II), tailored for actuator placement and tuning that incorporates input and output user preference. The analysis focuses on optimizing the vibration control of a 20-story steel frame building. The PMR-NSGA-II could reduce the computational expenses of three objectives optimization by guiding the initial population using prospective population prediction and orienting the search towards a reference point. The pre-calculated input energy distribution guides the determination of the prospective initial population. The reference point, along with the allowable drift and actuator capacity constraints, focuses the search process to efficiently obtain the Pareto fronts with less effort wasted to explore the less preferred areas in the search space. The non-dominated sorting and elitist operators are also employed to fasten the convergence. The structural analysis is conducted via non-linear time history analysis with seven ground motions considered. The PMR-NSGA-II exhibits significant computational efficiency in the active control system optimization. Results demonstrate that PMR-NSGA-II could provide the near-optimal solution closest to the reference point with a smaller population size and a faster convergence rate than the NSGA-II. The computational time per generation of the proposed PMR-NSGA-II is 1.36 to 2.43 times faster than NSGA-II for the seven ground motions analyzed. By applying PMR-NSGA-II, the number of individuals that need to be assessed to reach convergence is reduced by 50 % to 88 % compared to NSGA-II. Ultimately, the near-optimal configurations could significantly reduce the building responses and increase the performance level of the building based on FEMA 356 and ASCE 41 acceptance criteria.