The optimal design of a three-element dynamic vibration absorber (TEDVA) involves a
fundamental trade-off between minimizing the peak amplitude magnification (H∞ norm)
and the broadband energy absorption (H2 proxy), a conflict that is further complicated by
the lack of closed-form solutions, even for undamped primary systems. In this paper, we
present an algorithm that extends the golden jackal optimizer with dynamic multi-map
chaotic initialization, a Pareto-guided two-leader search structure driven by crowding
distance, and a Pareto-gated self-adaptive differential evolution mutation to jointly ensure
convergence and diversity. The algorithm is validated on the benchmark TEDVA case with
mass ratio µ = 0.1 and primary damping ζ1 = 0.3, and benchmarked against standard
multi-objective algorithms (NSGA-II and MOPSO) as well as the single-objective AM-PSO
baseline. Simulation results indicate that MODCGJO achieves a 7.3% reduction in peak
amplitude compared to the state-of-the-art single-objective adaptive multi-swarm particle
swarm optimization (AM-PSO), while maintaining a competitive H2 performance and
converging to the same Pareto-optimal region as NSGA-II and MOPSO. Comprehensive
Pareto metrics—hypervolume, generational distance, spread, and spacing—are adopted,
validating the front’s superior quality and uniform distribution. Sensitivity analyses on
both physical design parameters (spring and damping ratios) and algorithmic control
parameters (population size, iteration count, and archive size) confirm the robustness
of the obtained solution and the stability of MODCGJO’s performance across varying
configurations. The results show that MODCGJO is an effective and reliable tool for
the multi-objective design of vibration absorbers, providing a superior trade-off between
conflicting performance criteria, with the Pareto front offering engineers flexible design
choices for different application requirements. |
