Adaptive Chaotic Golden Jackal Optimization for the Multi-Objective Optimal Design of Three-Element Dynamic Vibration Absorbers

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.