Ziyang Zheng

Due to the complexity of multi-objective engineering problems, solutions obtained by many algorithms often exhibit poor distribution, and the algorithms tend to fall into local optima. To effectively alleviate these issues, an improved multi-objective moth–flame optimization algorithm (IETMFO) is proposed in this paper, with three core novelties: A hybrid mutation mechanism (integrating two mutation techniques) is first used to generate a new population, and then an indicator-based selection mechanism is adopted to produce a high-quality initial population, enhancing solution distribution. Enhanced Brownian motion is introduced as a local search strategy to reduce the risk of falling into local optima. An improved flame update mechanism is incorporated to maintain flame diversity, boosting the algorithm’s adaptability. The IETMFO is tested on 49 benchmark functions and 6 constrained engineering problems, and then compared with seven well-known algorithms (including NSGA-II, MOEA/D, and traditional MFO). The experimental results show the following: in benchmark function tests, IETMFO reduces the IGD value by an average of 32.7% and increases the HV value by an average of 28.5% compared with NSGA-II; on ZDT series functions, it outperforms the seven contrast algorithms in solution distribution uniformity; in the six engineering problems, its optimal solution proportion reaches 66.7%, and the risk of falling into local optima is reduced by 41.2%. These results demonstrate that the IETMFO achieves competitive performance in addressing multi-objective engineering problems.

Piezoelectric-actuated precision positioning stages are widely used in high-precision instruments and high-end equipment due to their advantages of high resolution, fast response, and compact size. However, due to the strong nonlinearity of hysteresis, the presence of hysteresis in piezoelectric actuators seriously affects the positioning accuracy of the system. In addition, it is challenging to identify the model parameters for hysteresis. In this paper, an adaptive backstepping time delay control method is proposed for piezoelectric devices system with unknown hysteresis. Firstly, the Bouc–Wen model is used to describe the hysteresis characteristics, and the model is interpreted as a linear term and a bounded uncertain hysteresis term. Then, the time delay estimation technique is used to estimate the hysteresis term of the Bouc–Wen model online, and the unknown parameters of the system and hysteresis model are obtained through adaptive updating laws. Furthermore, the stability of the control scheme is proved based on Lyapunov stability theory. Finally, the effectiveness and superiority of the proposed control scheme are demonstrated by comparing it with two typical hysteresis compensation control algorithms through three different sets of input signals.