Packing problems, also known as nesting problems or bin packing problems, are classic and popular NP-hard problems with high computational complexity. Inspired by classic reinforcement learning (RL), we established a mathematical model for two-dimensional (2D) irregular-piece packing combined with characteristics of 2D irregular pieces. An RL algorithm based on Monte Carlo learning (MC), Q-learning, and Sarsa-learning is proposed in this paper to solve a 2D irregular-piece packing problem. Additionally, mechanisms of reward–return and strategy-update based on piece packing were designed. Finally, the standard test case of irregular pieces was used for experimental testing to analyze the optimization effect of the algorithm. The experimental results show that the proposed algorithm can successfully realize packing of 2D irregular pieces. A similar or better optimization effect can be obtained compared to some classical heuristic algorithms. The proposed algorithm is an early attempt to use machine learning to solve 2D irregular packing problems. On the one hand, our hybrid RL algorithm can provide a basis for subsequent deep reinforcement learning (DRL) to solve packing problems, which has far-reaching theoretical significance. On the other hand, it has practical significance for improving the utilization rate of raw materials and broadening the application field of machine learning.

It is well known that the one-dimensional cutting stock problem (1DCSP) is a combinatorial optimization problem with nondeterministic polynomial (NP-hard) characteristics. Heuristic and genetic algorithms are the two main algorithms used to solve the cutting stock problem (CSP), which has problems of small scale and low-efficiency solutions. To better improve the stability and versatility of the solution, a mathematical model is established, with the optimization objective of the minimum raw material consumption and the maximum remaining material length. Meanwhile, a novel algorithm based on deep reinforcement learning (DRL) is proposed in this paper. The algorithm consists of two modules, each designed for different functions. Firstly, the pointer network with encoder and decoder structure is used as the policy network to utilize the underlying mode shared by the 1DCSP. Secondly, the model-free reinforcement learning algorithm is used to train network parameters and optimize the cutting sequence. The experimental data show that the one-dimensional cutting stock algorithm model based on deep reinforcement learning (DRL-CSP) can obtain the approximate satisfactory solution on 82 instances of 3 data sets in a very short time, and shows good generalization performance and practical application potential.

As a branch of the two-dimensional (2D) optimal blanking problem, rectangular strip packing is a typical non-deterministic polynomial (NP-hard) problem. The classical packing solution method relies on heuristic and metaheuristic algorithms. Usually, it needs to be designed with manual decisions to guide the solution, resulting in a small solution scale, weak generalization, and low solution efficiency. Inspired by deep learning and reinforcement learning, combined with the characteristics of rectangular piece packing, a novel algorithm based on deep reinforcement learning is proposed in this work to solve the rectangular strip packing problem. The pointer network with an encoder and decoder structure is taken as the basic network for the deep reinforcement learning algorithm. A model-free reinforcement learning algorithm is designed to train network parameters to optimize the packing sequence. This design can not only avoid designing heuristic rules separately for different problems but also use the deep networks with self-learning characteristics to solve different instances more widely. At the same time, a piece positioning algorithm based on the maximum rectangles bottom-left (Maxrects-BL) is designed to determine the placement position of pieces on the plate and calculate model rewards and packing parameters. Finally, instances are used to analyze the optimization effect of the algorithm. The experimental results show that the proposed algorithm can produce three better and five comparable results compared with some classical heuristic algorithms. In addition, the calculation time of the proposed algorithm is less than 1 second in all test instances, which shows a good generalization, solution efficiency, and practical application potential.

The two-dimensional (2D) irregular packing problem is a classical optimization problem with NP-hard characteristics and has high computational complexity. To date, packing problems have generally been solved by artificial experience and heuristic algorithms. However, these algorithms are not highly efficient and the excellent cases cannot be preserved, which both time and economic costs are high. Inspire by transfer learning and considering the characteristics of 2D irregular packing problems, we propose a sequence transfer-based particle swarm optimization algorithm (ST-PSO) to solve the multi-constraint packing problem. A piece-matching strategy based on an improved shape context algorithm, and a piece-sequencing generation strategy for transferring the packing sequence are developed for particle swarm optimization(PSO) initialization. In the process of PSO, an adaptive adjustment strategy is used with an improved positioning strategy to adjust the packing position of the pieces. The results indicate that this method can robustly, quickly, and efficiently achieve the packing of 2D irregular pieces. Compared with the data prior to transfer, the ST-PSO can inherit and transfer the historical packing sequence in less time and retain or exceed the actual packing data onto the samples. This algorithm could be applied to industrial applications to reduce waste, packing time, and production costs.

Two-dimensional transition metal dichalcogenides (TMDs) are key materials in ultrafast photonics. However, the performance of conventional TMDs is limited by their bandwidth and carrier recovery time. The novel Dirac semimetal nickel ditelluride (NiTe₂), with its broad-band response and excellent nonlinear properties, emerges as an ideal candidate for saturable absorber (SA) materials. In this work, we report, for the first time, the application of NiTe₂ in the ytterbium-doped fiber laser, demonstrating stable passive Q-switching operation. The nonlinear transmission curve reveals a modulation depth of 6.82% at 1 µm and a saturation intensity of 2.12 MW/cm². Using an all-fiber ring cavity structure, stable Q-switched pulses with a central wavelength of 1031 nm were achieved at a pump threshold of 94 mW, with a maximum pulse repetition frequency of 30.1 kHz. The minimum pulse width reached 2.3 μs, and the single-pulse energy increased to 3.05 nJ, with an impressive radio frequency (RF) spectral signal-to-noise ratio (SNR) of 58.9 dB. This study demonstrates the potential of NiTe₂ as a high-performance SA in the near-infrared region, providing a solid foundation for its future application in ultrafast laser technologies.

To address the high-precision thermal control requirements of semiconductor lasers in laser soldering applications, we propose a thermal control method based on long short-term memory model predictive control (LSTM-MPCs). First, we constructed precise mathematical models for the thermoelectric cooler and components of the thermal control system using non-equilibrium thermodynamics and other methods. The LSTM-MPC thermal control system was derived by introducing the diophantine equation, and an experimental platform for the thermal control of semiconductor lasers in laser soldering was established. The experimental results from random current input variations showed that the average temperature overshoot caused by changes in the laser input current remained within 0.86%. The stability of the laser’s central wavelength improved, with the proposed method reducing the central wavelength drift by 88%. In laser soldering performance experiments, this control method effectively controlled the output power of the semiconductor laser, enhancing the linear fit of the weld point temperature curve to the ideal temperature curve by 21.05%. These findings provide theoretical and engineering guidance for the development of high-performance, reliable laser soldering systems.