Combinatorial optimization problems are widespread in all areas of production practice, and the main means of solving combinatorial optimization problems usually include the use of heuristic algorithms manually designed by domain experts and the design of sophisticated solvers to construct a solution in a certain order. As the complexity of the actual problem gradually increases, such methods can not achieve good results in online solving, and the results obtained may often be suboptimal. And reinforcement learning gives a good alternative to solve such problems rapidly by well-training an intelligent body model. Therefore, this paper reviews the recent research on applying the reinforcement learning framework to combinatorial optimization problems, summarizes and reviews its basic principles, related methods and application studies, and points out several problems that need to be addressed in this direction in the future.

In order to solve the problem of slow convergence rate and easy to get into local optimum when solving multi-objective flexible job shop scheduling problem, with traditional intelligence optimization algorithm, this paper proposes a hybrid optimization algorithm that fuses three important performance parameters of QPSO with the wolf pack algorithm. Firstly, a multi-objective mathematical model with maximum completion time, total machine load and bottleneck machine load as optimization indexes is constructed. Secondly, the probability density function of Gaussian distribution is used to generate random variables for population initialization so as to improve the diversity and quality of the initial population. Neighborhood structure search strategy is used to adjust the optimal sequence, and the global search performance of the algorithm is improved. Finally, the matter-element analysis method is used to update the population and to improve the adaptive ability of the population. By comparing with the simulation experiment of many intelligent optimization algorithms, we can see that the hybrid wolf pack algorithm proposed in this paper is feasible and advantageous for solving the multi-objective flexible job shop scheduling problem.

The design of a chaotic image encryption algorithm plays an essential role in enhancing information and communication security. The performance of such algorithms is intricately linked to the complexity of the chaotic sequence and the underlying encryption algorithm. To additionally enhance the complexity of hyperchaotic systems, this study presents a novel construction of a Five-Dimensional (5D) memristive hyperchaotic system through the introduction of the flux-controlled memristor model. The system’s dynamic characteristics are examined through various analytical methods, including phase portraits, bifurcation diagrams, and Lyapunov exponent spectra. Accordingly, the sequences produced by the hyperchaotic system, which passed the National Institute of Standards and Technology (NIST) test, are employed to inform the creation of a novelty image encryption technique that combines hash function, Deoxyribonucleic Acid (DNA) encoding, logistic, and Two-Dimensional Hyperchaotic Map (2D-SFHM). It improves the sensitivity of key and plaintext images to image encryption, expands the algorithm key space, and increases the complexity of the encryption algorithm. Experimental findings and analysis validate the exceptional encryption capabilities of the novel algorithm. The algorithm exhibits a considerable key space 2⁵¹², and the ciphertext image demonstrates an information entropy of 7.9994, with inter-pixel correlation approaching zero, etc., showcasing its resilience against different types of attacks on images.

A fractional-order memristor load Buck-Boost converter causes periodic system oscillation, electromagnetic noise, and other phenomena due to the frequent switching of the switch in actual operation, which is detrimental to the stable operation of the power electronic converter. It is of great significance to the study of the modeling method and chaos control strategy to suppress the nonlinear behavior of the Buck-Boost converter and expand the safe and stable operation range of the power system. An estimation-correction modeling method based on a fractional active voltage-controlled memristor load peak current Buck-Boost converter is proposed. The discrete numerical solution of the state variables in the continuous mode of the inductor current is derived. The bursting oscillation phenomenon when the system introduces external excitation is analyzed. Using bifurcation, Lyapunov exponent, and phase diagrams, a large number of numerical simulations are performed. The results show that the Buck-Boost converter is chaotic for certain selected parameters, which is the prerequisite for the introduction of the controller. Based on the idea of parameter perturbation and state association, a three-dimensional hybrid control strategy for a fractional memristor Buck-Boost converter is designed. The effectiveness of the control strategy is verified by simulations, and it is confirmed that the system is controlled in a stable periodic state when the external tunable parameter s, which represents the coupling strength between the state variables in the system, gradually decreases in [−0.4, 0]. Compared with integer-order controlled systems, the stable operating range of fractional-order controlled systems is much larger.

The study of the intelligent algorithms for the flexible job shop scheduling issue (FJSP), a scheduling problem with a broad range of application backgrounds, is very relevant both academically and practically. To address FJSP with the objective of minimizing the maximum completion time, this paper proposes a discrete state transfer algorithm based on proximal policy optimization (DSTA-PPO). DSTA-PPO has the following three characteristics. Considering that FJSP requires simultaneous scheduling arrangements for operation sequencing and machine assignment. This state feature can adequately express the current scheduling problem that was designed by combining operation coding and machine coding. Various critical path based search operations have been designed for operation sequencing and machine allocation. Reinforcement learning training is an efficient way to direct intelligence to choose the best search operation to maximize the current scheduling sequence.. The effectiveness of each component of the algorithm is verified through simulation experiments on different datasets. Furthermore, a comparison is conducted with existing algorithms using the objective of minimizing the maximum completion time in the same instances. The comparison results show that the suggested method successfully resolves the flexible job shop scheduling issue by typically achieving shorter completion times.