In view of the shortcomings of the whale optimization algorithm (WOA), such as slow convergence speed, low accuracy, and easy to fall into local optimum, an improved whale optimization algorithm (IWOA) is proposed. First, the standard WOA is improved from the three aspects of initial population, convergence factor, and mutation operation. At the same time, Gaussian mutation is introduced. Then the nonfixed penalty function method is used to transform the constrained problem into an unconstrained problem. Finally, 13 benchmark problems were used to test the feasibility and effectiveness of the proposed method. Numerical results show that the proposed IWOA has obvious advantages such as stronger global search ability, better stability, faster convergence speed, and higher convergence accuracy; it can be used to effectively solve complex constrained optimization problems.

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example.

Aiming at the problem of dynamic flexible job shop scheduling, a multi-step genetic algorithm is proposed. Firstly, special encoding and decoding methods are used according to the characteristics of the problem; then, introducing differential evolution mutation in the mutation process to improve the diversity of the population; at the same time, during the crossover process, in order to ensure the validity of the solution, the group was divided into two groups for pair wise crossover pairing using the random crossover method. Finally, aiming at the actual operation problems of enterprises, the dynamic scheduling in the event of a machine failure and the dynamic scheduling in the case of urgent orders are discussed separately. The test results show that the method proposed in this paper can get a good scheduling scheme and is an effective method for solving dynamic flexible job shop scheduling problems.

In this paper, we mainly study an exponential spline function space, construct a basis with local supports, and present the relationship between the function value and the first and the second derivative at the nodes. Using these relations, we construct an exponential spline-based difference scheme for solving a class of boundary value problems of second-order ordinary differential equations (ODEs) and analyze the error and the convergence of this method. The results show that the algorithm is high accurate and conditionally convergent, and an accuracy of 1/240h6 was achieved with smooth functions.

High-pressure fuel line is a basic component of many modern industrial devices, and its pressure stability affects operating efficiency and safety. In this paper, the working mechanism of high-pressure fuel line with double fuel injectors and pressure reducing valve is studied as the main object, the differential equation for changes in pressure with time is established, and the rotating speed of high-pressure fuel pump cam, fuel injection time of fuel injector, and the threshold of pressure reducing valve are optimized using fuzzy logic systems to control the pressure in high-pressure fuel line within a safe range and improve the operating efficiency and safety of high-pressure fuel line. The results of numerical simulation show that the pressure reducing valve can effectively control the pressure in high-pressure fuel line.