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.

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.

The problem of finding roots of equations has always been an important research problem in the fields of scientific and engineering calculations. For the standard differential evolution algorithm cannot balance the convergence speed and the accuracy of the solution, an improved differential evolution algorithm is proposed. First, the one-half rule is introduced in the mutation process, that is, half of the individuals perform differential evolutionary mutation, and the other half perform evolutionary strategy reorganization, which increases the diversity of the population and avoids premature convergence of the algorithm; Second, set up an adaptive mutation operator and a crossover operator to prevent the algorithm from falling into the local optimum and improve the accuracy of the solution. Finally, classical high-order algebraic equations and nonlinear equations are selected for testing, and compared with other algorithms. The results show that the improved algorithm has higher solution accuracy and robustness, and has a faster convergence speed. It has outstanding effects in finding roots of equations, and provides an effective method for engineering and scientific calculations.

For the traditional whale optimization algorithm to solve the 0-1 knapsack combinatorial optimization problem, there are shortcomings of insufficient solution energy and easy to fall into local optima. A whale optimization algorithm based on domain search is proposed. This method focuses on the development of global search capabilities in the early stage of the evolution of the whale optimization algorithm, introduces the Lévy flight strategy, and uses a two-stage domain search method to enhance the diversity of the population and avoid the algorithm from falling into local optima; In the later stage, it focuses on the development of local search capabilities, and uses a greedy search method to perform fine search on some high-quality solutions to improve the accuracy of the solutions. Finally, the algorithm is used to conduct two sets of tests on the classic data set: the first group is a small and medium-scale data set, and the second group is a large-scale one. The test results show that the first group can find the optimal solution 100%, the second group has a strong advantage. The results show that the proposed algorithm has good robustness and optimization ability. It’s an effective method to solve the 0-1 knapsack problem.