Prior studies are lacking which address permutation flow shop scheduling problems and hybrid flow shop scheduling problems together to help firms find the optimized scheduling strategy. The permutation flow shop scheduling problem and hybrid flow shop scheduling problems are important production scheduling types, which widely exist in industrial production fields. This study aimed to acquire the best scheduling strategy for making production plans. An improved fireworks algorithm is proposed to minimize the makespan in the proposed strategies. The proposed improved fireworks algorithm is compared with the fireworks algorithm, and the improvement strategies include the following: (1) A nonlinear radius is introduced and the minimum explosion amplitude is checked to avoid the waste of optimal fireworks; (2) The original Gaussian mutation operator is replaced by a hybrid operator that combines Cauchy and Gaussian mutation to improve the search ability; and (3) An elite group selection strategy is adopted to reduce the computing costs. Two instances from the permutation flow shop scheduling problem and hybrid flow shop scheduling problems were used to evaluate the improved fireworks algorithm's performance, and the computational results demonstrate the improved fireworks algorithm's superiority.

The relay reliability has an impact on the reliability of the entire electric vehicle system. This paper contributes to propose the improving fireworks algorithm optimizing the grey neural network model to predict the relay lifetime. This paper shows how the mutation operation and mapping operation in the fireworks algorithm are used to improve the convergence ability and running speed; the convergence performance and running speed of improved fireworks algorithm are tested with standard test function and compared with fireworks algorithm; and the grey neural network model–improved fireworks algorithm is used to predict the relay life and compared with grey model, grey neural network, and grey neural network model–fireworks algorithm. The results show that the convergence accuracy of the improved fireworks algorithm is better than the fireworks algorithm. The running time of improved fireworks algorithm is the shortest; the improved fireworks algorithm–grey neural network model has the best prediction effect and the root mean square error value is 6.75% smaller than the fireworks algorithm–grey neural network model.