In the present paper, we will investigate weak laws of large numbers for weighted pairwise NQD random variables with infinite mean. The almost sure upper and lower bounds for a particular normalized weighted sum of pairwise NQD nonnegative random variables are established also.
Aiming at solving the problem of dual resource constrained flexible job shop scheduling problem (DRCFJSP) with differences in operating time between operators, an artificial intelligence (AI)-based DRCFJSP optimization model is developed in this paper. This model introduces the differences between the loading and unloading operation time of workers before and after the process. Subsequently, the quantum genetic algorithm (QGA) is used as the carrier; the process is coded through quantum coding; and the niche technology is used to initialize the population, adaptive rotation angle, and quantum mutation strategy to improve the efficiency of the QGA and avoid premature convergence. Lastly, through the Kacem standard calculation example and the reliability analysis of the factory workshop processing process example, performance evaluation is conducted to show that the improved QGA has good convergence and does not fall into premature ability, the improved QGA can solve the problem of reasonable deployment of machines and personnel in the workshop, and the proposed method is more effective for the DRCFJSP than some existing methods. The findings can provide a good theoretical basis for actual production and application.
Aiming at the distributed flexible job shop scheduling problem under dual resource constraints considering the influence of workpiece transportation time between factories and machines, a distributed flexible job shop scheduling problem (DFJSP) model with the optimization goal of minimizing completion time is established, and an improved mayfly algorithm (IMA) is proposed to solve it. Firstly, the mayfly position vector is discrete mapped to make it applicable to the scheduling problem. Secondly, three-layer coding rules of process, worker, and machine is adopted, in which the factory selection is reflected by machine number according to the characteristics of the model, and a hybrid initialization strategy is designed to improve the population quality and diversity. Thirdly, an active time window decoding strategy considering transportation time is designed for the worker–machine idle time window to improve the local optimization performance of the algorithm. In addition, the improved crossover and mutation operators is designed to expand the global search range of the algorithm. Finally, through simulation experiments, the results of various algorithms are compared to verify the effectiveness of the proposed algorithm for isomorphism and isomerism factories instances.
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