This paper investigates an energy-conscious hybrid flow shop scheduling problem with unrelated parallel machines (HFSP-UPM) with the energy-saving strategy of turning off and on. We first analyse the energy consumption of HFSP-UPM and formulate five mixed integer linear programming (MILP) models based on two different modelling ideas namely idle time and idle energy. All the models are compared both in size and computational complexities. The results show that MILP models based on different modelling ideas vary dramatically in both size and computational complexities. HFSP-UPM is NP-Hard, thus, an improved genetic algorithm (IGA) is proposed. Specifically, a new energy-conscious decoding method is designed in IGA. To evaluate the proposed IGA, comparative experiments of different-sized instances are conducted. The results demonstrate that the IGA is more effective than the genetic algorithm (GA), simulating annealing algorithm (SA) and migrating birds optimisation algorithm (MBO). Compared with the best MILP model, the IGA can get the solution that is close to an optimal solution with the gap of no more than 2.17% for small-scale instances. For large-scale instances, the IGA can get a better solution than the best MILP model within no more than 10% of the running time of the best MILP model.

Disassembly is indispensable to recycle and remanufacture end-of-life products, and a disassembly line-balancing problem (DLBP) is studied frequently. Recent research on disassembly lines has focused on a complete disassembly for optimising the balancing ability of lines. However, a partial disassembly process is widely applied in the current industry practice, which aims at reusing valuable components and maximising the profit (or minimising the cost). In this paper, we consider a profit-oriented partial disassembly line-balancing problem (PPDLBP), and a mathematical model of this problem is established, which is to achieve the maximisation of profit for dismantling a product in DLBP. The PPDLBP is NP-complete since DLBP is proven to be a NP-complete problem, which is usually handled by a metaheuristics. Therefore, a novel efficient approach based on gravitational search algorithm (GSA) is proposed to solve the PPDLBP. GSA is an optimisation technique that is inspired by the Newtonian gravity and the laws of motion. Also, two different scale cases are used to test on the proposed algorithm, and some comparisons with the CPLEX method, particle swarm optimisation, differential evolution and artificial bee colony algorithms are presented to demonstrate the excellence of the proposed approach.

With the rapid development of computer technology and related softwares for mathematical models, mathematical modelling of scheduling problems is receiving growing attention from researchers. In this work, the hybrid flow shop scheduling problem with unrelated parallel machines (HFSP-UPM) with the objective aimed to minimise the makespan is studied. According to the characteristics of the HFSP-UPM, eight mixed integer linear programming (MILP) models are formulated in order to obtain optimal solutions based on different modelling ideas. Then, these models are extended to solve HFSP-UPM with sequence-dependent setup times (HFSP-UPM-SDST), no-wait HFSP-UPM (HFSP-UPM-NW) and HFSP-UPM with blocking (HFSP-UPM-B). All the proposed models and the existing model are detailedly compared and evaluated under three aspects namely modelling process, size complexity and computational complexity. Numerical experiments show that MILP models dependent on diverse modelling ideas perform very differently. The model developed based on stage precedence is the best one and should be given preference in future applications. In addition, the proposed models of HFSP-UPM-NW and HFSP-UPM-B improve several best known solutions for the test instances in the existing literature.

Bearing fault diagnosis is essential for ensuring the safety and reliability of industrial systems. Recently, deep learning approaches, especially the convolutional neural network, have demonstrated exceptional performance in bearing fault diagnosis. However, the limited availability of training samples has been a persistent issue, leading to a significant reduction in diagnostic accuracy. Additionally, noise interference or load variation during bearing operation pose significant challenges for fault diagnosis. To tackle the above issues, this paper explores the application of quadratic neuron with attention-embedded for fault diagnosis networks and introduces a trusted multi-scale learning strategy that fully considers the characteristics of bearing vibration signals. Building upon these concepts, a trusted multi-scale quadratic attention-embedded convolutional neural network is proposed for bearing faults diagnosis. Experimental results indicate that the proposed network outperforms six stateof-the-art networks under noise interference or load variation superimposed on small samples.

Multicriteria decision making (MCDM) problems are often encountered in complex system design. Most of them need to be evaluated with a large number of interactive and qualitative indices, which are difficult to be addressed effectively through the existing methods. In this paper, a novel fuzzy Choquet integral-based grey comprehensive evaluation (GCE) method, called fuzzy grey Choquet integral (FGCI), is proposed to evaluate MCDM problems with many interactive and qualitative indices. In this method, expert evaluation of qualitative indices is represented through fuzzy linguistic values. Fuzzy values are defuzzified and standardized to obtain the original evaluation matrix. The original values are replaced by the correlation coefficients, which, to a certain extent, eliminate the influence of experts' subjective preference. An improved teaching-learning-based optimization algorithm is employed to identify λ -fuzzy-measures following the weights given by experts in order to enhance the consistency of weights. Then the correlation coefficients are aggregated through Choquet integral among λ -fuzzy-measures, which can reflect interactions among indices. In addition, according to the characteristics of λ -fuzzy-measures, the construction guidelines for a corresponding index system are given to overcome the limitations of FGCI. Finally, the performance of the proposed method is demonstrated via a practical example of green design evaluation and compared with the GCE method. The results validate its feasibility and effectiveness.

With the global warming problem and increasing energy cost, manufacturing firms are paying more and more attention to reducing energy consumption. This paper addresses the distributed flexible job shop scheduling problem (DFJSP) with minimizing energy consumption. To solve the problem, firstly, a novel mixed integer linear programming (MILP) model is developed to solve small-scaled problems to optimality. Due to the NP-hardness of DFJSP, we then propose an efficient hybrid shuffled frog-leaping algorithm (HSFLA) for solving DFJSP, particularly for large-sized problems. HSFLA combines the shuffled frog-leaping algorithm (SFLA) with powerful global search ability and variable neighborhood search (VNS) with good local search ability. Moreover, in HSFLA, the encoding method, the decoding method, the initialization method and the memetic evolution process are specifically designed. Finally, numerical experiments are conducted to evaluate the performance of the proposed MILP model and HFSLA.