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<p>Injection Moulding Flexible Job Shop Scheduling Problem (IM-FJSP) has become a current research hotspot. However, nearly all of existing injection moulding scheduling models have few constraints. This paper investigates an IM-FJSP with challenging characteristics, such as work calendars, material procurement cycles, lot streaming and setup times. A mixed integer linear programming model is established to describe the considered problem. The optimization goal is to minimize order delay time and to minimize total energy consumption, simultaneously. To solve this complex problem, the Feedback Differentiated Teaching Optimization (FDTLBO) algorithm is proposed. First, a hybrid initialization strategy with four heuristic methods is applied to provide a high-quality initial population. Second, an operation advance energy-efficient decoding strategy is designed to decrease the order delay and energy consumption. Finally, during the teaching phase, an external archive set feedback mechanism is proposed to balance exploration and exploitation by dynamically adjusting the proportion of differentiated teaching students. The performance of the FDTLBO algorithm is evaluated on 15 numerical test instances through comparison with five existing algorithms: TLBO, CTLBO, MOEA/D-AGR, NSGA-II and ADEJAYA. The experimental results demonstrate that the FDTLBO algorithm outperforms the five compared algorithms in both convergence and diversity, which highlights its effectiveness in solving the complex IM-FJSP problem.</p> Graphical abstract <p></p>

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A teaching–learning-based optimization with feedback differentiation for injection moulding flexible job shop scheduling under various practical constraints

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Maowei He,
  • Hanning Chen,
  • Yuxin Song

摘要

Injection Moulding Flexible Job Shop Scheduling Problem (IM-FJSP) has become a current research hotspot. However, nearly all of existing injection moulding scheduling models have few constraints. This paper investigates an IM-FJSP with challenging characteristics, such as work calendars, material procurement cycles, lot streaming and setup times. A mixed integer linear programming model is established to describe the considered problem. The optimization goal is to minimize order delay time and to minimize total energy consumption, simultaneously. To solve this complex problem, the Feedback Differentiated Teaching Optimization (FDTLBO) algorithm is proposed. First, a hybrid initialization strategy with four heuristic methods is applied to provide a high-quality initial population. Second, an operation advance energy-efficient decoding strategy is designed to decrease the order delay and energy consumption. Finally, during the teaching phase, an external archive set feedback mechanism is proposed to balance exploration and exploitation by dynamically adjusting the proportion of differentiated teaching students. The performance of the FDTLBO algorithm is evaluated on 15 numerical test instances through comparison with five existing algorithms: TLBO, CTLBO, MOEA/D-AGR, NSGA-II and ADEJAYA. The experimental results demonstrate that the FDTLBO algorithm outperforms the five compared algorithms in both convergence and diversity, which highlights its effectiveness in solving the complex IM-FJSP problem.

Graphical abstract