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<p>The growing demand for sustainable and energy-efficient manufacturing requires advanced scheduling strategies capable of optimizing both production performance and resource utilization. In flexible workshop environments with automated guided vehicle (AGV) transport, scheduling becomes a complex nonlinear multi-objective problem due to the simultaneous consideration of machine allocation and transport constraints. This article investigates a flexible multi-objective workshop scheduling problem with AGV transportation, extending the Black Widow Spider Algorithm to simultaneously minimize makespan and total energy consumption. The proposed Multi-Objective Black Widow Spider Algorithm (MOBWSA) incorporates a novel descending cannibalism mechanism that balances exploration and exploitation, alongside adaptive selection, crossover, and mutation operators specifically designed for integrated machine-AGV coordination. Experimental validation using Brandimarte benchmark instances (MK01-MK15) with 2–6 AGVs demonstrates MOBWSA’s superior performance, achieving average improvements of 8.7% in makespan and 6.3% in total energy consumption compared to NSGA-II and MOPSO. The algorithm achieved the lowest Average Relative Percentage Deviation in 13 of 15 instances, with particularly significant gains in complex problems (up to 15.9% improvement in MK06 makespan). Operator attribution analysis revealed that POX crossover drives 52.6% of convergence while cannibalism contributes 28.1% to diversity maintenance, confirming the balanced exploration–exploitation strategy. These results demonstrate MOBWSA’s potential as a robust and practical tool for efficient energy consumption programming in smart manufacturing systems.</p>

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A multi-objective black widow spider algorithm for solving the flexible job shop problem with energy efficiency and transport time

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Fabian Alexander Torres-Cardenas,
  • Lina Mayerly Lozano Suarez,
  • Carlos Eduardo Díaz Bohórquez

摘要

The growing demand for sustainable and energy-efficient manufacturing requires advanced scheduling strategies capable of optimizing both production performance and resource utilization. In flexible workshop environments with automated guided vehicle (AGV) transport, scheduling becomes a complex nonlinear multi-objective problem due to the simultaneous consideration of machine allocation and transport constraints. This article investigates a flexible multi-objective workshop scheduling problem with AGV transportation, extending the Black Widow Spider Algorithm to simultaneously minimize makespan and total energy consumption. The proposed Multi-Objective Black Widow Spider Algorithm (MOBWSA) incorporates a novel descending cannibalism mechanism that balances exploration and exploitation, alongside adaptive selection, crossover, and mutation operators specifically designed for integrated machine-AGV coordination. Experimental validation using Brandimarte benchmark instances (MK01-MK15) with 2–6 AGVs demonstrates MOBWSA’s superior performance, achieving average improvements of 8.7% in makespan and 6.3% in total energy consumption compared to NSGA-II and MOPSO. The algorithm achieved the lowest Average Relative Percentage Deviation in 13 of 15 instances, with particularly significant gains in complex problems (up to 15.9% improvement in MK06 makespan). Operator attribution analysis revealed that POX crossover drives 52.6% of convergence while cannibalism contributes 28.1% to diversity maintenance, confirming the balanced exploration–exploitation strategy. These results demonstrate MOBWSA’s potential as a robust and practical tool for efficient energy consumption programming in smart manufacturing systems.