Improved Jaya algorithm for energy-efficient distributed heterogeneous permutation flow shop scheduling: Improved Jaya algorithm for energy-efficient distributed

• Published in: The Journal of supercomputing 2025-01, Vol.81 (2)
• Main Authors: Zhang, Qiwen, Zhen, Tian
• Format: Article
• Language: English
• Subjects: Compilers; Computer Science; Interpreters; Processor Architectures; Programming Languages
• ISSN: 1573-0484
• DOI: 10.1007/s11227-025-06938-z

Most existing studies on distributed permutation flow shop scheduling assume identical shops, overlooking the impact of heterogeneous shops. This paper addresses the energy-efficient distributed heterogeneous permutation flow shop scheduling problem, which accounts for variations in energy consumption when jobs are processed on different machines in heterogeneous factories. Several research gaps are stated following: (1) Previous studies predominantly use the NEH algorithm and its variants, which require substantial computational resources, while a single random initialization strategy fail to generate a high-quality population. (2) The classical Jaya algorithm relies on a single learning target, which may lead the population to converge prematurely to local optima. (3) Confidence-based operator selection models are influenced by historical performance and cannot dynamically adjust operator weights based on recent performance. (4) The previous works lack of effective energy-saving strategies. To address these issues, we propose a competitive multilevel Jaya algorithm with SPA-based multi-directional local search (CMJA-SPALS). Key innovations of CMJA-SPALS as follows: (1) A hybrid initialization strategy that generates a high-quality initial population with good diversity and convergence using fewer evaluations. (2) The multilevel competition mechanism uses non-dominated sorting to divide the population into multiple levels. Individuals within the same level are randomly paired for competition to determine diversified learning targets, significantly enhancing population diversity and reducing the risk of converging to local optima. (3) Individuals apply specific search operators based on its optimization bias, while the surprisingly popular algorithm (SPA) dynamically adjusts the selection probabilities of operators, improving local search success rates and accelerating convergence. (4) A critical path-based energy-saving strategy designed to reduce machine idle time by adjusting the processing speed of non-critical jobs, effectively lowering total energy consumption. The proposed method’s performance is evaluated using three multi-objective metrics: HV, GD, and Spread. The effects of parameter settings are investigated, and extensive numerical experiments are conducted. Comparative results and statistical analyses demonstrate that CMJA-SPALS outperforms NSGA-II, SD-Jaya, MOEA/D, and KMOEA/D across multiple test instances of varying scales, confirming its e