t-MOHHO: An Adaptive Multi-Objective Harris Hawks Optimization Algorithm for Flexible Job Shop Scheduling

The Flexible Job Shop Scheduling Problem (FJSP) is central to smart manufacturing, yet standard algorithms often prioritize productivity (makespan) at the expense of cost and reliability. This paper introduces t-MOHHO, a collaborative optimization framework designed to equilibrate machine load, processing costs, and delivery timeliness alongside throughput. By incorporating an adaptive Student’s t-distribution mutation operator and a non-linear energy escape mechanism, t-MOHHO effectively navigates high-dimensional search spaces. Extensive validation on 10 MK benchmark instances reveals that t-MOHHO demonstrates significant advantages over classic HHO, MOPSO, and MOEA/D across most metrics. Notably, in comparison to the state-of-the-art NSGA-III, t-MOHHO executes a clear trade-off: it trades marginal makespan efficiency for substantial reductions in cost and tardiness. Specifically, on the large-scale MK10 instance, t-MOHHO reduces total tardiness by 56.2% and lowers processing costs by 3.4% compared to NSGA-III. These results demonstrate that t-MOHHO can strategically sacrifice maximum speed to secure superior punctuality and cost-efficiency, making it a robust decision-support tool for Just-in-Time (JIT) production environments.