Multi-Strategy Harris Hawks Optimization of Fuzzy Chance-Constrained Multi-Robot Hybrid Workshop Scheduling in Uncertain Environments

Effective task allocation is fundamental to the success of heterogeneous multi-robot cooperative missions in smart manufacturing workshops, yet real-world operational uncertainties pose severe challenges to solution feasibility and mission robustness. Addressing these challenges, this paper focuses on the inspection and maintenance task allocation problem for heterogeneous mobile robot teams operating under fluctuating equipment maintenance time windows, variable task execution durations, and uncertain robot travel speeds caused by workshop congestion and payload variations. First, the aforementioned uncertain parameters are characterized using triangular fuzzy numbers, upon which a fuzzy chance-constrained programming model is constructed with the objective of minimizing total operational cost while ensuring constraint satisfaction under uncertainty. The proposed model simultaneously handles two types of critical constraints: the service time window constraint, which requires each task to be completed before its latest allowable service deadline, and the time sequence constraint, which enforces that each equipment inspection task must be completed prior to the corresponding maintenance task. Then, to tackle the inherent NP-hardness of this problem, a multi-strategy hybrid Harris Hawks Optimization algorithm incorporating differential evolution, termed MSHHODE, is proposed. In detail, three targeted enhancement mechanisms are introduced: a hunting enthusiasm factor that governs the dynamic balance between global exploration and local exploitation throughout the search process; an elite-assisted guidance strategy that stabilizes convergence by leveraging high-quality solutions to direct population evolution; and an adaptive differential evolution mechanism that reinforces global search diversity and mitigates premature convergence to local optima. Finally, simulation experiments conducted across multiple workshop-scale scenarios demonstrate that MSHHODE consistently outperforms benchmark algorithms across different key performance metrics under varied uncertain conditions, which validates the effectiveness and robustness of the proposed approach in solving complex, constrained allocation problems, offering a practical and reliable framework for real-world heterogeneous multi-robot task planning in smart manufacturing environments.