A multi-objective MILP approach for coordination and communication scheduling in resource-constrained multi-agent systems

Cooperative Multi-Agent Systems (MAS) are increasingly deployed in automated warehouses, robotic fulfilment centres, and smart logistics environments, where agents must coordinate under communication, energy, and operational constraints. Inefficient communication policies can increase energy consumption, create bottlenecks, and overload specific agents, reducing long-term system robustness. This paper proposes a multi-period coordination and communication scheduling framework for industrial MAS formulated as a Mixed Integer Linear Programming (MILP) model. The framework jointly optimises coordination efficiency, communication-energy consumption, and workload balance (Fairness) while considering finite coordination capacities, bounded communication durations, dynamic communication conditions, and coordination-communication dependencies. Two multi-objective solution approaches are developed: a desirability-based reformulation to identify balanced compromise solutions and an ε-constraint formulation to analyze Pareto trade-offs among efficiency, energy use, and fairness. Industrial-scale benchmark instances inspired by autonomous warehouse operations are generated to evaluate the framework under heterogeneous capacities, workload variability, sparse communication topologies, and dynamic energy conditions. Computational experiments and sensitivity analyses show that communication energy is a major operational bottleneck. Results reveal scarcity and saturation regimes in which moderate increases in communication-energy availability significantly improve coordination performance, whereas further resource relaxation yields diminishing returns. The framework provides a tractable and interpretable tool for robust coordination and communication management in large-scale industrial MAS.