This paper investigates centralized scheduling of mobile service agents under staggered multi-wave task arrivals, limited service capacity, service-time windows, and cross-wave capacity reservation requirements. A spatiotemporal candidate-arc representation is developed to discretize the continuous scheduling process, where each arc encodes an agent-task-time triple along with predicted service points, approximate paths, endurance consumption, and execution costs. Based on the feasible arc set, a mixed-integer linear programming (MILP) model is formulated to jointly optimize task coverage, standby-agent activation, coordinated service times, spatiotemporal conflict avoidance, and cross-wave capacity reservation. Numerical experiments are conducted on a 3-wave, 37-task benchmark as well as extended scenarios with varying resource scarcity and task scales. Results show that in multi-wave rolling execution, the MILP strategy achieves a total weighted coverage rate of 71.19%, outperforming the nearest-neighbor greedy baseline by 5.56 percentage points; the advantage is most pronounced in the second-wave peak (+17.07%), directly validating the capacity reservation mechanism. Further sensitivity analysis reveals that the optimization gain of MILP is resource-sensitive—significant under abundant resources and gradually converging under extreme scarcity. The reported results demonstrate how global constrained selection balances current weighted coverage against retained service capacity for subsequent waves, and provide quantitative references for practical parameter tuning.
Miao Shen, Chuan-Fu Guo, Peng Wang et al.· 2026 12th International Conf...· 0 citations
This paper investigates the subspace consensus problem of matrix-weighted multi-agent networks, where each agent possesses a vector-valued state in $\mathbb{R}^{d}$ and interactions between neighboring agents are characterized by matrix-valued edge weights. Besides all dimensions of the agent states achieve full-state consensus, many practical applications appeal that agents are required to agree only on certain dimensions while maintaining desired relative configurations in the remaining ones. To address this gap, we introduce the concept of subspace consensus. A matrix-weighted network is said to achieve subspace consensus on a subspace $\mathbb{V}\subseteq\mathbb{R}^{d}$ if the projection of the agents'state differences onto $\mathbb{V}$ asymptotically converges to zero. This definition renders the traditional consensus as a special case when $\mathbb{V}=\mathbb{R}^{d}$. From an algebraic perspective, we derive necessary and sufficient conditions for subspace consensus by analyzing the interplay between the null spaces of edge weights. From a topological perspective, we present sufficient conditions characterized by $\mathbb{V}$-connectivity and the existence of a $\mathbb{V}$-spanning tree, as well as necessary conditions based on graph cuts. Furthermore, we provide refined necessary and sufficient conditions specifically for tree networks. This work uncovers a fundamental capability inherent to matrix-weighted networks and establishes a systematic framework for analyzing agreement behaviors on prescribed subspaces.
Yu-He Chen, Lulu Pan, Xiaohui Gong et al.· 0 citations
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