Breakout Local Search for Load-Balanced Federated Learning in Multi-BS Networks

Federated learning (FL) relies on timely participation of multiple devices, yet the round time is often dominated by the slowest user under heterogeneous wireless conditions. In multi-base-station (multi-BS) environments with nonlinear concurrent uplink and diverse backhaul capacities, selecting an appropriate set of participants becomes a challenging combinatorial optimization problem. We cast the problem as a round-time–centric optimization with reference-latency-scaled fairness penalties to enforce diversity, cohort size, and BS load balance. To solve it efficiently, we propose a Breakout Local Search (BLS) solver that couples k-opt local refinement with approximate screening and adaptive three-mode perturbations under a wall-clock budget, enabling efficient exploration–exploitation. Extensive simulations under hotspot and throttled-backhaul scenarios show that the proposed method reduces round time by 80–90% compared with particle swarm optimization (PSO) and Random, and by 29–75% compared with Greedy and simulated annealing (SA), while lowering the overall objective by 80–84% relative to PSO and Random and 50–67% relative to Greedy and SA, across various diversity weights and target participant sizes. The results highlight the effectiveness of our BLS method in FL participant selection under realistic and difficult network conditions.