Bio-Inspired Energy-Efficient Routing for Wireless Sensor Networks Based on Honeybee Foraging Behavior and MDP-Driven Adaptive Scheduling.

Wireless Sensor Networks (WSNs) enable energy-efficient data collection in dynamic environments but continue to face the dual challenges of severely constrained node energy and the spatiotemporal heterogeneity of data traffic. Inspired by honeybee foraging behavior, this paper proposes a hybrid optimization framework that integrates mixed-integer linear programming (MILP) and Markov decision processes (MDP), utilizing Q-learning for adaptive decision-making. The proposed framework systematically maps the dual-layer decision-making mechanism of honeybee foraging onto a synergistic architecture combining MILP-based global planning and MDP-based local adaptation, offering a novel bio-inspired solution for mobile sink trajectory planning and adaptive routing. Specifically, the upper-level MILP module simulates a colony-level global assessment of distant nectar sources, generating an initial global trajectory by determining the optimal access sequence of cluster heads to minimize the movement cost of the mobile sink. The lower-level Q-learning module simulates the individual-level local adaptation, where bees adjust harvesting behavior in real-time based on nectar quality and distance. This module continuously optimizes routing parameters based on real-time network states, including residual energy, the ratio of surviving nodes, data queue lengths, and cluster head density. The algorithm employs an ϵ-greedy strategy to balance exploration and exploitation, while a periodic decision-update mechanism is introduced to harmonize computational efficiency with learning stability. Furthermore, a multi-objective reward function is designed to jointly optimize energy efficiency, network lifetime, end-to-end latency, and path length. Extensive simulation results demonstrate that the proposed MILP-MDP hybrid framework significantly outperforms several representative baseline algorithms in terms of network lifetime extension and energy balance. These findings validate that the integration of bio-inspired foraging strategies and reinforcement learning provides an efficient and robust solution for trajectory planning and adaptive routing in dynamic WSNs.