A New Ant Colony Optimization-Based Dynamic Path Planning and Energy Optimization Model in Wireless Sensor Networks for Mobile Sink by Using Mixed-Integer Linear Programming.

Currently, wireless sensor networks (WSNs) have been mutually applied to environmental monitoring and industrial control due to their low-cost and low-energy sensor nodes. However, WSNs are composed of a large number of energy-limited sensor nodes, which requires balancing the relationship among energy consumption, transmission delay, and network lifetime simultaneously to avoid the formation of energy holes. In nature, gregarious herbivores, such as the white-bearded wildebeest on the African savanna, employ a "fast-transit and selective-dwell" strategy when searching for water; they cross low-value regions quickly and prolong their stay in nutrient-rich pastures, thereby minimizing energy cost while maximizing nutrient gain. Ants, meanwhile, dynamically evaluate the "energy-to-reward" ratio of a path through pheromone concentration and its evaporation rate, achieving globally optimal foraging. Inspired by these two complementary biological mechanisms, our study proposes a novel ACO-conceptualized optimization model formulated via mixedinteger linear programming (MILP). By mapping the pheromone intensity and evaporation rate into the MILP energy constraints and cost functions, the model integrates discrete decision-making (path selection) and continuous variables (dwell time) by dynamic path planning and energy optimization of mobile sink, constituting multi-objective optimization. Firstly, we can achieve flexible trade-offs between multiple objectives such as data transmission delay and energy consumption balance through adjustable weight coefficients of the MILP model. Secondly, the method transforms complex path planning and scheduling problems into deterministic optimization models with theoretical global optimality guarantees. Finally, experimental results show that the model can effectively optimize network performance, significantly improve energy efficiency, while ensuring real-time performance and extended network lifetime.