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The paper considers a hybrid wireless sensor network with static and mobile sensors, where each static sensor can detect only one attribute of event while a mobile sensor can analyze multiple attributes of events. Static sensors monitor the environment and report where events appear. Mobile sensors then move to these event locations to conduct more in-depth analysis. A critical issue is how to schedule the traveling paths of mobile sensors so as to extend their lifetime. We formulate this issue as a multi-round multi-attribute sensor dispatch problem and prove it to be NP-complete. Then, we develop a two-phase dispatch heuristic that adopts the concepts of Pareto optimality and spanning-tree construction. Our heuristic allows arbitrary numbers of mobile sensors and event locations and tries to reduce and balance the energy consumption of mobile sensors in each round. Through simulations, we verify the effectiveness of our heuristic. The paper contributes in defining a new sensor dispatch problem and developing an energy-efficient solution to the problem.