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For a 3-D underwater workspace with a variable ocean current, an integrated multiple autonomous underwater vehicle (AUV) dynamic task assignment and path planning algorithm is proposed by combing the improved self-organizing map (SOM) neural network and a novel velocity synthesis approach. The goal is to control a team of AUVs to reach all appointed target locations for only one time on the premise of workload balance and energy sufficiency while guaranteeing the least total and individual consumption in the presence of the variable ocean current. First, the SOM neuron network is developed to assign a team of AUVs to achieve multiple target locations in 3-D ocean environment. The working process involves special definition of the initial neural weights of the SOM network, the rule to select the winner, the computation of the neighborhood function, and the method to update weights. Then, the velocity synthesis approach is applied to plan the shortest path for each AUV to visit the corresponding target in a dynamic environment subject to the ocean current being variable and targets being movable. Lastly, to demonstrate the effectiveness of the proposed approach, simulation results are given in this paper.