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This paper proposes to investigate the performance of a path planning controller for a search-classify mission using multiple cooperative underwater vehicles. We present a control strategy for multi-agent cooperative systems, namely the Grid-based Multi-Objective Optimal Problem (GMOOP) solving technique, to find the optimal solutions for a search-classify mission using an action determination map subject to certain constraints and objectives. This technique is based on an Interval Programming (IvP) algorithm introduced in for representing and optimizing over multiple competing objective functions. We made improvements in this GMOOP technique to suit the harsh underwater acoustic communication environment by taking advantages of the Location-Aware Source Routing (LASR) protocol for underwater Mobile Ad hoc Network (MANET). Preliminary simulation trials based on two simplified scenarios have been carried out. Results show that the demanded cooperative search task could be finished satisfactorily under harsh acoustic constraints, and the performance of the GMOOP model are studied in various aspects.