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The coordination of fleet weapon compatibility is a typical constraint satisfaction problem based on multi-agent system. The conception of the most non-cooperation plan in fleet weapon resources allocation is given. A search algorithm for fleet weapon compatibility constraint satisfaction problem is proposed. By using back tracking and consistency examination in the operation scheme, the most non-cooperation plan is found and eliminated gradually, and the number of conflict plans in fleet weapon resource allocation decreases. Finally, the fleet operation scheme which has no conflicts is obtained. A practical example is provided to show the effectiveness of this algorithm.