Network disintegration comprises the problem of identifying the critical nodes or edges whose removal will lead to a network collapse. The solution of this problem is significant for strategies for dismantling terrorist organizations and for immunization in disease spreading. Network disintegration has received considerable attention in isolated networks. Here, we consider the generalization of optimal disintegration strategy problems to multiplex networks and propose a disintegration strategy based on tabu search. Experiments show that the disintegration effect of our strategy is clearly superior to those of typical disintegration strategies. Moreover, our approach sheds light on the properties of the nodes within the optimal disintegration strategies.