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In this paper, we consider the predefined-time distributed optimization problems of homogeneous and heterogeneous linear multi-agent systems under undirected and connected communication topologies, in which, all agents share coupled equality constraint. In order to make all agents converge to the optimal output at predefined-time cooperatively, we propose two distributed algorithms for homogeneous and heterogeneous multi-agent systems according to time-base generator technology and output feedback, therein, the optimal output can make the global cost function reach minimum. In the design of the algorithms, the control gains are not required, which can avoid the requirement of some global information in advance. Furthermore, all agents converge to the optimal output with exponential speed, and we can set the convergence time arbitrarily. Finally, we provide examples to illustrate the effectiveness of the proposed distributed algorithms. [ABSTRACT FROM AUTHOR]