<p>This paper presents a generalized framework for average consensus and distributed optimization in first-order multi-agent systems under dynamic undirected networks. The framework introduces a family of predefined-time consensus functions that are not based on the homogeneity principle, in which the convergence-time bound is a user-defined parameter, regardless of the initial condition. Moreover, unlike many piecewise algorithms in the current literature, the proposed distributed optimization protocol is based on the Zero-Gradient-Sum approach but does not require local minimization. Extensive numerical simulations are conducted to illustrate the efficacy of this framework.</p>