Predefined-time distributed multiobjective optimization for network resource allocation

We consider the multiobjective optimization problem for the resource allocation of the multiagent network, where each agent contains multiple conflicting local objective functions. The goal is to find compromise solutions minimizing all local objective functions subject to resource constraints as much as possible, i.e., the Pareto optimums. To this end, we first reformulate the multiobjective optimization problem into one single-objective distributed optimization problem by using the weighted L-p preference index, where the weighting factors of all local objective functions are obtained from the optimization procedure so that the optimizer of the latter is the desired Pareto optimum of the former. Next, we propose novel predefined-time algorithms to solve the reformulated problem by time-based generators. We show that the reformulated problem is solved within a predefined time if the local objective functions are strongly convex and smooth. Moreover, the settling time can be arbitrarily preset since it does not depend on the initial values and designed parameters. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed algorithms.