Abstract
In this work, we address a cross-layer multi-objective optimization problem of maximizing network lifetime and optimizing aggregate system utility with intra-flow network coding, solved in a distributed manner. Based on the network utility maximization (NUM) framework, we resolve this problem to accommodate routing, scheduling, and stream control from different layers in the coded networks. Specially, we consider that there are two scheduling primitives, namely hyperlink and transmission mode, to be concurrently activated for the multi-objective optimization. Given the constraints with respect to these primitives, the optimization problem is specifically formulated as a quadratically constrained quadratic programming(QCQP) problem that is NP-hard in general, and its scheduling subproblem even when reduced to account for only one of these primitives is a maximum weighted independent set(MWIS) problem that is NP-hard already. To alleviate this complex problem in a distributed manner, we resort to alternate convex search (ACS) and primal decomposition (PD) to approximate the optimal results by using biconvex programming model and subgradient-based algorithm that can iteratively approach to the optimal solution. For the wireless multihop net-works, wherein an optimal solution could be practically approximated as its validity would be out-of-date soon in the error-prone wireless environment, our simulation results show that the distributed method can fulfill our requirements, and can make a good trade-off on the heterogeneous objectives with well computational efficiency.