  Relay nodes are used to improve the throughput, delay and reliability
performance of energy harvesting networks by assisting both energy and
information transfer between information nodes and access point. Previous
studies on radio frequency energy harvesting networks are limited to single
source single/multiple relay networks. In this paper, a novel joint relay
selection, scheduling and power control problem for multiple source multiple
relay network is formulated with the objective of minimizing the total duration
of wireless power and information transfer. The formulated problem is
non-convex mixed-integer non-linear programming problem, and proven to be
NP-hard. We first formulate a sub-problem on scheduling and power control for a
given relay selection. We propose an efficient optimal algorithm based on a
bi-level optimization over power transfer time allocation. Then, for optimal
relay selection, we present optimal exponential-time Branch-and-Bound (BB)
based algorithm where the nodes are pruned with problem specific lower and
upper bounds. We also provide two BB-based heuristic approaches limiting the
number of branches generated from a BB-node, and a relay criterion based lower
complexity heuristic algorithm. The performance of the proposed algorithms are
demonstrated to outperform conventional harvest-then-cooperate approaches with
up to $88\%$ lower schedule length for various network settings.
