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Energy consumption is an important issue in the design of wireless sensor networks which typically rely on nonrenewable energy sources like batteries for power. Recent advances in ambient energy harvesting technologies have made it a viable alternative source of energy for powering wireless sensor networks perpetually. In this paper, we optimize network performance by finding the optimal routing algorithm and relay node placement scheme for wireless sensor networks powered by ambient energy harvesting. We evaluate the performance of three different variants of geographic routing algorithms and consider two relay node placement schemes, viz. uniform string topology and a cluster string topology. The performance metrics are network throughput (T), goodput (G), source sending rate (SR), efficiency (eta), data delivery ratio (DR) and hop count (H). Simulation results obtained using the Qualnet simulator show that there is an optimal combination of routing algorithm and relay node placement scheme that maximizes the required performance metric. These results aim to provide insights into the impact of routing algorithms and relay node placement schemes on wireless sensor networks that rely solely on ambient energy harvesting for power.