Lifetime is a key parameter in the design of routing protocols in energy-constrained wireless sensor networks (WSNs). Conventional single-path routing schemes may not be optimal in maximizing network lifetime. In this paper, we present a new routing algorithm based on the optimal number of hops to partition the path from the source to the sink. The algorithm is based on energy consumption constrained routing method. The mathematical model uses mixed-integer programming (MIP), based on the Lagrangian relaxation (LR) method, to define critical parameters that control the adaptive hop-by-hop switching. LINGO is used to investigate the performance trade-offs between energy efficiency and quality of service (QoS). Simulation results revealed that our algorithm significantly improves the lifetime by 46.91, 73.00, and 80.00% as compared to the well-known node density control, upper-bound, and WSN optimization of network lifetime algorithms, respectively.