Wireless sensor network (WSN) consists of densely distributed nodes that are deployed to observe and react to events within the sensor field. In WSNs, energy management and network lifetime optimization are major issues in the designing of routing protocols. Clustering is an efficient data gathering technique that effectively reduces the energy consumption by organizing nodes into groups. However, in clustering protocols, cluster heads (CHs) bear additional load for coordinating various activities within the cluster. Improper selection of CHs causes increased energy consumption and also degrades the performance of WSN. Therefore, proper CH selection and their load balancing using efficient routing protocol is a critical aspect for the long run operation of WSN. Clustering a network with proper load balancing is an NP-hard problem. To solve such problems having vast search area, optimization algorithm is the preeminent possible solution. In this paper, differential evolution based clustering algorithm for WSNs named threshold-sensitive energy-efficient delay-aware routing protocol (TEDRP), is proposed to prolong network lifetime. Dual-hop communication between CHs and BS is utilized to achieve load balancing of distant CHs and energy minimization. The paper also considers stability-aware model of TEDRP named stable TEDRP (STEDRP) with an intend to extend the stability period of the network. In STEDRP, energy aware heuristics is applied for CH selection in order to improve the stability period. The results demonstrate that the proposed protocols significantly outperform existing protocols in terms of energy consumption, system lifetime and stability period.