An iterative algorithm for the optimal solution is introduced in [8]. This algorithm is based on the upper bound of the network lifetime for specific network topologies. The objective function is to maximize the network lifetime and the flow bounded by the data rates. The complexity of the distributed algorithm is O(N4), where N is the number of nodes of the network. The duty cycle is tuned dynamically, based on the network conditions to achieve the desired end-to-end delay guarantees [9]. The delay and fault-tolerance are the objective of the optimization in the protocol design. The authors introduce a MOPT formulation for the two objectives and find a sub-optimal solution but with extra complexity that overloads the limited processing power of the sensor node.
An approach that optimizes the energy and the coverage is introduced in [10]. The coverage problem is defined as how to arrange the sensor nodes to achieve the best coverage in a reasonable way. Coverage in one limited region is the key to improve the performance of the whole network and it is one of the basic problems in WSNs. The introduced algorithm in [10] achieves good performance in terms of the network lifetime. However, it suffers from very high computational complexity. An evolutionary algorithm is presented in [11] which optimizes the packet speed and the set of candidate nodes for forwarding the traffic. A sub-optimal solution is obtained using the multi-objective evolutionary algorithm. The evolutionary algorithm achieves an acceptable performance but does not fit for large scale networks. A comparison of the existing MOPT algorithms is summarized in Table I.