## 4 Relationship between Different Desirable Objectives  
Most of the practical scenarios relating to wireless sensor networks are modeled as multi-objective optimization formulations where multiple desirable objectives compete with each other and the decision maker has to choose one of the tradeoff solutions. These multiple objectives may or may not conflict with each other. Figure 3 elaborates the relationship between different desirable objectives. Different objectives are connected together with lines having different pattern depending upon the relationship between objectives. Red solid line connects the two objectives which have conflicting relationship, for example, maximization of coverage conflicts with the packet error rate, delay, network/battery life time and the overall cost of the system. Whereas, the line consisting of dashes and dots connects the two objectives which have no direct relationship with each other rather they are design dependent for example, maximization of coverage has not direct relationship with the throughput, energy efficiency and the QoS. The supporting relationship between the two objectives has been shown with line consisting of dashes for example, maximization of network/battery life supports the maximization of energy efficiency and minimization of the overall cost of the system. In the following, we discuss each objective separately and its relation with other objectives. Coverage control or coverage maximization is one of the critical research issues in wireless sensor networks and reflects the performance of the network in terms of monitoring a field of interest by properly deploying the nodes [149, 150]. Coverage and lifetime of the sensor network have been jointly optimized in [86] by using a multi-objective optimization algorithm based on memetic algorithm. The sensor node deployment problem has been considered in [145] to jointly optimize the two objectives namely, maximum coverage and minimum energy consumption. Coverage, delay and energy consumption are optimized by using multi-objective optimization algorithm in [151]. The authors argued that the proposed probabilistic network model can achieve a comprehensive view of the trade-offs that result from coverage, delay and energy. Multi-objective formulation has been used in [152] to optimize the two conflicting objectives _i.e._, coverage and cost of WSNs. Like coverage, packet error rate is another  
Figure 3: Relation between desirable objectives in wireless sensor networks (WSNs), where “N/B” = network/battery life; “QoS” = quality of service; “Cov” = coverage; “D” = delay; “Cost” = total cost of the system; “T” = throughput of the system; “EE” = energy efficiency; “PER” = packet error rate. performance parameter which also conflicts with other desirable objectives. For example in [147], three conflicting objectives namely, packet error rate, energy consumption and throughput are being considered. Packet error rate conflicts with the network/battery lifetime, as increasing the transmit power can reduce the error rate which is desirable but at the same time it will deplete the battery power more rapidly which is undesirable. Similarly, the other desirable objectives which conflict with the bit error rate are delay, energy efficiency, cost and throughput. Whereas, coverage and QoS do not have direct relationship with the error rate, rather these are design dependent. Maximization of throughput is another desirable objective which conflicts with packet error rate, cost, energy efficiency, delay and network/battery life. A multi-objective optimization framework for optimal resource allocation in cognitive radio wireless sensor networks (CRSNs) is presented in [141] to jointly optimize the conflicting objectives of maximization of throughput and minimization of total transmission power. In [143], the authors have proposed a multi-objective optimization algorithm to achieve a balance between the throughput and energy consumption of CRSNs.