## 2 Related Literature  
Due to the scarcity of spectrum resulting from the proliferation of wireless devices and services, dynamic spectrum access is becoming popular in WSNs since it also provides spectrum efficient communication for the WSNs. Factors like transmission power, fading and interference with licensed users affect the communication between nodes in a CRSN. They also hinder the data transmission among the energy constrained CRS nodes. Hence, there is need for an adaptive energy-efficient optimization scheme which takes into account the varying environment conditions. One of the techniques that has been used in the literature involves the use of optimization of one of the factors, while maintaining an acceptable level (called a constraint) on the other factors. This motivated [PERSON] et al. [12] to propose a dynamic packet size optimization scheme (DyPSOCS) for CRSN. They employ a constrained Markov decision process (CMDP) to solve the optimization problem with Quality of Service (QoS) constraints. Their scheme improves the QoS performance and energy efficiency but does not support re-transmissions and multiple data transmission per node per cycle. An optimization problem to optimally allocate power in fading channels of a CRN are considered in [13]. Under different channel fading constraints and power constraints, the aim of [13] is to determine an optimal power allocation of SUs that give Ergodic and outage capacities. With a constraint on transmission rate and BER, a model that minimizes power consumption is also developed in [14]. The resulting optimization model in [14] is solved using game theory. It is shown that the Nash equilibrium of the resulting problem is a Pareto-optimal point. An optimization model that determines the optimal packet size of a CRSN, under different QoS constraints is developed by [PERSON] et al. [4]. The authors further show that the obtained packet size also maximizes energy efficiency of the system. Heuristic algorithms to solve the devised model in [4] are handled in [3]. Another power optimization model that maximizes energy efficiency of SUs is handled in [15]. The model is constructed with SINR constraints for both PUs and SUs. When average power constraints and rate constraints are included into the power allocation model, the problem is extensively studied in [16]. Transmission power optimization through a convex design using lower SINR as an SU QoS constraint is studied in [17]. Here, SU power allocation is done through a distributed sub-optimal joint coordination and power control scheme. An optimization model to maximize the transmission rate of SUs in a QoS constrained environment is handled in [17]. The resulting non-linear optimization problem is solved using geometric programming techniques. The main shortfall of single objective optimization is the fact that only one factor is optimized in the entire system. This paper considers a multi-objective optimization problem. The study of single objective optimization models for the various network variables like power, rate, energy, etc., leads to the obvious question of; _what happens if the variables are jointly optimized?_ The answer to this question then gave birth to the many multi-objective optimization models that exist in the literature. A joint power and transmission delay optimization for green wireless access networks is developed in [18; 19] as a bi-objective model. The problem is formulated as a mixed integer linear programming problem. However, these make no attempt to include QoS constraints in their model. With delay used as a constraint, a joint power and rate optimization model is developed by [20]. The model is formulated as a dynamic programming problem and solved using three problem-dependent heuristic algorithms. A joint optimization of power and rate with QoS constraints (in terms of minimum SINR and transmission rate and PU interference), is considered by [21].