## 3 The Proposed Solution Method Using the PA-Jaya Algorithm
### PA-Jaya for the Fundamental Issue in the Cognitive OFDM Radio Network
Another important improvement of the proposed Jaya algorithm is that it sets an inner loop to reduce the generation of infeasible solutions. Considering that the basic resource allocation problem in this article is a constrained optimization problem, all the candidate solutions obtained need to meet the requirements of Equations (5) and (6). In this case, if the traditional Jaya algorithm is directly applied, a large number of infeasible solutions will be generated in the population after each iteration, and these solutions will be discarded, resulting in unsatisfactory efficiency of the iterative solution. Therefore, an intuitive idea is to consider how to reduce these infeasible solutions during the update process of each iteration. The PA-Jaya algorithm addresses this problem through an inner loop in each iteration to repeat the update of a single candidate solution to satisfy the constraints as much as possible; thus, most of the solutions in the population after each iteration will be feasible solutions. Specifically, for the basic spectrum resource allocation problem discussed in this article, when we obtain the first candidate solution during the first iteration, we will immediately observe whether it meets the requirements of Equations (5) and (6). If these requirements are met, we continue to update the subsequent solutions  
Figure 1: Structure of population and individuals designed for the power allocation problem. in the population while also paying attention to the constraints, until all the candidate solutions are updated during this iteration. Otherwise, if the first candidate solution does not meet these constraints, the candidate solution will be regenerated until it meets all the requirements or the maximum number of inner loops is reached, and then the subsequent operations are consistent with the above. Thus, based on the above two tricks, the framework of the improved asynchronous Jaya algorithm can be described by Algorithm 2. Furthermore, motivated by some successful work [46; 47; 48; 49], we introduce the parallel structure into the proposed algorithm to make full use of computing resources and reduce the running time. Generally, parallel models of the common GA can be divided into four categories, including the master-slave model, coarse-grained model, fine-grained model, and hybrid model [47]. Here, we use the coarse-grained model, also called the land-based model, which is the most adaptable and widely used GA parallel model. The initial population is divided into several independent subpopulations, and the improved asynchronous Jaya iterative algorithm is used to perform evolution operations independently in each subpopulation. After a certain number of iterations, information exchange is conducted between different subpopulations, and the convergence speed is further accelerated by introducing the optimal individuals to the entire population. By adopting a parallelization structure, the independence between each subpopulation can be ensured, and the individual diversity of each subpopulation can be enriched. This not only ensures the exchange of excellent antibodies within the population, but also prevents the rapid spread of local optimal solutions and the occurrence of immature convergence. The update procedure of the improved PA-Jaya algorithm is shown in Algorithm 3.