## 1 Introduction  
With the rapid development of the Internet of Things (IoT) within the cyber-physical-social system (CPSS), there is an ever-increasing demand for communication network bandwidth for achieving high-performance applications which enrich and broaden the interactions and connections in the cyber-physical-social world. Thus, some communication technologies have been developed using new frequency bands. Moreover, various improved modulation and coding technologies have also been proposed to utilize the existing frequency spectrum more efficiently [1; 2; 3]. However, spectrum resources are limited. They are a kind of extremely valuable natural resource and are becoming increasingly restricted or even depleted. In response to this limitation, it is necessary to improve the current spectrum management methods. Fortunately, the recent advances of big data and artificial intelligence technologies make it possible to address the issue. Cognitive radio network (CRN), as an intelligent wireless communication system, can dynamically share and allocate the spectrum in accordance with the current state of the channel, and it has been seen as an effective solution to the current low utilization of spectrum resources [4; 5]. Furthermore, CRNs have been employed to develop the high-performance IoT [6; 7; 8; 9; 10; 11; 12; 13]. For example, CRN technology applied to wireless sensor network (WSN) systems in IoT can well sense the surrounding environment and adapt to environmental changes by changing the transmission parameters in real time through information acquired from the environment. Such characteristics make it especially suitable for practical production scenarios. Generally, in the CRN-aided IoT, the secondary user (i.e., cognitive user) may selectively access the idle frequency band of the primary user (i.e., authorized user) to improve the utilization of the licensed spectrum. Meanwhile, some limit requirements should be met by the interference of the secondary user to the primary user for the frequency band. These limits include the constraints of total power, the bit error rate (BER), and the acceptable interferences of the primary user [14]. Furthermore, orthogonal frequency division multiplexing (OFDM), as a multi-carrier parallel wireless transmission technology, has been identified as one suitable alternative to deal with the allocation and transmission of spectrum resources in CRNs [15; 16]. Hence, the issue of how to adaptively allocate downlink resources in a cognitive multi-user OFDM system for IoT has drawn much attention from researchers. Generally, there exist three types of CRNs, including interweave, underlay, and overlay CRNs. In an interweave scenario, the secondary users adaptively utilize the spectrum band whenever it is not used by the primary users [17]. In the underlay case, the secondary users are allowed to coexist with the primary users, provided that the interference caused to the primary users is below a predefined threshold [17]. In the latter category, the secondary system has the knowledge of the primary system codebook, channel gains, and transmitted information. A part of the secondary users' power can be used to retransmit the primary users' message so that the secondary users are able to maintain or improve the primary rate while achieving their own communication goals [18]. Generally speaking, the existing solutions mostly use the traditional mathematical optimization method or some greedy searching algorithms, which may suffer from a quite high computational complexity during the implementation process [18; 19]. Some evolutionary algorithms, including simulated annealing (SA) [20], genetic algorithm (GA) [21], particle swarm optimization (PSO) [22; 23], differential evolution (DE) [24], and immune clonal optimization (ICO) [25], are employed to deal with this issue, with the help of their effective computational features in the swarm intelligence paradigm.