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# Optimization of Cognitive Radio System Using Enhanced Firefly Algorithm

1 University Center for Research and Development, Chandigarh University, Mohali, Punjab, 140413, India

2 Faculty of Physics and Applied Computer Science, AGH University of Science & Technology, Krakow, Poland

3 Faculty of Information Technology, Middle East University, Amman, 11813, Jordan

4 Department of Computer Engineering and Applications, GLA University, Mathura, 281406, India

5 Department of Computer Engineering & Technology, Guru Nanak Dev University, Amritsar, Punjab, 143005, India

6 Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

7 Department of Computational Mathematics, Science and Engineering, College of Engineering, Michigan State University, East Lansing, MI, 48824, USA

8 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

* Corresponding Author: Mohamed Abouhawwash. Email:

*Intelligent Automation & Soft Computing* **2023**, *37*(3), 3159-3177. https://doi.org/10.32604/iasc.2023.041059

**Received** 09 April 2023; **Accepted** 17 June 2023; **Issue published** 11 September 2023

## Abstract

The optimization of cognitive radio (CR) system using an enhanced firefly algorithm (EFA) is presented in this work. The Firefly algorithm (FA) is a nature-inspired algorithm based on the unique light-flashing behavior of fireflies. It has already proved its competence in various optimization problems, but it suffers from slow convergence issues. To improve the convergence performance of FA, a new variant named EFA is proposed. The effectiveness of EFA as a good optimizer is demonstrated by optimizing benchmark functions, and simulation results show its superior performance compared to biogeography-based optimization (BBO), bat algorithm, artificial bee colony, and FA. As an application of this algorithm to real-world problems, EFA is also applied to optimize the CR system. CR is a revolutionary technique that uses a dynamic spectrum allocation strategy to solve the spectrum scarcity problem. However, it requires optimization to meet specific performance objectives. The results obtained by EFA in CR system optimization are compared with results in the literature of BBO, simulated annealing, and genetic algorithm. Statistical results further prove that the proposed algorithm is highly efficient and provides superior results.## Keywords

All the radio transmissions use a part of electromagnetic spectrum. The management and regulation of the spectrum is done by Federal Communications Commission (FCC) which has categorized the spectrum into licensed and unlicensed spectrum [1,2]. Due to the fast growth of wireless applications, the unlicensed spectrum is becoming overcrowded, which in turn leads to spectrum scarcity. It is also observed that the spectrum utilization is not effectively carried out by the licensed users, resulting in a situation where a few channels remain unoccupied in the wireless spectrum. Cognitive radio (CR) has been proposed as an efficient way to tackle with this problem and to permit the secondary users for the usage of licensed spectrum bands when primary users are not using it [3]. A CR system is generally characterized by two important parameters: cognitive capability and re-configurability. In the earlier one, the information about frequency, bandwidth, power and modulation type of signal is collected from the surrounding environment. Re-configurability is the ability of a radio system to rapidly configure its operational parameters in accordance with the sensed information for achieving the optimal performance [4]. By utilizing the spectrum in an opportunistic manner, CR system permits secondary users to sense and select the best unoccupied channel, share spectrum access information with others and vacate the occupied channel when primary users demand it back [5]. CR is widely used in many fields, e.g., software radios, mobile broadband, public security, and in medical applications [6–8].

CR is essential for providing time-varying Quality of Service (QoS) due to the dynamic nature of spectrum availability and the characteristics of radio channels. In addition to efficient spectrum utilization, CR aims to achieve objectives such as maximizing data throughput, minimizing bit-error-rate (BER), reducing power consumption, and minimizing interference [9]. To address these goals and meet the QoS requirements of users, CR needs to regularly sense the environment and adjust transmission parameters accordingly [10]. This adaptive behavior requires a cognitive engine that is aware of the environment, user demands, transmission links, and regulatory constraints, and is capable of balancing multiple objectives. The cognitive engine makes CR intelligent by dynamically adjusting itself to changing conditions [9–11].

Optimization algorithms, particularly evolutionary algorithms, have been successfully applied to various engineering and real-world applications [12–16]. These algorithms are well-suited for solving multi-objective CR optimization problems. Optimizing the CR system using evolutionary algorithms enables decision-making, learning, and awareness processing in the cognitive functionality [17]. As a result, researchers have focused on optimizing CR systems using various optimization algorithms in the past. These studies have employed various approaches to enhance the performance and efficiency of CR systems [9–11,17–26].

The first CR engine was developed by Virgina Tech institute using genetic algorithm (GA) [9]. The result outcomes showed that the implementation of GA altered the transmission parameters in accordance with a set of objectives. GA has been also used to find the optimal transmission parameters for single-carrier as well as multi-carrier fitness functions [18]. Zhang et al. have employed the Shuffled Frog Leap Algorithm to optimize power in the CR system [23]. Biogeography based optimization (BBO) has been utilized to obtain the optimum set of CR parameters [24]. Zhao et al. have optimized the CR system for three objectives with the ant colony optimization (ACO) technique [26]. However, all these methods either converge prematurely or take too much time to attain the optimal solution. For example, SA and GA exhibit slow convergence speed and require a significant amount of time to converge to the final solution.

The Firefly Algorithm (FA) is a swarm intelligence-based metaheuristic inspired by the behavior of fireflies. It has been successfully applied to a wide range of optimization problems in various domains. However, FA may face challenges in complex problems where it tends to oscillate around the global optimum due to random walks. To address these challenges and improve performance, it is necessary to explore alternative solutions. The No Free Lunch Theorem [27] highlights the need for developing new algorithms specifically tailored to different problem dimensions. This approach allows researchers to propose algorithm variants that are more suitable for specific areas, leading to advancements in solving complex optimization problems. In this paper, an enhanced variant of FA called enhanced FA (EFA) is introduced. EFA incorporates Mantegna’s algorithm to enhance the convergence speed of FA. The proposed algorithm is applied to benchmark functions as well as the optimization of a cognitive radio (CR) system to demonstrate its capabilities and effectiveness. By continuously developing and applying new algorithm variants like EFA, researchers can make progress in addressing the challenges of complex optimization problems and further improve the performance of metaheuristic algorithms.

The main contributions of this work are as follows:

• The proposed work addresses the challenges of local optima stagnation, poor exploration, and unbalanced exploitation and exploration operations in FA. The research introduces an enhanced version of FA called EFA, which incorporates improvements to enhance its performance and overcome the identified issues.

• EFA incorporates ideas from Mantegna’s algorithm and utilizes Lévy stable distribution to improve the exploration and exploitation operations. This enhances the algorithm’s ability to explore extensively and exploit effectively.

• EFA is evaluated on different benchmark problems and CR system optimization as a real-world application.

After this brief introduction, this paper is arranged as follows: Section 2 discusses FA, Section 3 introduces the concept of EFA, and Section 4 explains the fitness functions required for CR system optimization. Results of benchmark functions and CR system optimization using EFA are presented in Section 5. Finally, conclusions are given in Section 6.

The attractiveness of a firefly in the Firefly Algorithm (FA) is determined by its brightness, which is related to the fitness function being optimized [28–31]. FA is inspired by the flashing behavior of fireflies, where their flashing light helps them find potential mating partners and defend against predators [32]. In FA, the following idealized rules are applied [33]: (i) All fireflies in FA are unisexual, meaning they are attracted to each other regardless of their sex. (ii) Fireflies are differentiated based on their light intensity. Less bright fireflies are attracted to brighter ones, simulating the attraction behavior observed in fireflies. (iii) The brightness of a firefly in FA is related to the fitness function that needs to be optimized. Fireflies with higher fitness (better solutions) are represented as brighter, while those with lower fitness are dimmer.

By applying these rules, FA mimics the behavior of fireflies to guide the optimization process. It utilizes the attractiveness between fireflies to search for optimal solutions in the search space. The algorithm has shown effectiveness in various optimization applications across different fields. For the optimization problem, the brightness I of any firefly i at a particular position x =

where

where

As the attractiveness of a firefly is proportional to the light intensity seen by neighbouring fireflies, so attractiveness β of a firefly [33] is

where

The equation used for the attractiveness of ith firefly toward jth [33] is given by

where the second term is due to attraction, the third term is due to randomization,

FA is an efficient algorithm and has served as a global problem solver but with the increase in problem complexity, the algorithm takes longer time to give the appropriate results. When given enough computational time, FA is able to provide good results. However, due to the random walk mechanism in FA, the search process can be time-consuming, which can reduce the effectiveness of the algorithm.

In FA, it is assumed that the fireflies are randomly distributed in the search space at the beginning of the optimization process. During the initial iterations, fireflies are indeed separated by large distances which leads to smaller value of

To overcome the shortcomings of FA, a modified version of FA is proposed and is termed as EFA. The quality of solutions is improved by reducing the randomness in EFA. In general, there are three ways to carry out randomization: uniform randomization, random walk and heavy-tailed walks. Uniform randomization keeps the new solution between upper and lower bounds. For global and local randomization, random walks provide the solution depending upon the step size used. Heavy-tailed are the most suitable forms of randomization on global scale and a Lévy flight is one of its type [35].

Generating a random number via Lévy flights consist of two steps: (i) choice of a random direction drawn from a uniform distribution and (ii) generation of steps obeying a Lévy distribution which is a tricky affair [35]. In the present work, steps for a symmetric Lévy stable distribution are generated using the Mantegna algorithm [36]. The major advantage of using the Mantegna algorithm is its better efficiency and simplicity. The step length d in Mantegna’s algorithm [36] is calculated by

where u and v are two normally distributed stochastic random variables used to generate distribution for d that exhibits similar behavior to a Lévy distribution.

where

For |d| ≥ |d0|, where d0 is the smallest step, this distribution obeys a Lévy distribution. In the Mantegna algorithm, the transition from the current location to the next location is achieved through two main steps: (a) Entry-wise multiplication of random integers, (b) Distance-based transition probability. By combining these two steps, the Mantegna algorithm creates a Markov chain-like process, where the current solution is modified by the random multiplication and the transition probability determines the likelihood of moving to the next location. This approach promotes the exploration by allowing its movement towards potentially better solutions while also considering the distance to the best solution. The required random variable is defined as follows:

where

where

In a CR system, two types of operating parameters are present: transmission parameters and environmental parameters. The transmission parameters of a CR system behave like decision variables [38–44]. These are tunable parameters of the system and the radio adjusts its transmission knobs to matching values from the optimal set of parameters and are shown in Table 1.

The environmental parameters are necessary to get the information about the surrounding environmental characteristics and provide this information to the CR system, which helps the CR control system to make the accurate decisions. The environmental variables used are given in Table 2.

A CR system may have to meet a number of objectives in the wireless communication environment. Here five objectives or scenarios have been taken which are same as formulated in [23,24,39]. These objectives are given in Table 3 with their fitness functions and description about different variables.

It is not possible to achieve the best values of all the objectives simultaneously because of the fact that these are conflicting e.g., minimizing BER increases the power consumption. Hence, rather than targeting these objectives independently, a multi-objective function [39] is taken by linearly combining these factors as follows:

The weighting factors

The performance of the EFA algorithm is evaluated in this section by using benchmark functions. Eight unconstrained real objective benchmark functions [38,39] are employed for the optimization using EFA. The set of functions along with variable range for determining optimality is shown in Table 5. Artificial bee colony (ABC), BBO, bat algorithm (BA), and FA are used for the purpose of comparison. The associated set of initial conditions for the competitive algorithms is illustrated in Table 6. In order to ensure that the algorithm finds optimal solution consistently, each algorithm runs over 20 times. In each scenario, the maximum number of function evaluations (NFEs) has been set at 500 × 20 = 10,000.

In Table 7, best values are shown in the bold text. For functions, f2, f5, f6, f7 and f8, the standard deviation of EFA is much better except for f1 in which FA is better, f3 where ABC is better and f4 where BA is better. The mean value attained by proposed algorithm is better for seven function except for only f2 and f3 where FA is better. As far as, the best value is concerned, EFA gives best for most of the test function except for f6 where BA is better. The results of the experiments demonstrate that the proposed EFA outperforms other algorithms such as ABC, BBO, BA, and FA across most of the test functions. EFA exhibits better mean and standard deviation values compared to the competing algorithms, indicating its superior performance.

To validate the significant improvement offered by EFA, two statistical tests Wilcoxon’s rank-sum test and Friedman rank (f-rank) test were conducted. The f-rank test assigns rank to each algorithm based on their performance. From the first row of Table 8, it is evident that EFA significantly outperforms the other algorithms and secures the first rank in the benchmark suite. The rank-sum test is performed for each individual function to determine whether EFA is significantly better or not. The performance of EFA is expressed as

5.2 Simulation Results for CR Optimization

The optimization of CR systems is considered a complex problem due to the conflicting nature of the parameters that need to be optimized. As mentioned in previous literature [23–24], five scenarios have been selected for optimization in this study. These scenarios are determined by five transmission variables, namely transmitted power (

Values of different parameters taken in EFA as well as in FA are given as follows:

• Population size = 20

• Generations = 200

• Randomization parameter, α = 0.25

• Attractiveness coefficient βo = 0.2

• Absorption coefficient, γ = 1

The fitness values found by EFA are compared with that of SA [23], GA [23], and BBO [24]. The FA is also applied to the CR system in order to contrast the performance of EFA with FA. The best values of fitness attained in each case are highlighted in the last column of Table 10.

From Table 10, it can be seen that in each of the five scenarios, EFA was consistently able to secure better value of fitness as compared to SA [23], GA [23], and BBO [24]. In comparison to FA, EFA performed significantly better in the minimum interference and maximum efficiency scenarios, while still achieving comparable results in the other three scenarios. Both FA and EFA were able to score the same fitness values except in the maximum efficiency mode where EFA performed better than FA. This demonstrates the capability of EFA to effectively identify the global optimum in various scenarios.

The convergence performance of an optimization algorithm is indeed a crucial factor in determining its practicality. If an algorithm takes excessively long to reach a near-optimal solution, it may not be suitable for real-world applications. The convergence curves for all the five objectives of optimization are shown in Fig. 1. The convergence performance of EFA is compared with basic FA. Fig. 1a shows the convergence curve obtained by EFA and FA for the minimum power consumption mode. FA took nearly 80 generations or iterations to converge whereas EFA converged in 40 iterations. EFA also outperformed BBO which required 90 iterations to attain its final value for the same scenario [24]. In the maximum throughput mode, EFA needed 40 iterations to converge to minimum value whereas FA found its minimum value in about 150 generations. In this case, EFA managed to show a big improvement over FA. Figs. 1d and 1e give the convergence properties of EFA and FA for the minimum interference mode and maximum efficiency mode respectively. Here, EFA not only achieved faster convergence but also delivered better value of the fitness as compared to FA. This may be attributed to changes made in the basic firefly algorithm to prevent oscillation of the algorithm around the final solution which results in finding the optimum more efficiently.

The EFA has demonstrated its efficiency in solving the benchmark functions and the CR system optimization problem. It has shown significant advancements compared to other state-of-the-art algorithms. The simplicity of its structure and ease of implementation make it suitable for inclusion in the expert and hybrid intelligent systems. The convergence properties of EFA further confirm its suitability as an optimization algorithm.

However, like other stochastic algorithms, EFA is susceptible to getting stuck at local minima and may not always achieve the global optima for all benchmark functions. The benchmark set used in the evaluation consists of various types of problems, including unimodal, multimodal, and composite functions. An algorithm that can solve the entire benchmark set and consistently reach the global solution can be considered as a state-of-the-art algorithm. While EFA may encounter local optima in some cases, it still possesses the potential to become a standard algorithm.

Further research and improvements are needed to address the limitations of EFA and enhance its ability to achieve global solutions. By addressing these challenges, EFA can progress towards becoming a widely accepted and recognized state-of-the-art algorithm.

This paper introduced a novel variant of FA named EFA. In the proposed technique, the unique and fascinating features of FA are retained and performance is improved by reducing the randomness in the search mechanism using Mantegna’s algorithm. The proposed technique was employed to optimize benchmark functions and the CR system. EFA yielded superior results in the optimization of benchmark functions in contrast to ABC, FA, BA, and BBO. CR transmission parameters, such as transmitted power, modulation index, bandwidth, TDD and symbol rate, have been optimized by EFA in different environments to meet various objectives. The EFA scored better fitness values than BBO, SA, GA. In addition, EFA converged in almost half or fewer generations than basic FA and BBO. Both these factors make EFA an attractive choice as an optimization tool. Finally, it can be concluded that EFA is a robust optimization technique, and it is anticipated that it can be used to optimize other real-world problems like animal tracking, cancer classification, logistics, coal mine workers’ tracking, gene expression modeling, feature selection, clustering problems, underwater wireless sensor networks, and various industrial applications.

In addition to these applications, exploring the implementation of another hybrid meta-heuristic algorithm can offer improved accuracy and reduced convergence time for EFA. Future work can focus on incorporating a balanced exploration and exploitation strategy to further enhance the algorithm’s performance. Introducing different mutation operators and chaotic maps can also be considered to analyze their impact on the performance of the EFA algorithm. To enhance the global and local search capabilities of EFA, new exploratory and exploitative search equations can be introduced. These additions can help improve the algorithm’s ability to effectively explore the solution space and exploit promising regions. By incorporating these enhancements, the algorithm’s overall performance can be further improved, making it more efficient and effective in solving optimization problems.

Acknowledgement: This project is funded by King Saud University, Riyadh, Saudi Arabia.

Funding Statement: This project is funded by King Saud University, Riyadh, Saudi Arabia. Researchers Supporting Proiect Number (RSP2023R167), King Saud University, Riyadh, Saudi Arabia.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

## References

- A. K. L. K. Yau, A. P. Komisarczuk and P. D. Teal, “Cognitive radio-based wireless sensor networks: Conceptual design and open issues,” in Proc. of IEEE 34th Conf. on Local Computer Network, Zurich, Switzerland, pp. 955–962, 2009.
- I. F. Akyildiz, W. Y. Lee, M. C. Vuran and S. Mohanty, “A survey on spectrum management in cognitive radio networks,” IEEE Communications Magazine, vol. 15, no. 3, pp. 1–15, 2008.
- S. Haykin, “Cognitive radio: Brain-empowered wireless communications,” IEEE Journal Selection Areas Communication, vol. 23, no. 2, pp. 201–220, 2005.
- I. Akyildiz, W. Lee, M. Vuran and S. Mohanty, “Next generation/dynamic spectrum access/cognitive radio wireless networks: A survey,” Computer Networks, vol. 50, no. 13, pp. 2127–2159, 2006.
- M. Calabrese, “The end of spectrum scarcity: Building on the TV bands database unused public airwaves,” New American Foundation, vol. 12, no. 6, pp. 25–43, 2009.
- B. Wang and K. Liu, “Advances in cognitive radio networks: A survey,” IEEE Journal of Selected Topics in Signal Processing, vol. 5, no. 1, pp. 5–23, 2011.
- J. Wang, M. Ghosh and K. Challapali, “Emerging cognitive radio applications: A survey,” IEEE Communications Magazine, vol. 49, no. 3, pp. 74–81, 2011.
- J. Mitola and G. Maguire, “Cognitive radio: Making software radios more personal,” IEEE Personal Communications, vol. 6, no. 4, pp. 13–18, 1999.
- S. Chen, T. R. Newman, J. B. Evans and A. M. Wyglinski, “Genetic algorithm-based optimization for cognitive radio networks,” in Sarnoff Symp., Princeton, NJ, USA, pp. 1–6, 2010.
- T. W. Rondeau, B. Le, C. J. Rieser and C. W. Bostian, “Cognitive radios with genetic algorithms: Intelligent control of software defined radios,” in Proc. of Software Defined Radio Forum Technical Conf., Phoenix, Arizona, USA, pp. C3–C8, 2004.
- K. T. Deepak, K. U. Siba and L. S. Samrat, “Cognitive radio parameter adaptation using multi-objective evolutionary algorithm,” Advances in Intelligent and Soft Computing, vol. 130, no. 11, pp. 1–12, 20
- A. Goli, A. M. Golmohammadi and J. L. Verdegay, “Two-echelon electric vehicle routing problem with a developed moth-flame meta-heuristic algorithm,” Operation Management Research, vol. 15, no. 4, pp. 891–912, 2022.
- A. Ala, A. Mahmoudi, S. Mirjalili, V. Simic and D. Pamucar, “Evaluating the performance of various algorithms for wind energy optimization: A hybrid decision-making model,” Expert Systems with Applications, vol. 221, no. 3, pp. 119731, 2023.
- A. Ala, F. E. Alsaadi, M. Ahmadi and S. Mirjalili, “Optimization of an appointment scheduling problem for healthcare systems based on the quality of fairness service using whale optimization algorithm and NSGA-II,” Scientific Reports, vol. 11, no. 1, pp. 19816, 2021.
- A. Goli and E. B. Tirkolaee, “Designing a portfolio-based closed-loop supply chain network for dairy products with a financial approach: Accelerated Benders decomposition algorithm,” Computers and Operations Research, vol. 155, no. 6, pp. 106244, 2023.
- S. M. Abd-Elazim and E. S. Ali, “Load frequency controller design of a two-area system composing of PV grid and thermal generator via firefly algorithm,” Neural Computing and Applications, vol. 30, no. 4, pp. 607–616, 2018.
- C. J. Rieser, T. W. Rondeau, C. W. Bostian and T. M. Gallagher, “Cognitive radio testbed: Further details and testing of a distributed genetic algorithm based cognitive engine for programmable radios,” in IEEE Military Communications Conf., Monterey, CA, USA, vol. 3, pp. 1437–1443, 2004.
- T. R. Newman, B. A. Barker, A. M. Wyglinski, A. Agah, J. B. Evans et al., “Cognitive engine implementation for wireless multicarrier transceivers,” Wireless Communication Mobile Computer, vol. 7, no. 9, pp. 1129–1142, 2007.
- Y. Hei, W. Li, M. Li, Z. Qiu and W. Fu, “Optimization of multiuser MIMO cooperative spectrum sensing in cognitive radio networks,” Cognitive Computer, vol. 7, no. 3, pp. 359–368, 2014.
- I. Basit, W. K. Qureshi and A. Malik, “Range–angle-dependent beamforming for cognitive antenna array radar with frequency diversity,” Cognitive Computer, vol. 8, no. 2, pp. 204–216, 2015.
- W. Chen, T. Li and T. Yang, “Intelligent control of cognitive radio parameter adaption: Using evolutionary multi-objective algorithm based on user preference,” Ad Hoc Networks, vol. 26, no. 4, pp. 3–16, 2015.
- J. A. Tan, “Genetic algorithm application in optimizing transmission parameters on adaptive mechanism of cognitive radio,” Dissertation University Technology Malaysia, Faculty of Electrical Engineering, pp. 1–235, 2009.
- X. Zhang, Y. Zhang, Y. Shi, L. Zhao and C. Zou, “Power control algorithm in cognitive radio system based on modified shuffled frog leaping algorithm,” AEU-International Journal of Electronics and Communications, vol. 66, no. 6, pp. 448–454, 2012.
- K. Kaur, M. Rattan and M. Patterh, “Biogeography-based optimisation of cognitive radio system,” International Journal of Electronics, vol. 101, no. 1, pp. 24–36, 2013.
- R. Deka, S. Chakraborty and S. Roy, “Optimization of spectrum sensing in cognitive radio using genetic algorithm,” Faculty University Electron Emerging, vol. 25, no. 3, pp. 235–243, 2012.
- N. Zhao, S. Li and Z. Wu, “Cognitive radio engine design based on ant colony optimization,” Wireless Personal Communication, vol. 65, no. 1, pp. 15–24, 2011.
- D. H. Wolpert and W. G. Macready, “No free lunch theorems for optimization,” IEEE Transactions on Evolutionary Computation, vol. 1, no. 1, pp. 67–82, 1997.
- U. Singh and M. Rattan, “Design of thinned concentric circular antenna arrays using firefly algorithm,” IET Microwaves, Antennas & Propagation, vol. 8, no. 12, pp. 894–900, 2014.
- L. Coelho and V. Mariani, “Firefly algorithm approach based on chaotic tinkerbell map applied to multivariable PID controller tuning,” Computers & Mathematics with Applications, vol. 64, no. 8, pp. 2371–2382, 2012.
- M. Marichelvam, T. Prabaharan and X. Yang, “A discrete firefly algorithm for the multi-objective hybrid flowshop scheduling problems,” IEEE Transactions on Evolutionary Computation, vol. 18, no. 2, pp. 301–305, 2014.
- I. Fister, I. Fister, X. Yang and J. Brest, “A comprehensive review of firefly algorithms,” Swarm and Evolutionary Computation, vol. 13, no. 6, pp. 34–46, 2013.
- X. S. Yang, “Firefly algorithms for multimodal optimization,” Stochastic Algorithms: Foundations and Applications, SAGA 2009, Lecture Notes in Computer Sciences, vol. 5792, pp. 169–178, 2009.
- H. Gomes, “A firefly metaheuristic structural size and shape optimization with natural frequency constraints,” International Journal of Metaheuristics, vol. 2, no. 1, pp. 38, 2012.
- C. Liu, F. Gao and N. Jin, “Design and simulation of a modified firefly algorithm,” in Seventh Int. Joint Conf. on Computational Sciences and Optimization (CSO), Beijing, China, pp. 21–25, 2014.
- X. S. Yang, Nature Inspired Mataheuristic Algorithms. UK: Luniver Press, vol. 12. no. 2 pp. 1–324, 2008.
- R. Mantegna, “Fast, accurate algorithm for numerical simulation of Lévy stable stochastic processes,” Physical Review E, vol. 49, no. 5, pp. 4677–4683, 1994.
- H. Soneji and R. C. Sanghvi, “Towards the improvement of cuckoo search algorithm,” in Proc. of World Congress on Information and Communication Technologies (WICT), Trivandrum, India, pp. 878–883, 2012.
- A. Wyglinski, “Cognitive radio communications and networks,” IEEE Communications Magazine, vol. 46, no. 4, pp. 30–31, 2008.
- T. R. Newman, “Multiple objective fitness functions for cognitive radio adaptation,” Dissertation, Electrical Engineering & Computer Science, University of Kansas, 2008.
- G. Singh, M. Rattan, S. S. Gill and N. Mittal, “Hybridization of water wave optimization and sequential quadratic programming for cognitive radio system,” Soft Computing, vol. 23, no. 17, pp. 7991–8011, 2019.
- R. Salgotra, U. Singh, S. Singh, G. Singh and N. Mittal, “Self-adaptive salp swarm algorithm for engineering optimization problems,” Applied Mathematical Modelling, vol. 89, no. 1, pp. 188–207, 2021.
- S. Bansal and M. Rattan, “Design of cognitive radio system and comparison of modified whale optimization algorithm with whale optimization algorithm,” International Journal of Information Technology, vol. 1, no. 1, pp. 1–12, 2019.
- G. Dinesh, P. Venkatakrishnan and K. M. A. Jeyanthi, “Modified spider monkey optimization—An enhanced optimization of spectrum sharing in cognitive radio networks,” International Journal of Communication Systems, vol. 1, no. 1, pp. 1–20, 2020.
- N. Mittal, H. Singh, V. Mittal, S. Mahajan, A. K. Pandit et al., “Optimization of cognitive radio system using self-learning salp swarm algorithm,” Computers, Materials & Continua, vol. 70, no. 2, pp. 3821– 3835, 2022.

## Cite This Article

N. Mittal, R. Salgotra, A. Sharma, S. Kaur, S. S. Askar*et al.*, "Optimization of cognitive radio system using enhanced firefly algorithm,"

*Intelligent Automation & Soft Computing*, vol. 37, no.3, pp. 3159–3177, 2023.