Standard Firefly Algorithm Research Articles

Firefly algorithm-based LSTM model for Guzheng tunes switching with big data analysis

Guzheng tune progression involves intricately harmonizing melodic motif transitions. Effectively navigating this vast creative possibility space to expose musically consistent elaborations presents challenges. We develop a specialized large long short-term memory (LSTM) model for generating musically consistent Guzheng tune transitions. First, we propose novel firefly algorithm (FA) enhancements, e.g., adaptive diversity preservation and adaptive swim parameters, to boost exploration effectiveness for navigating the vast creative combinatorics when generating Guzheng tune transitions. Then, we develop a specialized stacked LSTM architecture incorporating residual connections and conditioned embedding vectors that can leverage long-range temporal dependencies in Guzheng music patterns, including unsupervised learning of concise Guzheng-specific melody embedding vectors via a variational autoencoder, encapsulating unique harmonic signatures from performance descriptors to provide style guidance. Finally, we use LSTM networks to develop adversarial generative large models that enable realistic synthesis and evaluation of Guzheng tunes switching. We gather an extensive 10+ hour corpus of solo Guzheng recordings spanning 230 musical pieces, 130 distinguished performing artists, and 600+ audio tracks. Simultaneously, we conduct thorough Guzheng data analysis. Comparative assessments against strong baselines over systematic musical metrics and professional listeners validate significant generation fidelity improvements. Our model achieves a 63 % reduction in reconstruction error compared to the standard FA optimization after 1000 iterations. It also outperforms baselines in capturing characteristic motifs, maintaining modality coherence with under 2 % dissonant pitch errors, and retaining desired rhythmic cadences. User studies further confirm the superior naturalness, novelty, and stylistic faithfulness of the generated tune transitions, with ratings close to real data.

Parameter identification of Yoshida–Uemori combined hardening model by using a variable step size firefly algorithm

Abstract The material behavior under cyclic loading is more complex than under monotonic loading and the usage of the sophisticated constitutive models is required to accurately define the elastoplastic behaviors of the advanced high-strength steels and aluminum alloys. These models involve the numerous material parameters that are determined from cyclic tests and accurate calibration of the variables has a great influence on the description of the material response. Therefore, the development of a precise and robust identification method is needed to obtain reliable results. In this study, a systematic methodology depending upon the firefly algorithm (FA) with variable step size has been developed and Yoshida–Uemori combined hardening model parameters of a dual-phase steel (DP980) and an aluminum alloy (AA6XXX-T4) are determined. The identified parameters are verified based on comparisons between the finite element simulations of the cyclic uniaxial tension-compression tests and experimental data and also the search performance of the variable FA is evaluated by comparing it with the standard FA. It is seen from these comparisons that variable FA can easily find and rapidly converge to the global optimum solutions.

Development of a COVID-19 Patients’ Fatality Prediction System Using Swarm Intelligent Convolution Neural Network

Aims: This work aims to develop a system that can be used to accurately and timely predict the fatality of a positively tested COVID-19 patient through the use of a deep learning technique – a swarm intelligent convolutional neural network.
 Methodology: The dataset used in this study was acquired from the Kaggle repository database. The dataset contains the Lung Chest X-Ray images of COVID-19 patients. The images were pre- processed to obtain the desired image quality for further processing. This was followed by segmenting the pre-processed images. An Enhanced Firefly Algorithm (EFA) was formulated by applying the roulette wheel selection procedure to model the movement process of the firefly as a deterministic process to assist the standard Firefly Algorithm (FA) and application of Chaotic Sinusoidal Map Function to model the attractive process of the firefly which establishes a balance between exploration and exploitation in FA. The EFA was applied to optimize Convolution Neural Network (CNN) hyper-parameters (number of layers, number of filters per layer, filter size and batch size). The segmented result was subsequently presented to EFA-CNN feature extraction and prediction of COVID-19 patient fatality cases. The formulated deep learning models (EFA-CNN and CNN) were implemented using Matrix Laboratory 2020a software. The implemented models were evaluated using specificity, sensitivity, false positive rate, accuracy, and recognition time/rate to determine the performance of the developed models.
 Results: The findings revealed that the EFA-CNN model performs better in the prediction of COVID-19 patients’ fatality compared to the CNN model. It was also discovered that the formulated EFA applied to select optimal values of the hyper-parameters for the CNN architecture accounted for improved recognition accuracy and reduced recognition time of the developed COVID-19 Patients’ Fatality Prediction System.
 Conclusion: The system developed will assist both the government and healthcare workers in providing the needed computational capability for the prediction of the fatality level of a positively tested COVID-19 patient.

An OCF-IoTivity enabled smart-home optimal indoor environment control system for energy and comfort optimization

The growing energy demand with diminishing energy resources calls for development of optimal indoor control system through accurate energy and occupant comfort modeling in a smart-home. While some major obstacles faced by smart-home IoT network are heterogeneity and disparate IP frameworks resulting in a connectivity and interoperability issues. In this paper we developed a new Open Connectivity Foundation (OCF) based prediction assisted optimal control framework for optimizing energy consumption and maximizing occupant comfort in smart-home. To the best of our knowledge, we are the first to design a scalable, secure, and inter-operable optimal control solution for smart-home IoT networks. The developed framework offloads machine learning models on IoT device for accurate energy and thermal comfort modeling to enable prediction assisted optimization. The system enables edge analytics using deep learning based inference models for proactive response. For optimization standard Firefly algorithm is modified based on inertia weight approach to achieve improved performance. OCF based optimal actuator control test-bed deployment and real-time experimentation is conducted to evaluate the performance of the system. Empirical investigation verified the effectiveness of proposed framework with energy saving scope of 36.82%, 5 s average response time and 3.36 MS Round Trip Time.

Scouting Firefly Algorithm and its Performance on Global Optimization Problems

For effective optimization, metaheuristics should maintain the proper balance between exploration and exploitation. However, the standard firefly algorithm (FA) posted some limitations in its exploration process that can eventually lead to premature convergence, affecting its performance and adding uncertainty to the optimization results. To address these constraints, this study introduces an additional novel search mechanism for the standard FA inspired by the behavior of the scout bee in the artificial bee colony (ABC) algorithm, termed the "Scouting FA". Specifically, fireflies stuck in the local optima will take directed extra random walks to escape toward the region of the optimum solution, thus improving convergence accuracy. Empirical findings on the five standard benchmark functions have validated the effects of this modification and revealed that Scouting FA is superior to its original version.

A new firefly algorithm with improved global exploration and convergence with application to engineering optimization

Firefly algorithm (FA) is a powerful and efficient meta-heuristic algorithm which has shown effective performance in the recent literature when applied to solving engineering optimization problems. FA imitates the flashing behavior of fireflies. FA generates solutions randomly and assumes them as fireflies. However, these algorithms may suffer from premature convergence and poor global exploration when used to optimize complex and high dimension engineering problems. Therefore, this study has proposed a novel FA, called firefly algorithm 1 to 3 (FA1→3), via different types of movements of fireflies in an attempt to improve the global exploration and convergence characteristics of FA. A comprehensive study has been carried out on the CEC2014 test functions to compare FA1→3 with the standard FA and several modern improved FA algorithms to validate its performance. The experimental results demonstrate that FA1→3 has achieved acceptable performance. In addition, it has been applied to six real-world engineering problems to show the optimization capability, robustness, and efficacy of FA1→3 in comparison with modern algorithms As per simulations, FA1→3 has provided suitable performance and higher accuracy than traditional and modified algorithms introduced in the last years. According to simulations, FA1→3 is significantly powerful and robust when dealing with various complex engineering problems and finds the design variables straightforwardly. Note that the source code of the proposed FA1→3 algorithm is publicly available at https://www.optim-app.com/projects/FA.

Pseudolite Constellation Optimization for Seamless Train Positioning in GNSS-Challenged Railway Stations

Advantages of Global Navigation Satellite System (GNSS) in precise and reliable localization can be exploited to enable low-cost and train-centric railway train control systems by reducing track-side facilities like Balises and track circuits. However, constrained observability of satellite signals in specific railway station areas leads to a great challenge to the continuity and availability of GNSS-based train positioning. The pseudolite (PL) technology has a great potential for seamless localization under GNSS-challenged or even signal-denied environments. In this paper, we consider the optimized solution of pseudolite constellation design for seamless train positioning in railway station environments. An integrated train positioning architecture is presented based on a combined GNSS/PL measurement model. Using the trackmap, the proposed solution firstly establishes a feature point set covering all tracks in the station by extracting key Points-of-interest (POIs) from track database. Based on that, a K-means-enhanced generalized center-guided firefly algorithm (KGFA) is proposed to improve the standard firefly algorithm (FA) for deriving an optimized pseudolite constellation solution. The performance indicator for each candidate pseudolite layout scheme is defined according to the scenario-based GNSS/PL constellation configuration. The capability of the KGFA-enabled solution is validated by comparisons with similar FA methods. Through a case study, performance of the optimized pseudolite constellation and its influence to GNSS/PL-based seamless train positioning have been demonstrated over the involved reference pseudolite layout strategies. It is noteworthy that the proposed solution enables the enhanced inherent capability of the local pseudolite network to achieve seamless train positioning over the conventional GNSS-alone train positioning mode.

Greedy Firefly Algorithm for Optimizing Job Scheduling in IoT Grid Computing.

The Internet of Things (IoT) is defined as interconnected digital and mechanical devices with intelligent and interactive data transmission features over a defined network. The ability of the IoT to collect, analyze and mine data into information and knowledge motivates the integration of IoT with grid and cloud computing. New job scheduling techniques are crucial for the effective integration and management of IoT with grid computing as they provide optimal computational solutions. The computational grid is a modern technology that enables distributed computing to take advantage of a organization’s resources in order to handle complex computational problems. However, the scheduling process is considered an NP-hard problem due to the heterogeneity of resources and management systems in the IoT grid. This paper proposed a Greedy Firefly Algorithm (GFA) for jobs scheduling in the grid environment. In the proposed greedy firefly algorithm, a greedy method is utilized as a local search mechanism to enhance the rate of convergence and efficiency of schedules produced by the standard firefly algorithm. Several experiments were conducted using the GridSim toolkit to evaluate the proposed greedy firefly algorithm’s performance. The study measured several sizes of real grid computing workload traces, starting with lightweight traces with only 500 jobs, then typical with 3000 to 7000 jobs, and finally heavy load containing 8000 to 10,000 jobs. The experiment results revealed that the greedy firefly algorithm could insignificantly reduce the makespan makespan and execution times of the IoT grid scheduling process as compared to other evaluated scheduling methods. Furthermore, the proposed greedy firefly algorithm converges on large search spacefaster , making it suitable for large-scale IoT grid environments.

A dynamic firefly algorithm based on two-way guidance and dimensional mutation

As a stochastic optimiser, the firefly algorithm (FA) has been successfully and widely used in the solutions to various optimisation problems. Recent related research shows that the standard FA does not sufficiently balance between exploration and exploitation. Especially in high-dimensional problems, it is easy for the standard FA to fall into the local optimum and lead to premature convergence. To overcome the problems as mentioned above, DMTgFA uses three strategies: dynamic step length setting strategy (DS), non-elite two-way guidance model (TG) and elites dimensional mutation strategy (DM). The dynamic step length setting strategy makes the algorithm convergence speed faster. The non-elite two-way guidance model and the elite dimensional mutation strategy cooperate to solve the balance problem between global search and local search. Experimental results show that DMTgFA has stronger optimisation ability and faster convergence speed than other state-of-the-art FA variants.

Advanced discrete firefly algorithm with adaptive mutation‐based neighborhood search for scheduling unrelated parallel machines with sequence‐dependent setup times

The unrelated parallel machine scheduling problem with sequence-dependent setup times is addressed in this paper with the objective of minimizing the elapsed time between the start and finish of a sequence of operations in a set of unrelated machines. The machines are considered unrelated because the processing speed is dependent on the job being executed and not on the individual machines. Generally, the problem is considered NP-hard, as it presents additional complexity to find an optimal solution in terms of minimum makespan. An advanced firefly metaheuristic optimization algorithm is introduced to solve this problem. The proposed method, called the FAII algorithm, aims to improve the standard firefly algorithm's performance by incorporating an enhanced global best solution update mechanism and adaptive mutation-based local and global neighborhood search scheme to improve the quality of the proposed algorithm's generated solution. Several experiments were conducted to compare and validate the proposed algorithms' performance on small and large-scale benchmarked problem instances with up to 12 machines and 120 job combinations. Moreover, the performance of the FAII was also compared with eight other metaheuristic algorithms, which were implemented in parallel with the FAII method. Furthermore, the numerical results of the FAII algorithm were compared with the scheduling results of six other well-known metaheuristics from the literature. The comparison results backed with a comprehensive statistical analysis showed the superiority of the enhanced FA-style scheduling optimization over other metaheuristic methods to find good quality solutions or minimum average makespan.

An improved firefly algorithm with dynamic self-adaptive adjustment.

The firefly algorithm (FA) is proposed as a heuristic algorithm, inspired by natural phenomena. The FA has attracted a lot of attention due to its effectiveness in dealing with various global optimization problems. However, it could easily fall into a local optimal value or suffer from low accuracy when solving high-dimensional optimization problems. To improve the performance of the FA, this paper adds the self-adaptive logarithmic inertia weight to the updating formula of the FA, and proposes the introduction of a minimum attractiveness of a firefly, which greatly improves the convergence speed and balances the global exploration and local exploitation capabilities of FA. Additionally, a step-size decreasing factor is introduced to dynamically adjust the random step-size term. When the dimension of a search is high, the random step-size becomes very small. This strategy enables the FA to explore solution more accurately. This improved FA (LWFA) was evaluated with ten benchmark test functions under different dimensions (D = 10, 30, and 100) and with standard IEEE CEC 2010 benchmark functions. Simulation results show that the performance of improved FA is superior comparing to the standard FA and other algorithms, i.e., particle swarm optimization, the cuckoo search algorithm, the flower pollination algorithm, the sine cosine algorithm, and other modified FA. The LWFA also has high performance and optimal efficiency for a number of optimization problems.

A Fast Firefly Algorithm for Function Optimization: Application to the Control of BLDC Motor

Firefly Algorithm (FA) is a recent swarm intelligence first introduced by X.S. Yang in 2008. It has been widely used to solve several optimization problems. Since then, many research works were elaborated presenting modified versions intending to improve performances of the standard one. Consequently, this article aims to present an accelerated variant compared to the original Algorithm. Through the resolving of some benchmark functions to reach optimal solution, obtained results demonstrate the superiority of the suggested alternative, so-called Fast Firefly Algorithm (FFA), when faced with those of the standard FA in term of convergence fastness to the global solution according to an almost similar precision. Additionally, a successful application for the control of a brushless direct current electric motor (BLDC) motor by optimization of the Proportional Integral (PI) regulator parameters is given. These parameters are optimized by the FFA, FA, GA, PSO and ABC algorithms using the IAE, ISE, ITAE and ISTE performance criteria.

Energy saving scheduling strategy for job shop under TOU and tiered electricity price

In view of the energy-saving scheduling problem of job shop in the order-oriented manufacturing enterprise, it is necessary to consider the energy consumption of equipment processing and standby. Considering the Time-of-Use (TOU) and tiered electricity price, a mathematical model is established by introducing the switch strategy in the idle time of equipment to reduce the cost of power consumption in production and assembly. In order to solve the discontinuous domain problem that the standard Firefly Algorithm (FA) is not suitable for workshop energy-saving scheduling, an improved FA is used to solve the mathematical model. The coding, decoding and location updating of the algorithm are redesigned. A three-layer coding structure based on the workpiece sequence, starting time and switch strategy is designed; for the iterative process of workpiece sequence encoding, the Hamming distance is used to replace the Euclidean distance to calculate the position distance between the firefly individuals. Precedence preservation order-based crossover (POX) crossover is used to replace the position updating operation to ensure the feasibility of the solution. Finally, the correctness of the mathematical model and the effectiveness of the algorithm are verified by examples.

Stepping ahead Firefly Algorithm and hybridization with evolution strategy for global optimization problems

Intelligent optimization algorithms based on swarm principles have been widely researched in recent times. The Firefly Algorithm (FA) is an intelligent swarm algorithm for global optimization problems. In literature, FA has been seen as an efficient and robust optimization algorithm. FA is an algorithm that has obtained good to best results in complex problems. Therefore, there are many instances of modification, and hybridization of FA with other optimizing algorithms, but further improvements are still possible. This research first proposes a new modification of FA by introducing a novel and unique stepping ahead parameter. The concept is based on being proactive rather than reactive, which is the normal behavior of a standard FA. The notion behind stepping ahead is to send a firefly ahead then the best known position to look for even better solution. Second, a new design of a hybrid of the newly modified FA with Covariance Matrix Adaptation Evolution Strategy (CMAES) to improve the exploitation further while maintaining good exploration in the fireflies is presented. The main use of CMAES in this hybrid algorithm is to provide diversity to fireflies, as a result it improves exploitation. Traditionally, hybridization has combined two or more algorithms in terms of structure only, and consideration was not given to the increase in time complexity or diversity. In this paper, the two algorithms are not run in separate cycles rather CMAES is placed inside the FA. Through this novelty, CMAES is initiated inside FA loop and an extra loop is avoided and at the same time CMAES diversifies FA solutions. The structure of algorithm together with the strength of individual solution are used. The newly established modified FA and hybrid are used to solve selected sixty five global optimization benchmark problems together with eight real-world problems from CEC 2011. The proposed algorithms have outperformed FA algorithm in both benchmark and real-world problems. The optimal solutions found by FA in benchmark problems was 69.2% while FA-Step algorithm achieved 73.9% and FA-CMAES algorithm obtained 92.3%. In real-world problem, FA obtained 37.5%, FA-Step was 50% while FA-CMAES was 75%. The results invariably show that the proposed algorithms perform significantly better than the standalone methods as well as the algorithms from the literature.

A self-adaptive strategy based firefly algorithm for constrained engineering design problems

Firefly algorithm (FA) is an effective meta-heuristic method, which has drawn extensive attentions and inspired many variants. However, it is difficult to balance the relation of the exploration and exploitation of FA. To this end, FA with self-adaptive strategy (SAFA) is proposed to improve the performance of the algorithm for constrained engineering design problems. Firstly, the characteristics of the standard FA are analyzed, and the essence of FA easily trapped into the local optima is revealed by theory analysis and case study. Secondly, a self-adaptive strategy for attraction model is proposed to improve the exploitation ability, and another self-adaptive strategy for stochastic model is developed to ensure a better balance between the exploration and exploitation. Thirdly, a self-adaptive penalty function is presented to treat constraint conditions. Then, the initial parameter setting is investigated, and the proper initial parameter value corresponding to the optimal performance of SAFA is obtained. And then, SAFA and other FA variants are used to optimize a set of classical and Congress on Evolutionary Computation (CEC) 2015 benchmark functions. Meanwhile, the contributions of self-adaptive strategies for attraction model and stochastic model are investigated with experimental analysis, respectively Finally, SAFA and other meta-heuristic methods are employed to solve constrained engineering design problems. The effects of SAFA with standard and self-adaptive penalty function are compared. Numerical experimental results show that self-adaptive strategies for attraction model and stochastic model improve the performance of FA, and SAFA obtains the best solutions on most of the benchmark functions. In addition, SAFA has the advantage in solving problems with different kind of dimensions, and maintains reasonable population diversity throughout the iteration compared with the other FA variants. Meanwhile, SAFA can reduce the computational complexity and ensure the solution accuracy in solving constrained optimization problems.

Performance evaluation of firefly algorithm with unconstrained optimization issues

In this paper, we have investigated a new spectral Quasi-Newton (QN) algorithm. New search directions of the proposed algorithm increase its stability and increase the arrival to the optimum solution with a lowest cost value and our numerical applications on the standard Firefly Algorithm (FA)and the new proposed algorithm are powerful as in meta-heuristic field. Our new proposed algorithm has quite common uses in several sciences and engineering problems. Finally, our numerical results show that the proposed technique is the best and its accuracy higher than the accuracy of the standard FA. These numerical results are compared using statistical analysis to evaluate the efficiency and the robustness of new proposed algorithm.

Printed Circuit Board Assembly Planning for Multi-Head Gantry SMT Machine Using Multi-Swarm and Discrete Firefly Algorithm

This research proposes a Multi-swarm and Discrete Firefly Algorithm (MDFA) to deal with the component sequencing problem (CSP) and feeder assignment problem (FAP) simultaneously for a multi-head gantry surface-mounted technology (SMT) machine. The MDFA is an improved version of standard Firefly Algorithm (FA) which is a kind of nature-inspired and population-based metaheuristic. To our best knowledge, the FA has never been used to deal with the CSP and FAP simultaneously for the multi-head gantry SMT machine. Empowered by novel features such as multiple swarms as well as adaptive and discrete moving step, in addition to using an exploration-to-exploitation strategy, the MDFA is found capable of searching a solution space effectively. To investigate its effectiveness, the MDFA has been compared to the standard FA, particle swarm optimization (PSO), and genetic algorithm (GA). The experimental results show that the MDFA outperforms the others in terms of assembly time.

Globalized firefly algorithm and chaos for designing substitution box

This study adopted a metaheuristic approach based on the firefly algorithm (FA) optimization to generate an appropriate configuration for an 8 × 8 Substitution boxes (S-boxes). The FA can construct a strong S-box that satisfies the stipulated criteria by rapidly searching for the optimal or near-optimal feature subsets that minimize a given fitness function. The FA is a newly developed computation technique inspired by fireflies and their flash lighting process. However, FA may suffer from premature convergence when solving optimization problems. This study proposes a new FA modification, namely, globalized firefly algorithm (GFA), which employs random movement based on the best firefly using chaotic maps. The best firefly does not conduct any search in the standard firefly algorithm (SFA). The proposed algorithm utilizes a new design for retrieving strong S-boxes based on SFA and GFA.Bijectivity, strict avalanche criteria, nonlinearity, input/output XOR distribution, bit independence criteria, and linear probability were also analyzed. The result was compared with a few previous S-box generation methods. Overall, the experimental outcome revealed that the design of the proposed S-boxes has satisfactory cryptographic characteristics.

A hybrid approach of firefly and genetic algorithm for solving optimisation problems

Firefly algorithm (FA) is a newly developed nature-inspired, metaheuristic, stochastic algorithm that has seen many applications in solving problems of optimisation nature since its introduction just a couple of years ago. FA is a simple, flexible, easily implementable and robust approach inspired from natural phenomenon of light emission by fireflies but a major drawback associated with FA is the random initial solution set generation that degrade the solution quality. In this work, the targeted issue has been resolved by introducing genetic algorithm (GA) operators namely selection, mutation and cross over operators during initial solution set generation for standard FA. The proposed technique has been applied to few standard benchmark minimisation and maximisation functions and the results have been compared with standard FA and GA. A significant amount of improvement in the convergence rate can be observed that results in high quality solution for solving optimisation problems.

A novel hybrid optimization approach for reactive power dispatch problem considering voltage stability index

This paper proposes a novel, reliable, and effective hybrid approach based on the integration of the firefly algorithm (FA) and the adaptive particularly tunable fuzzy particle swarm optimization (APT-FPSO) method to address reactive power dispatch (RPD) problem, a crucial optimization problem in the operation of power systems. Similar to many other original meta-heuristic optimization techniques, the standard FA suffers from some severe drawbacks, most importantly being easily trapped into a locally optimal solution. In order to tackle these difficulties, in the current study, an improved version of fuzzy-based particle swarm optimization is utilized in the internal structure of the original FA. The developed hybrid approach, which is capable of avoiding premature convergence of the original FA by enhancing exploration and exploitation procedures, is employed to determine the optimum control variables (i.e., the voltage of generation buses, tap positions of tap-changer transformers, and reactive power output of shunt compensators) through optimizing three distinct objective functions consisting of total transmission real power loss, the voltage magnitude deviations as well as voltage stability index. To validate the accuracy and competency of the proposed hybrid approach, it is firstly used for solving several benchmark optimization functions and then applied to three test systems at different scales, consisting of IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus power systems, for solving the RPD problem. Eventually, the results of the presented hybrid method will be compared to those obtained by other implemented swarm intelligence-based approaches. The statistical analysis of this research substantiates the robustness and effectiveness of the developed algorithm to handle sophisticated optimization problems, particularly the RPD problem.