International Electrical Engineering Journal (IEEJ) Vol. 6 (2015) No.7, pp. 1945-1952 ISSN 2078-2365 http://www.ieejournal.com/
The Firefly Meta-Heuristic Algorithms: Developments and Applications A. Y. Abdelaziz1, S. F. Mekhamer2, M.A.L. Badr3, M. A. Algabalawy4 1, 2, 3
Electrical Power and Machines Department, Ain Shams University, Abbassia, Cairo, Egypt 4
Electrical Maintenance Engineer, General Motors Egypt 1
[email protected] 2 3
[email protected] [email protected] 4
[email protected]
Abstract—The global solution becomes the dream of the researchers, who are interested in optimization techniques. They believe that, the global solution will provide the optimum conditions for the operation. Operations research is the main umbrella for the optimization techniques that study the shortest and critical path to achieve the activities of a project. Thus, the researchers concern the optimization techniques development; especially the meta-heuristic techniques. Researchers aim to obtain the techniques that provide the global solution with minimum time of operation. Firefly algorithm (FA) has been considered one of the meta-heuristic techniques developed to solve the optimization problems using the simulation of the behavior of the fireflies. Much searches prove the high accuracy and quality of the results of the optimization techniques solved by the FA. This paper analyses and summarizes most of these developments and applications. This paper gives a literature survey for different combinations of HPGS that consist of different combinations of PV, WT, SB MT, diesel generator, and Fuel Cell. Index Terms -Operations research, optimization techniques, meta-heuristic techniques, optimization problems, firefly algorithms
I. INTRODUCTION Most optimization problems in engineering are nonlinear with many constraints. These constraints are classified into linear and nonlinear. In general, optimization algorithms can be classified into two main categories: deterministic and stochastic. Deterministic algorithms produce the same set of solutions if the iterations start with the same initial guess. On the other hand, stochastic algorithms often produce
different solutions even with the same initial starting point. However, the results, though slightly different, will usually converge to the same optimal solutions within a given accuracy. Deterministic algorithms are almost local search algorithms. They are quite efficient in finding local optimal point. However, there is a risk for the algorithms to be trapped at local optimal points, while the global optimal points are out of reach. A common practice is to introduce some stochastic component to an algorithm so that it becomes possible to jump out of such locality. Stochastic algorithms often have a deterministic component and a random component. The stochastic component can take many forms such as simple randomization by randomly sampling the search space or by random walks. Most stochastic algorithms can be considered as meta-heuristic. Good examples of them are genetic algorithms (GA) and particle swarm optimization (PSO). Many modern metheuristic algorithms had been developed based, in nature, on the swarm intelligence. New modern meta-heuristic algorithms are being developed and begin to show their power and efficiency. For example, the Firefly algorithm (FA) that is developed and show superiority over some traditional algorithms [1, 2]. This paper shows the initiating process of the Firefly algorithm (FA), and how the researchers simulate the behavior of the fireflies to solve the optimization problems. In addition, it shows the modifications of this algorithm. A Literature survey has been carried out in this paper to show the benefits and applications of using this algorithm. The technique applications in various fields are studied to show the algorithm flexibility and superiority in many fields.
1945 Abdelaziz et. al.,
The Firefly Meta-Heuristic Algorithms: Developments and Applications
International Electrical Engineering Journal (IEEJ) Vol. 6 (2015) No.7, pp. 1945-1952 ISSN 2078-2365 http://www.ieejournal.com/ II. FIREFLY ALGORITHM [1, 2] The Firefly Algorithm is based on the idealized behavior of the flashing characteristics of fireflies. These flashing characteristics can be presented as the following three rules: 1- All fireflies are unisex so that one firefly is attracted to other fireflies regardless of their sex; 2- Attractiveness is proportional to their brightness, thus for any two flashing fireflies, the less bright one will move towards the brighter one. The attractiveness is proportional to the brightness and they both decrease as their distance increases. If no one is brighter than a particular firefly, it moves randomly; 3- The brightness or light intensity of a firefly is affected or determined by the landscape of the objective function to be optimized. For a maximization problem, the brightness can simply be proportional to the objective function. Other forms of brightness can be defined in a similar way to the fitness function in genetic algorithms or the bacterial foraging algorithm (BFA). In the FA, there are two important issues: the variation of light intensity and formulation of the attractiveness. For simplicity, it is assumed that, the attractiveness of a firefly is determined by its brightness or light intensity which in turn is associated with the encoded objective function. For maximum optimization problems, the brightness 𝐼of a firefly at a particular location 𝑋 can be chosen as 𝐼(𝑥) ∝ 𝑓(𝑥). However, the attractiveness 𝛽 is relative; it should be seen in the eyes of the beholder or judged by the other fireflies. Thus, it should vary with the distance 𝑟𝑖𝑗 between firefly 𝑖and firefly 𝑗. As light intensity decreases with the distance from its source and light is also absorbed in the media, the attractiveness to vary with the degree of absorption. In the simplest form, the light intensity𝐼(𝑥) varies with the distance 𝑟monotonically and exponentially as in equation 1. 𝐼 = 𝐼0 𝑒 −𝛾𝑟 (1) where, 𝐼0 is the original light intensity 𝛾is the light absorption coefficient The firefly’s attractiveness is proportional to the light intensity seen by adjacent fireflies. The attractiveness 𝛽of a firefly is defined as 2 𝛽 = 𝛽0 𝑒 −𝛾𝑟 (2) where, 𝛽0 is the attractiveness at 𝑟 = 0 It is worth pointing out that the exponent 𝛾𝑟 can be replaced by other functions such as 𝛾𝑟 𝑚 , when 𝑚 > 0. The Firefly Algorithm (FA) may be summarized in thefollowing pseudo code: The objective function 𝑓(𝑥), 𝑋 = (𝑥1 , 𝑥2 , … . . , 𝑥𝑑 )𝑇 Initialize a population of Firefly 𝑋𝑖 (𝑖 = 1,2, … … 𝑛) Define light absorption coefficient 𝛾 While (𝑡 < 𝑀𝑎𝑥𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛) for𝑖 = 1: 𝑛 all 𝑛 fireflies
for𝑗 = 1: 𝑖 all 𝑛 fireflies Light intensity 𝐼𝑖 at 𝑥𝑖 is determined by 𝑓(𝑥𝑖 ) if (𝐼𝑗 < 𝐼𝑖 ) Move firefly 𝑖 towards 𝑗 in all 𝑑 dimensions end if Attractiveness varies with distance 𝑟 via 𝑒 −𝛾𝑟 Evaluate new solutions and update light intensity end for 𝑗 end for 𝑖 Rank the fireflies and find the current best end while Post process results and visualization The distance between any two fireflies 𝑖 and 𝑗 is 2
𝑟𝑖𝑗 = √∑𝑛𝑘=1(𝑥𝑖,𝑘 − 𝑥𝑗,𝑘 ) (3) where, 𝑥𝑖,𝑘 is the 𝑘 𝑡ℎ component of the 𝑖 𝑡ℎ firefly The movement of a firefly 𝑖 is attracted to another more attractive (brighter) firefly 𝑗is determined as 1 𝑥𝑖 = (1 − 𝛽𝑖,𝑗 ). 𝑥𝑖 + 𝛽𝑖,𝑗 𝑥𝑗 + 𝛼(𝑟𝑎𝑛𝑑 − )(4) 2 where, the first and second terms are due to the attraction while the third term is randomization with α being the randomization parameter and “rand” is a generator of random numbers uniformly distributed in [0, 1].
III. MODIFIED FIREFLY ALGORITHM [3, 4] In many Meta heuristic optimization algorithms there exists a kind of memory, which transfers some information from iteration to the other. For example, in the PSO a memory is defined to retain the best particle and the global best positions. This information is then used in the next iteration for updating the particles. In addition, in the genetic algorithm the offspring inherit the genes from its parents and then transfer them to the next generation via crossover operator. Unfortunately, the traditional FA suffers from lack of memory and no specific information is transferred from iteration to the other. For further explanation, consider a firefly, which reaches to an optimum or near optimum point in one iteration. This firefly will participate in the updating process to generate the next population. It will attract other fireflies but it has no more chance to do this in successive iterations because the position of this firefly will also be changed and its information lost. To overcome this point, it is necessary to allow some information of high rank fireflies to be transferred to the next iteration. In the current work, two approaches are discussed, and described as follows: 1- In the first approach, each iteration scores a number of the high rank fireflies (𝑚1 ), which are directly transferred to the next iteration without any change in their position. It has been occurred, if the updating operator is not applied on the first 𝑚1 high rank fireflies for each iteration, and therefore 1946
Abdelaziz et. al.,
The Firefly Meta-Heuristic Algorithms: Developments and Applications
International Electrical Engineering Journal (IEEJ) Vol. 6 (2015) No.7, pp. 1945-1952 ISSN 2078-2365 http://www.ieejournal.com/ the rest of them (𝑛 − 𝑚1 fireflies) participate in the updating process. 2- In the second approach, each iteration scores a number of low rank fireflies (𝑚2 ), which are removed from the population and replaced by equal numbers of high rank fireflies from the previous iteration. It has been occurred, if the mentioned iteration has a copy of 𝑚2 high rank fireflies stored and in the next iteration. The updating operator applies only to the first 𝑛 − 𝑚2 fireflies and the 𝑚2 low rank fireflies are replaced with the 𝑚2 high rank fireflies stored in the previous iteration. The updating formula of the original FA will be presented in Equation 5. It changes the position of each firefly towards all of the brighter fireflies in a stepwise manner regardless of the objective function of this firefly in these steps. Figure 1 schematically represents the updating path of a firefly in a two dimensional search space with 11 fireflies. In this figure, as in the original FA, the fireflies are sorted according to their objective functions. For example, the fireflies 1 to 5 are brighter that the firefly 6. As it is shown, using Equation 5, the firefly 6 changes its position repetitively toward the fireflies 1 to 5 and eventually reaches its final position. Therefore, relocation of this firefly is based on its objective at its initial position. As it is shown schematically in Figure 1, it seems that this firefly is wandering and follows a zigzag updating path. This behavior of the original FA decreases overall performance of the algorithm.
𝑃𝑖 is the representative point that, shows the overall distribution of the brighter fireflies and its equation is: 1
∑𝑖−1 𝑥 (6) 𝑃𝑖 = 𝑖−1 𝑠=1 𝑠 𝛼is the randomization parameter with, 0 < 𝛼 < 1 𝜀 is the vector of random numbers Based on the modifications described in the foregoing sections, a pseudo code is prepared and shown as follows: Define the upper bound U and lower bound L for the design variables Generate an initial population of fireflies 𝑥𝑖 (i=1 to n) Evaluate the response function 𝐹𝑖 for each firefly 𝑥𝑖 Sort the fireflies based on their response function for t=1 to Maximum iteration 𝑥𝑖 =𝑦𝑖 (i=1 to n) for i=𝑚1 to 𝑛 − 𝑚1 -k p=average of coordinates of fireflies that are brighter than xi r=norm(𝑥𝑖 -p) 2 𝛽 = 𝛽0 𝑒 −𝛾𝑟 𝜀 = (𝑟𝑎𝑛𝑑 − 0.5) × (𝑈 − 𝐿) 𝑥𝑖 = 𝑥𝑖 + 𝛽(𝑃𝑖 − 𝑥𝑖 ) + 𝛼𝜀 next𝑖 end Check the side constraints for firefly 𝑥𝑖 for𝑖 = 𝑛 − 𝑚2 − 𝑘 + 1 to 𝑛 − 𝑘 𝑥𝑖 = 𝑦𝑖−𝑛+𝑚2+𝑘 next𝑖 end for𝑖 = 𝑛 − 𝑘 + 1 to 𝑛 𝑥𝑖 = 𝐿 + 𝑟𝑎𝑛𝑑(𝑈 − 𝐿) next𝑖 end Evaluate the response function 𝐹𝑖 only for the updated fireflies Sort the fireflies based on their response function Present the first firefly as the best solution obtained in this iteration next𝑡 end
Fig. 1 Firefly updated path compared with original Firefly algorithm.
Wherethe triangle shows position of a firefly whose updating path is drawn. And the solid circles are brighter fireflies and the hollow circles are the rest of them. The approach shows that, the moving of each firefly toward the brighter ones in a stepwise manner, a representative point which shows the overall distribution of the brighter fireflies is defined at first and then the firefly moves toward this point in only one step. 𝑥𝑖 = 𝛽(𝑃𝑖 − 𝑥𝑖 ) + 𝛼𝜀(5) where,
IV. LITERATURE SURVEY OF THE FIREFLY ALGORITHM APPLICATIONS In this section, a literature review has been carried out to show some electrical engineering applications using the Firefly algorithm. Many researchers use this algorithm because of its accuracy and superiority. Comparisons with other optimization techniques have been made to prove its flexibility and less time required. T. Apostolopoulos and A. Vlachos, reference [5], present and test the recently developed Firefly algorithm for application to the multi-objective minimization problem of 1947
Abdelaziz et. al.,
The Firefly Meta-Heuristic Algorithms: Developments and Applications
International Electrical Engineering Journal (IEEJ) Vol. 6 (2015) No.7, pp. 1945-1952 ISSN 2078-2365 http://www.ieejournal.com/ economic emissions load dispatch. They show that, the implementation of this method clearly give the efficiency and effectiveness of the technique for solving the particular optimization problem and can find the true Pareto optimal solutions. The algorithm achieved good results comparable to those achieved by other stochastic nature-inspired algorithms reported in the literature. In reference [6], K. Chandrasekaran and P. S. Simon propose a binary real coded firefly (BRCFF) algorithm based on the flashing behavior of fireflies proposed for solving network and reliability constrained unit commitment (UC) problem. In the first stage of the UC problem, the reliability constrained UC solved using proposed binary coded firefly algorithm without satisfying network security constraints. They use the real coded firefly algorithm in the second stage of the problem to solve optimal power flow (OPF) to determine whether a converged and secure ac power flow can be obtained. Both stages of the algorithm incorporate repair strategies and searche for a better solution. Reliability of the system recognized by loss of load probability (LOLP) index. The results of the proposed technique show the effect of the control parameters on the performance of firefly algorithm for the studied UC problem. In reference [7], M. H. Sulaiman, M. W. Mustafa, A. Azmi, O. Aliman, and S. R. Abdul Rahim present an application of Firefly Algorithm (FA) in determining the optimal location and size of Distributed Generation (DG) in distribution power networks. IEEE 69-bus distribution test system has been used to show the effectiveness of the FA. A Comparison with another method is also given to see the performance of FA where it is as good as GA in solving the optimal allocation problem. In reference [8], S. Merkel, C. Werner, and B. H. Schmeck introduce the firefly algorithm to calculate hop counts and, thereby, derive distances between devices. This algorithm is based on synchronization of all devices in the mobile ad hoc networks (MANET). They show that an intentional phase shift of a periodically sent signal allows estimating the distance between all devices in a network and a specific reference device. In addition, this approach significantly reduces the communication overhead leading to a more resource-efficient operation of the communication module and, thus, potentially extending the lifetime of the mobile devices. They perform many experiments to demonstrate that a network with an average of ten devices within communication range can be synchronized using the FA. Finally, they show that their results have a higher accuracy compared to some other algorithms that are based on asynchronous exchange of messages. In reference [9], K. Naidua, H. Mokhlisa, and A. H. A. Bakarb apply the firefly algorithm (FA) to the problem of
load frequency control (LFC) in the interconnected reheat thermal power system. They investigate the efficiency and robustness of the FA as an optimization technique for a PID controller under three different loading scenarios. Investigation is carried out by comparing the performance of FA based PID against a conventional one. They show that the FA based PID give results better than those of the conventional PID controller, where their controller optimization is able to find the optimal gains for the LFC. The results indicate that the FA is robust and has a good tuning capability. In reference [10], R. Subramanian and K. Thanushkodi present an efficient and reliable Firefly Algorithm (FA), for solving the ED Problem. The main objective is to minimize the total fuel cost of the generating units having quadratic cost characteristics subjected to limits on generator true power output and transmission losses. In addition, they show the superiority of the FA results compared with the application of FA to those using the simulated annealing (SA), genetic algorithm (GA), differential evolution (DE), particle swarm optimization (PSO), artificial bee colony optimization (ABC), and biogeography-based optimization (BBO) optimization techniques. K. Nadhir, D. Chabane, and B. Tarek, reference [11], apply the Firefly Algorithm (FA) to minimize power losses caused by high current and improve the voltage profile in the distribution network. They suggest installing distributed generation (DG) units for the distribution network. This installation performed with the goal of obtaining the optimal sizing and placement of DGs in the system. FA has been applied to solve this combinatorial problem. They have used some known models; IEEE69-bus and IEEE33-bus test systems to evaluate the algorithm effectiveness. In addition, they compare results with those obtained by genetic algorithm (GA) and shuffled frog leaping algorithm (SFLA) to prove the effectiveness of FA. In reference, [12], D. R. Prabha, A. K. Prasad, R. S. Saikumar, R. Mageshvaran, and T. N. Babu apply the Bacterial Foraging Optimization Algorithm (BFOA) and Firefly Algorithms (FA) to solve the Economic Load Dispatch (ED) problem for three-generator system and thirteen generator system with both inclusion and omission of valve point loading. The obtained results compared with other algorithms in order to show the ability of this algorithm to solve efficiently the non-linear ED issues. S. J. Huang, X. Z. Liu, W. F. Su, and S. H. Yang, [13], present a hybrid firefly algorithm (HFA) to assist in decision-making for reactor arrangement in underground cable transmission systems. The HFA shown method is based on the analysis of photo taxis behavior of fireflies, and enables solving the optimization problem effectively. Their study has been applied to determine the appropriate reactor placement in an underground transmission system. They 1948
Abdelaziz et. al.,
The Firefly Meta-Heuristic Algorithms: Developments and Applications
International Electrical Engineering Journal (IEEJ) Vol. 6 (2015) No.7, pp. 1945-1952 ISSN 2078-2365 http://www.ieejournal.com/ show that, through the tests made on different transmission lines along with the results compared to other methods, their approach provides satisfactory decision support for reactor placement and serves as a beneficial reference for underground transmission planning and design. In reference [14], K. Thenmalar and A. Allirani apply the Firefly Algorithm (FA) to the economic dispatch problem for three-generator system, six-generator system, and twelve-generator system with emission constraints. They apply other techniques such as artificial colony algorithm (ABC), particle swarm optimization algorithm (PSO), simulated annealing algorithm (SA) to compare the obtained results with those obtained by FA to show that it is capable of yielding good optimal solutions with proper selection of control parameters. The result also shows that the solution method is practical and valid for real time applications. In reference [15], G. Kannan and N. Karthik apply the Firefly Algorithm to solve the Economic load dispatch problem. They propose algorithm utilized firefly’s food searching mechanism to optimize economic load dispatch problem in power system. They apply this algorithm in testing of the 6-bus, IEEE-14 bus and IEEE-30 bus systems with several heuristic load patterns in order to demonstrate the effectiveness of it. The numerical results reveal that the algorithm can provide appreciably better solutions within reasonable time. In reference [16], H. Shareef, A.A. Ibrahim, N. Salman, A. Mohamed, and W. Ling Ai present a method to improve the power quality (PQ) and reliability of distribution systems by employing optimal network reconfiguration (NR). Optimal NR is applied independently to a system in a specified period to minimize the number of propagated voltage sags (𝑁𝑠𝑎𝑔 ) and other reliability indexes such as the average system interruption frequency index, sustained average interruption frequency index, and momentary average interruption frequency index. The quantum-inspired binary firefly algorithm (QBFA) has been used to find the optimal NR. Case studies are conducted using other objective functions, and reliability assessment performed to observe the reliability improvement caused by the new network topology. Simulation results show that their optimum NR effectively enhances system reliability level and PQ. In reference [17], L. Jebaraj, C. Rajan, and K. Sriram propose an application of firefly based algorithm (FA), extended voltage stability margin and minimization of active (or) real power loss incorporating Series-Shunt flexible AC transmission system (FACTS) controller named as static synchronous series compensator (SSSC) combined with static VAR compensator (SVC). They utilize a circuit model of SSSC and variable model of SVC to control the line power flows and bus voltage magnitudes. The line quality
proximity index (LQP) has been used to assess the voltage stability of a power system. They apply their algorithm to improve the values of voltage profile, minimize real power loss, and find the optimal location and size of FACTS devices. IEEE 14- and 30-bus test systems are used to show the superiority of their technique. In reference [18], U. Singh and M. Rattan present the application of Firefly Algorithm for the design of thinned multiple concentric circular antenna arrays. The study aims to achieve an array of uniformly excited isotropic elements that will generate a pencil beam pattern in the vertical plane with minimum side lobe level (SLL). They apply this algorithm for two different cases for thinning of concentric circular (ring) arrays. The first case is with uniform interelement spacing fixed at 0.5λ or multiple and the second case is with optimum inter-element spacing or multiple. The thinning percentage of the array is kept equal to or more than 50% and the beam width is kept equal to or less than that of a fully populated, uniformly excited and 0.5λ spaced ring array of same number of elements and rings. They show that the obtained results compared with previous published results show the effectiveness of their approach. In reference [19], B.V. Rao and G.V. Kumar propose the Firefly algorithm (FA) to solve Optimal Power Flow problem in the presence of Static VAR Compensator (SVC). They show that the obtained results demonstrate the effectiveness and robustness of the proposed method with SVC in contingency analysis. Where, they test the FA using the 5-bus system and IEEE 30-bus system. Their results indicate that, with proposed Algorithm, the system collapse states can be avoided and power system security under network contingency has been improved. Moreover, by incorporating SVC in Firefly Algorithm, based Optimal Power Flow the system performance has been improved. They do a comparative study of the optimal power flow based on Firefly and Genetic Algorithm, where the results reflect the effectiveness of the proposed approach. The obtained results also show that, the SVC is the most effective shunt compensation device that can significantly increase the security of the power system. In reference [20], M.M. Othman, W. El-Khattam, A.Y. Abdelaziz, and Y.G. Hegazy apply the Firefly algorithm (FA) to determine the optimal location and the capacity of voltage controlled DG in order to achieve a planned power loss is proposed. The DG in the proposed algorithm is modeled as voltage controlled (PV) bus with the flexibility to be converted to constant power (PQ) bus in case of reactive power limit violation. They examine this method on the IEEE 37-bus test system. They compare the obtained results from the proposed algorithm with the results, which obtained from other optimization techniques.
1949 Abdelaziz et. al.,
The Firefly Meta-Heuristic Algorithms: Developments and Applications
International Electrical Engineering Journal (IEEJ) Vol. 6 (2015) No.7, pp. 1945-1952 ISSN 2078-2365 http://www.ieejournal.com/ In reference [21], S. U. R. Massana, A. I. Waganb, M. M. Shaikh, and R. Abrod calculate the total energy capacity of a given wind farm by using the Firefly Algorithm and compare it with the past approach using the genetic algorithm. They show that, the results obtained by the firefly approach are more optimal and yield a lower cost per unit power than using other mentioned approaches.
V. LITERATURE SURVEY OF APPLICATIONS CARRIED OUT USING MODIFIED FIREFLY ALGORITHM In this section, a literature review has been done to show the effectiveness of the modifications made to the Firefly algorithm. I. M. S. Oliveira and R. Schirru [22], study the problem of the Nuclear Reactor Reload Problem (NRRP). This problem is related with the periodic operation of replacing part of the fuel of a nuclear reactor. They introduce a case study lasts for more than 40 years. The optimization problem of the NRRP remains a challenge for many optimization techniques due to its multiple objectives concerning economics, safety and reactor physics calculations. In addition, the characteristics of non-linearity, multi-modality and high dimensionality make the NRRP a very complex optimization problem. They define the primary goal as to design fuel Loading Patterns (LPs) so that the core produces the required energy output in an economical way, without violating safety limits. Since multiple feasible solutions can be obtained to this problem, therefore, they present a contribution in this area and introduce a modified Firefly Algorithm (FA) to perform LPs optimization for a Pressurized Water Reactor (PWR). The experiments performed and the comparisons with some other optimization techniques show the effectiveness of applying the MFA. G. Wang, L.Guo, H.Duan, L. Liu, and H. Wang [23], use the modified firefly algorithm (MFA) to solve the uninhabited combat air vehicle UCAV path planning problem. They state that, their approach can accelerate the global convergence speed while preserving the strong robustness of the basic FA. They prove the effectiveness of MFA performance by comparing it with FA and other population-based optimization methods, such as, ACO, BBO, DE, ES, GA, PBIL, PSO and SGA. Their work shows that the approach is more effective and feasible in UCAV path planning than the other model. T. Niknam, R. A. Abarghooee, and A. Roosta [24], present the self-adaptive modified firefly algorithm to solve the reserve constrained dynamic economic dispatch that considers highly realistic constraints, such as transmission losses, ramp rate limits, and valve-point effects over a shortterm time span. They show that, their used technique is
suitable from an economic aspect view, and is appropriate for high-speed real-time application due to fast and less execution time. Small, medium, and large test systems presented as case studies in order to evaluate the efficiency and feasibility of their proposed framework in practical power systems. M. H. Sulaiman, H. Daniyal, and M. W. Mustafa, [25], present a modified Firefly Algorithm (MFA) for solving economic dispatch (ED) problems as one of the most challenging problems of power system since it is difficult to determine the optimum generation scheduling to meet the particular load demand with the minimum fuel costs while all constraints are satisfied. The practical ED problems which are involving objective functions with quality and inequality constraints including the practical operation constraints of generators such as ramp rate limit, prohibited operating zones and generation limits make it harder to find the global optimum results of ED. To demonstrate the effectiveness and feasibility of MFA in solving ED, two ED test systems with non-convex solution features have been tested and compared with those solved by other techniques. The results show that MFA is able to find more economical solution than those determined by other methods. M. Shafaatiand and H.Mojallali [26], introduce the modification of the Firefly algorithm to develop the learning rule for identification of three benchmark infinite impulse response (IIR) and nonlinear plants. IIR models, due to their reduced number of parameters and better performance, are preferred over finite impulse response (FIR) systems. MFA’s performance is compared with standard firefly algorithm (FA), GA and three versions of PSO. The results demonstrate that MFA is superior in identifying dynamical systems. J Olamaei, M Moradi, and T Kaboodi [27], use the Firefly Algorithm (FA) to handle the optimal capacitor placement problem suitably. A sufficient two-phase modification technique is introduced to improve the total search ability of the algorithm effectively. The objective function to be optimized is the total annually cost including the cost of power losses as well as the capacitor placement cost simultaneously. During the optimization process, several equality and inequality constraints should be considered. The 9-bus and 34-bus standard distribution test systems have been used to show the superiority and effectiveness of the examined method. A. K. Fard, H. Samet, and F.Marzbani [28], present a hybrid prediction algorithm comprised of Support Vector Regression (SVR) and Modified Firefly Algorithm (MFA) to provide the short-term electrical load forecast. The SVR models utilize the nonlinear mapping feature to deal with nonlinear regressions. However, such models suffer from a methodical algorithm for obtaining the appropriate model 1950
Abdelaziz et. al.,
The Firefly Meta-Heuristic Algorithms: Developments and Applications
International Electrical Engineering Journal (IEEJ) Vol. 6 (2015) No.7, pp. 1945-1952 ISSN 2078-2365 http://www.ieejournal.com/ parameters. Therefore, in their proposed method the MFA is employed to obtain the SVR parameters accurately and effectively. In order to evaluate the efficiency of the proposed methodology, it is applied to the electrical load demand in Fars, Iran. The obtained results are compared with those obtained from, artificial neural network (ANN), SVR-GA, SVR-PSO and SVR-FA. The extracted results affirm that the algorithm outperforms other techniques. S. Gholizadeh [29], presents a modified firefly algorithm (MFA) to obtain the optimum seismic design of the of steel moment frames. To illustrate the effectiveness of his methodology, he tests the proposed method for many different cases; 3, 6 and 12 planar steel moment. The results demonstrate the effectiveness of the proposed soft computing based methodology for the seismic design of steel structures spending low computational cost. A. Y. Abdelaziz, Y. G. Hegazy, W. El-Khattam and M. M. Othman [30] present an algorithm for optimal planning of a distributed generator connected to the distribution networks. They modify the traditional firefly method to be able to deal with the practically constrained optimization problems by proposing formulas for tuning the algorithm parameters and updating equations. The optimal location and size of the distributed generation units have been determined in order to minimize the system power loss without violating the system practical constraints using the proposed algorithm rigidly determines. Moreover, the optimal distributed generator location and minimum size for achieving a certain specified power loss are determined using the proposed method. They compare the obtained results from the proposed algorithm with the results, which obtained from other optimization techniques. The distributed generation units in the proposed algorithms are modeled as voltage controlled nodes with the flexibility to be converted to constant power nodes in the case of reactive power limit violation. They verify the effectiveness of the proposed algorithms through implementing it on the IEEE 33-bus and the IEEE 37-nodes feeder. The results that are via comparison with published results obtained from other competing methods show the effectiveness, accuracy, and speed of the proposed method.
modifications, carried out by many searches are discussed and reviewed to show how close this technique to provide the optimal solution. It is clear from the existing literature that the FA meta-heuristic technique, is challenging and still needs further research.
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VI. CONCLUSION The global solution of the optimization problems such as cost function, economic dispatch, and unit commitment problems is the dream of the scientists and researchers. Modern optimization techniques have been initiated and modified to achieve this dream. Therefore, meta-heuristic techniques including the Firefly algorithm are created. In this paper, the FA accompanied with its different modifications have been studied. Applications, using the FA and its
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