Firefly Algorithm for optimization problems with non-continuous variables: A Review and Analysis
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paper_title: INTEGRATING FUZZY PREFERENCE IN GENETIC ALGORITHM TO SOLVE MULTIOBJECTIVE OPTIMIZATION PROBLEMS

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Population based solution methods have become more common in solving multiobjective optimization problems. These methods overcome the limitation of classical methods of finding a single solution with a single run of the algorithms. The studies of incorporating the decision maker's preference to genetic algorithm had done so far use binary importance comparison of objectives, which lacks uniformity. This study shows how to incorporate the fuzzy preference of a decision maker in evolutionary algorithm so that the solutions will zoom to the region in which the preference of the decision maker lies. Cumulative fuzzy tradeoffs are expressed using an appropriate probability distribution function which agrees with the fuzzy membership function. It will then be incorporated in the fitness evaluation stage of genetic algorithm. From the simulation result on selected test functions and comparing this with previous studies, it is shown that incorporating the decision maker's fuzzy preference will give solutions which satisfy the decision maker's preference better.
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paper_title: Chemical process optimization using Newton-like methods

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Various interrelated issues that effect the reliability and efficiency of Newton-like methods for chemical process optimization are studied. An algorithm for solving large, sparse quadratic programming (QP) problems that is based on an active set strategy and a symmetric, indefinite factorization is presented. The QP algorithm is fast and reliable. A simple asymmetric trust region method is proposed for improving the reliability of successive QP methods. Ill-defined QP subproblems are avoided by adjusting the size of the trust region in an automatic way. Finally, it is shown that reliable initial values of the unknown variables and multipliers can be generated automatically using generic problem information, short-cut techniques and simulation tools. Many relevant numerical results and illustrations are presented.
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paper_title: Fuzzy preference of multiple decision-makers in solving multi- objective optimisation problems using genetic algorithm

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Most real-life optimisation problems involve multiple objective functions. Finding a solution that satisfies the decision-maker is very difficult owing to conflict between the objectives. Furthermore, the solution depends on the decision-maker's preference. Metaheuristic solution methods have become common tools to solve these problems. The task of obtaining solutions that take account of a decision-maker's preference is at the forefront of current research. It is also possible to have multiple decision-makers with different preferences and with different decision-making powers. It may not be easy to express a preference using crisp numbers. In this study, the preferences of multiple decision-makers were simulated and a solution based on a genetic algorithm was developed to solve multi-objective optimisation problems. The preferences were collected as fuzzy conditional trade-offs and they were updated while running the algorithm interactively with the decision-makers. The proposed method was tested using well-known benchmark problems. The solutions were found to converge around the Pareto front of the problems.
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paper_title: Bus Timetabling as a Fuzzy Multiobjective Optimization Problem Using Preference-based Genetic Algorithm

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Transportation plays a vital role in the development of a country and the car is the most commonly used means. However, in third world countries long waiting time for public buses is a common problem, especially when people need to switch buses. The problem becomes critical when one considers buses joining different villages and cities. Theoretically this problem can be solved by assigning more buses on the route, which is not possible due to economical problem. Another option is to schedule the buses so that customers who want to switch buses at junction cities need not have to wait long. This paper discusses how to model single frequency routes bus timetabling as a fuzzy multiobjective optimization problem and how to solve it using preference-based genetic algorithm by assigning appropriate fuzzy preference to the need of the customers. The idea will be elaborated with an example.
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paper_title: Nature-Inspired Metaheuristic Algorithms

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Modern metaheuristic algorithms such as bee algorithms and harmony search start to demonstrate their power in dealing with tough optimization problems and even NP-hard problems. This book reviews and introduces the state-of-the-art nature-inspired metaheuristic algorithms in optimization, including genetic algorithms, bee algorithms, particle swarm optimization, simulated annealing, ant colony optimization, harmony search, and firefly algorithms. We also briefly introduce the photosynthetic algorithm, the enzyme algorithm, and Tabu search. Worked examples with implementation have been used to show how each algorithm works. This book is thus an ideal textbook for an undergraduate and/or graduate course. As some of the algorithms such as the harmony search and firefly algorithms are at the forefront of current research, this book can also serve as a reference book for researchers.
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paper_title: Modeling the expansion of Prosopis juliflora and determining its optimum utilization rate to control the invasion in Afar Regional State of Ethiopia

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Prosopis juliflora is as an alien invasive tree species which is expanding at an alarming rate in the Horn of Africa region. In this paper a mathematical model is developed to estimate the rate of expansion in the Afar region of Ethiopia based on the coverage obtained with GIS analysis from the year 2000 satellite image for the region. The exponential model estimates that the tree species has been expanding at a rate of 50,000 hectares per year in the last ten years in the Afar region. The model further projects, if the tree species is used for productive uses such as energy and consumed at a rate of 90,000 hectares per year, the invaded land can be restored effectively in 15 years time. Furthermore, the model proposes that after the end of the 15 year, Prosopis can be contained within 200,000 hectares and provide 26,000 hectares of wood per annum sustainably for productive uses.
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paper_title: Optimization of tourism impacts within protected areas by means of genetic algorithms

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Abstract The search for a balance between nature conservation and tourism development within protected areas is becoming an increasingly multifaceted problem worldwide, as outlined by an increasing number of authors and highlighted at several international events. Since it is unlikely that all management objectives will reach their optimum values simultaneously, an optimization approach is required to meet multiple, conflicting goals and to obtain an overall trade-off in terms of the conceived objectives. In this paper we propose a new model for optimizing the allocation of tourist infrastructures (refuges and camping sites), and apply it to a protected area in the European Alps, where tourism has grown considerably in recent years. To reach this goal, a complex model based on genetic algorithms was required (instead of a common multicriteria analysis) to obtain a complex interplay in the form of a dynamical simulation where candidate solutions are interactively evaluated. In accordance with local actors, we selected 18 quantifiable criteria encompassing all relevant tourist activities within the study area. These were translated into geographic information system (GIS) layers, submitted to a genetic optimization procedure and compared the performances of the optimized tourist allocations with those of existing infrastructures and with worst case scenarios. Resulting tourist allocations perform very well, while existing tourist sites behaved halfway between the fittest and the least fit genetic solutions, since they prioritized logistic and safety criteria rather than ecological ones. The proposed model is a very flexible and effective tool, easily exportable to any protected area, with implications for researchers and policymakers who aim to provide an effective balance between nature and human impact.
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paper_title: Optimization Techniques for Transportation Problems of Three Variables

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Transportation problem is considered a vitally important aspect that has been studied in a wide range of operations including research domains. As such, it has been used in simulation of several real life problems. Thus, optimizing transportation problem of variables has remarkably been significant to various disciplines. In this paper, three variables will be optimized to reduce transportation cost using four methods which will include: Northwest corner method, least cost method, Vogel method and modi method. This will mainly aim at finding the best and cheapest route on how supply will be used to satisfy demand at specific points. This will imply that, a variable cost of shipping products from suppliers to demand points will be considered.
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paper_title: Particle swarm optimization

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A concept for the optimization of nonlinear functions using particle swarm methodology is introduced. The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed. Benchmark testing of the paradigm is described, and applications, including nonlinear function optimization and neural network training, are proposed. The relationships between particle swarm optimization and both artificial life and genetic algorithms are described.
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paper_title: Nature-Inspired Metaheuristic Algorithms

paper_content:

Modern metaheuristic algorithms such as bee algorithms and harmony search start to demonstrate their power in dealing with tough optimization problems and even NP-hard problems. This book reviews and introduces the state-of-the-art nature-inspired metaheuristic algorithms in optimization, including genetic algorithms, bee algorithms, particle swarm optimization, simulated annealing, ant colony optimization, harmony search, and firefly algorithms. We also briefly introduce the photosynthetic algorithm, the enzyme algorithm, and Tabu search. Worked examples with implementation have been used to show how each algorithm works. This book is thus an ideal textbook for an undergraduate and/or graduate course. As some of the algorithms such as the harmony search and firefly algorithms are at the forefront of current research, this book can also serve as a reference book for researchers.
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paper_title: Firefly-inspired Heartbeat Synchronization in Overlay Networks

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Heartbeat synchronization strives to have nodes in a distributed system generate periodic, local "heartbeat" events approximately at the same time. Many useful distributed protocols rely on the existence of such heartbeats for driving their cycle-based execution. Yet, solving the problem in environments where nodes are unreliable and messages are subject to delays and failures is non-trivial. We present a heartbeat synchronization protocol for overlay networks inspired by mathematical models of flash synchronization in certain species of fireflies. In our protocol, nodes send flash messages to their neighbors when a local heartbeat triggers. They adjust the phase of their next heartbeat based on incoming flash messages using an algorithm inspired by mathematical models of firefly synchronization. We report simulation results of the protocol in various realistic failure scenarios typical in overlay networks and show that synchronization emerges even when messages can have significant delay subject to large jitter.
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paper_title: Modeling the expansion of Prosopis juliflora and determining its optimum utilization rate to control the invasion in Afar Regional State of Ethiopia

paper_content:

Prosopis juliflora is as an alien invasive tree species which is expanding at an alarming rate in the Horn of Africa region. In this paper a mathematical model is developed to estimate the rate of expansion in the Afar region of Ethiopia based on the coverage obtained with GIS analysis from the year 2000 satellite image for the region. The exponential model estimates that the tree species has been expanding at a rate of 50,000 hectares per year in the last ten years in the Afar region. The model further projects, if the tree species is used for productive uses such as energy and consumed at a rate of 90,000 hectares per year, the invaded land can be restored effectively in 15 years time. Furthermore, the model proposes that after the end of the 15 year, Prosopis can be contained within 200,000 hectares and provide 26,000 hectares of wood per annum sustainably for productive uses.
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paper_title: Optimum placement of active power conditioners by a dynamic discrete firefly algorithm to mitigate the negative power quality effects of renewable energy-based generators

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This paper presents a novel solution for the optimal placement and sizing of active power conditioners in future smart distribution systems by using the dynamic discrete firefly algorithm. The proposed method aims to mitigate the power quality effects of hybrid renewable energy-based generators and electric vehicle stations in smart grids. A multi-objective optimization problem is formulated to improve the voltage profile, minimize the voltage total harmonic distortion, and reduce the total investment cost. The performance analysis of the proposed algorithm is conducted on a modified IEEE 16-bus test system by using Matlab software. The results are then compared with the conventional stationary firefly algorithm, hybrid improved genetic algorithm, and dynamic particle swarm optimization. The comparison proves that the proposed optimization algorithm is the most effective method among the other methods and that the proposed method can precisely determine the optimum location and size of active power conditioners in distribution systems.
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paper_title: A cryptanalytic attack on the knapsack cryptosystem using binary Firefly algorithm

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This paper presents a binary Firefly Algorithm (FA), for cryptanalysis of knapsack cipher algorithm so as to deduce the meaning of an encrypted message (i.e. to determine a plaintext from the cipher text). The implemented algorithm has been characterized, in this paper, by a number of properties and operations that build up and evolve the fireflies' positions. These include light intensity, distances, attractiveness, and position updating, fitness evaluation. The results of the Firefly algorithm are compared with the results shown by Genetic Algorithm (GA), to discover the plaintext from the cipher text. Experimental results show that binary firefly algorithm is capable of finding correct results more efficiently than GA.
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paper_title: A Discrete Firefly Algorithm for the Scaffolding Modular Construction in Mega Projects

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Productivity is critical to large and complex capital projects in sectors like infrastructure and resources. It normally relates to a significant scheduling issue when pursuing both time and cost objectives. A poor planning of project schedule might incur both excessive labour cost and project delay. Looking at scaffolding activity, a foremost and prerequisite construction activity for the subsequence LNG equipment erection, this study identifies the present research gaps: very limited research emphasis has been placed on the impact of design of time-cost optimization in scaffolding, as well as the feasible solutions. Therefore, the practical guidance in scaffolding construction planning is treated as a critical research focal point in this study. Modular construction of scaffolding has been extensively implemented in LNG projects due to the risks of working on offshore platform and the enormous working area. The emphasis of this study therefore is placed on addressing time-cost tradeoff problems (TCTPs) of scaffolding modular construction. In particular, the questions of how to resolve the relatively multi-objective optimization issues using the Firefly algorithm and how to model the time and cost objective functions under specified constrains are answered. It is concluded that this paper, for the first time, looks into the complexity of scaffolding scheduling and gives solutions using such a robust optimization algorithm. In parallel, a simulation case study has been carrying out to test this algorithm based solution, to see how it can help scaffolding planners develop practical project schedules in either cost effective or time saving manners, or other trade-offs in between.
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paper_title: The unit commitment problem based on an improved firefly and particle swarm optimization hybrid algorithm

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In this paper, to solve the unit commitment problem economically and quickly, an improved firefly algorithm (FA) and particle swarm optimization (PSO) algorithm including both discrete and continuous parts was proposed. The starting and shutdown state of units were optimized according to using discrete binary real coded firefly algorithm. The inheritance from earlier state and constraints to later period of time for running time and shutdown time were considered in repair strategy. The continuous PSO was used in units' load dispatch after the process of deciding starting-stopping states, where constraints of power balance, unit ramp, spinning reserve and lower and upper limits were considered. Deal with the upper limits using Penalty function. To solve the constraints of power balance, zooming in the particles of each dimension variables same proportionally, and through sharing the penalty terms among particle swarms the constraints of units' ramping rates are settled. Simulation results of 10-unit and 24-hour system show that the proposed method is correct, effective and predominant.
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paper_title: Optimum placement of active power conditioner in distribution systems using improved discrete firefly algorithm for power quality enhancement

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This paper presents an improved solution for optimal placement and sizing of active power conditioner (APC) to enhance power quality in distribution systems using the improved discrete firefly algorithm (IDFA). A multi-objective optimization problem is formulated to improve voltage profile, minimize voltage total harmonic distortion and minimize total investment cost. The performance of the proposed algorithm is validated on the IEEE 16- and 69-bus test systems using the Matlab software. The obtained results are compared with the conventional discrete firefly algorithm, genetic algorithm and discrete particle swarm optimization. The comparison of results showed that the proposed IDFA is the most effective method among others in determining optimum location and size of APC in distribution systems.
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paper_title: Discrete Optimum Design of Truss Structures by an Improved Firefly Algorithm

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This paper presents an improved firefly algorithm (FA) for fast optimization of truss structures with discrete variables. The enhanced accelerated firefly algorithm (AFA) is a simple, but very effective modification of FA. In order to investigate the performance and robustness of the proposed algorithm, some benchmark (structural optimization) problems are solved and the results are compared with FA and other algorithms. The results show that in some test cases, AFA not only finds lighter structures compared to other algorithms, but also converges faster. In the rest test cases, the optimal solutions are found with very less computational effort. The study also shows that the proposed AFA remarkably improves stability of the firefly algorithm in discrete design of truss structures.
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paper_title: An Improved Discrete Firefly and t-Test based Algorithm for Blind Image Steganalysis

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Feature Selection is a preprocessing technique with great significance in data mining applications that aims at reducing computational complexity and increase predictive capability of a learning system. This paper presents a new hybrid feature selection algorithm based on Discrete Firefly optimization technique with dynamic alpha and gamma parameters and t-test filter technique to improve detectability of hidden message for Blind Image Steganalysis. The experiments are conducted on important dataset of feature vectors extracted from frequency domain, Discrete Cosine Transformation and Discrete Wavelet Transformation domain of cover and stego images. The results from popular JPEG steganography algorithms nsF5, Outguess, PQ and JP Hide and Seek show that proposed method is able to identify sensitive features and reduce the feature set by 67% in DCT domain and 37% in DWT domain. The experiment analysis shows that these algorithms are most sensitive to Markov features from DCT domain and variance statistical moment from DWT domain.
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paper_title: Network and reliability constrained unit commitment problem using binary real coded firefly algorithm

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In this paper, the binary real coded firefly (BRCFF) algorithm based on the flashing behavior of fireflies is proposed for solving network and reliability constrained unit commitment (UC) problem. In the first stage of the UC problem, the reliability constrained UC is solved using proposed binary coded firefly algorithm without satisfying network security constraints. The second stage of the problem solves optimal power flow (OPF) using real coded firefly algorithm to determine whether a converged and secure ac power flow can be obtained. Both the stages of the algorithm incorporate repair strategies and searches for a better solution. Here a random disturbance such as generation outages is modeled to evaluate the system reliability. Reliability of the system is recognized by loss of load probability (LOLP) index. The effectiveness of the proposed algorithm is demonstrated on 10 unit and IEEE RTS 24 bus system. The results of the proposed technique are compared with that of other techniques reported in the literature. In addition, the effect of the control parameters on the performance of firefly algorithm for UC problem is studied.
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paper_title: Mixed variable structural optimization using Firefly Algorithm

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In this study, a recently developed metaheuristic optimization algorithm, the Firefly Algorithm (FA), is used for solving mixed continuous/discrete structural optimization problems. FA mimics the social behavior of fireflies based on their flashing characteristics. The results of a trade study carried out on six classical structural optimization problems taken from literature confirm the validity of the proposed algorithm. The unique search features implemented in FA are analyzed, and their implications for future research work are discussed in detail in the paper.
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paper_title: Binary real coded firefly algorithm for solving unit commitment problem

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Abstract This paper presents a new biologically-inspired binary real coded firefly (BRCFF) algorithm to solve the unit commitment problem (UCP) by considering system and generating unit constraints. The firefly (FF) algorithm is inspired by the flashing behavior of fireflies and the phenomenon of bioluminescent communication. Upon solving UCP, the proposed binary coded FF algorithm determines the ON/OFF status of the generating units, while the economic dispatch problem (EDP) is solved using the real coded FF algorithm. The manner of firefly communication through luminescent flashes and their synchronization is imitated and suitably implemented in UCP. An effective constraint handling mechanism is introduced to solve complicated system and unit constraints. Finally, the proposed algorithm is applied to 3, 12, 17, 26, and 38 generating unit systems for a 24 h scheduling horizon and a comparative study is conducted using other recently reported results. Numerical results clarify and verify the significance of the proposed algorithm. The results obtained indicate that the proposed biologically-inspired algorithm could be an important player in swarm-based optimization.
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paper_title: Genetic Algorithms and Random Keys for Sequencing and Optimization

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In this paper we present a general genetic algorithm to address a wide variety of sequencing and optimization problems including multiple machine scheduling, resource allocation, and the quadratic assignment problem. When addressing such problems, genetic algorithms typically have difficulty maintaining feasibility from parent to offspring. This is overcome with a robust representation technique called random keys . Computational results are shown for multiple machine scheduling, resource allocation, and quadratic assignment problems. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
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paper_title: A Discrete Firefly Algorithm for the Multi-Objective Hybrid Flowshop Scheduling Problems

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Hybrid flowshop scheduling problems include the generalization of flowshops with parallel machines in some stages. Hybrid flowshop scheduling problems are known to be NP-hard. Hence, researchers have proposed many heuristics and metaheuristic algorithms to tackle such challenging tasks. In this letter, a recently developed discrete firefly algorithm is extended to solve hybrid flowshop scheduling problems with two objectives. Makespan and mean flow time are the objective functions considered. Computational experiments are carried out to evaluate the performance of the proposed algorithm. The results show that the proposed algorithm outperforms many other metaheuristics in the literature.
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paper_title: Firefly-inspired algorithm for discrete optimization problems: An application to manufacturing cell formation

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Abstract The canonical firefly algorithm is basically developed for continuous optimization problems. However, lots of practical problems are formulated as discrete optimization problems. The main purpose of this paper is to present the discrete firefly algorithm (DFA) to solve discrete optimization problems. In the DFA, we define a firefly's position in terms of changes of probabilities that will be in one state or the other. Then by using this metaheuristic algorithm, the manufacturing cell formation problem is solved. To illustrate the behavior of the proposed model and verify the performance of the algorithm, we introduce a number of numerical examples to illustrate the use of the foregoing algorithm. The performance evaluation shows the effectiveness of the DFA. The proposed metaheuristic algorithm should thus be useful to both researchers and practitioners.
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paper_title: Heuristic-Based Firefly Algorithm for Bound Constrained Nonlinear Binary Optimization

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Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper, we address the practical testing of a heuristic-based FA (HBFA) for computing optima of discrete nonlinear optimization problems, where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in turn affects its movement in the search space. Dynamic updating schemes are proposed for two parameters, one from the attractiveness term and the other from the randomization term. Three simple heuristics capable of transforming real continuous variables into binary ones are analyzed. A new sigmoid “erf” function is proposed. In the context of FA, three different implementations to incorporate the heuristics for binary variables into the algorithm are proposed. Based on a set of benchmark problems, a comparison is carried out with other binary dealing metaheuristics. The results demonstrate that the proposed HBFA is efficient and outperforms binary versions of differential evolution (DE) and particle swarm optimization (PSO). The HBFA also compares very favorably with angle modulated version of DE and PSO. It is shown that the variant of HBFA based on the sigmoid “erf” function with “movements in continuous space” is the best, in terms of both computational requirements and accuracy.
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paper_title: Firefly Algorithm for Cardinality Constrained Mean-Variance Portfolio Optimization Problem with Entropy Diversity Constraint

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Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results.
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paper_title: Multi-objective loading pattern enhancement of PWR based on the Discrete Firefly Algorithm

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Abstract In this paper, we develop a new optimization approach, i.e., Discrete Firefly Algorithm (DFA), in order to implement in the loading pattern optimization of nuclear reactor core. For the evaluation of proposed strategy, we use a multi-objective fitness function with two main goals in the nuclear core pattern design i.e. maximizing the core multiplication factor ( K eff ) in order to extract the maximum cycle energy and minimizing the power peaking factor due to safety constraints. For this purpose, Discrete Firefly Algorithm Nodal Expansion Code (DFANEC) has been developed with two main modules including a neutronic solver which models reactor core with coarse meshes using second order nodal expansion method and also DFA module to core pattern optimization. These codes have been coupled in the DFANEC for our fuel management operation. For two PWR type test cases, i.e., BIBLIS and KWU, DFANEC has been applied and its predictions indicate that the proposed DFA has the capability and sufficient strength to obtain the near optimized loading pattern for the considered multi-objective fitness function. All in all, the reliability and efficiency of proposed DFA have been ascertained from loading pattern optimization results.
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paper_title: OPTIMIZATION OF THE SUPPLIER SELECTION PROBLEM USING DISCRETE FIREFLY ALGORITHM

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In this article I show a firefly optimization based algorithm which helps to choose the appropriate suppliers in a case of given order quantity of a given product. The developed algorithm takes account of the minimum and maximum order quantities at the different suppliers as constraints. It also takes account of the quantity discounts offered by the different suppliers, which can be described as step function. The algorithm takes account of the capacity and the cost of the used transport vehicles too. The article describes the operation of the algorithm and the penalty functions applied. In the last part the firefly algorithm and the solution given by the MS Excel solver’s general reduced gradient and the evolutionary algorithm is compared.
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paper_title: The modified firefly algorithm considering fireflies’ visual range and its application in assembly sequences planning

paper_content:

This paper proposes a modified discrete firefly algorithm (MDFA) to solve the problem of assembly sequence planning. Firstly, to improve the performance of the firefly algorithm (FA), we proposed a MDFA by endowing the fireflies with the capability of changeable visual range. The computing case shows the proposed algorithm is more effective and robust than standard FA, genetic algorithm and particle swarm optimization algorithm. Secondly, a method of how to set parameters for FA and MDFA is proposed. This method is practical in the application of FA to solve discrete problem. Thirdly, to make the sequences more closer to real industrial requirements, a so called process precedence relations (PPR) evaluation function is presented, which not only considering the interference between parts, assembly tools and clamps, but also regarding the assembly order between parts and their reference parts. Finally, the evolution performance of the MDFA is investigated, and the performance of the proposed approach to solve ASP is verified through two cases study.
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paper_title: Software modularization using the modified firefly algorithm

paper_content:

Software modularization is a significant way to increase the maintenance of software systems. Designers depict the structure of software systems as a directed graph referred to as Module Dependency Graph in which nodes correspond to the software modules (such as files and classes) and edges relate to their relations (like function calls and inheritance relationship); These graphs can be partitioned into the meaningful clusters to be more accessible. Since Graph Partitioning is considered as a NP problem, here the application of exhaustive search algorithms are not so cost-effective that even for very small graphs they are not applicable. Therefore, many random approaches have been proposed for solving the problem. In this paper, a Firefly based method is presented to partition the software systems. However, some adjustments are needed to be made for using the FA for the problem. These modifications are as follows: change of the definition of fireflies, how to move fireflies toward better positions, and the alteration of fireflies' distance definition. Experimental results reveal that in most of the cases the proposed approach has a remarkable superiority over both the Genetic and the Learning Automaton algorithms in solving the problem.Keywords— e-learning, higher education, ICT, search for information.
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paper_title: A novel optimization method, Effective Discrete Firefly Algorithm, for fuel reload design of nuclear reactors

paper_content:

Inspired by fireflies behavior in nature, a firefly algorithm has been developed for solving optimization problems. In this approach, each firefly movement is based on absorption of the other one. For enhancing the performance of firefly algorithm in the optimization process of nuclear reactor loading pattern optimization (LPO), we introduce a new variant of firefly algorithm, i.e. Effective Discrete Firefly Algorithm (EDFA). In EDFA, a new behavior is the movement of fireflies to current global best position with a dynamic probability, i.e. the movement of each firefly can be determined to be toward the brighter or brightest firefly’s position in any iteration of the algorithm. In this paper, our optimization objectives for the LPO are the maximization of Keff along with the minimization of the power peaking factor (PPF). In order to represent the increase of convergence speed of EDFA, basic firefly algorithms including the continuous firefly algorithm (CFA) and the discrete firefly algorithm (DFA) also have been implemented. Loading pattern optimization results of two well-known problems confirm better performance of EDFA in obtaining nearly optimized fuel arrangements in comparison to CFA and DFA. All in all, we can suggest applying the EDFA to other optimization problems of nuclear engineering field in order to investigate its performance in gaining considered objectives.
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paper_title: Adaptive firefly algorithm with chaos for mechanical design optimization problems

paper_content:

Proposing an extension of firefly algorithm.Employment of picewise chaos, for an further enhanced diversity.Making use of a simple but effective constraint handling method.Making use of an improved local search procedure. Firefly algorithm (FA) is a newer member of bio-inspired meta-heuristics, which was originally proposed to find solutions to continuous optimization problems. Popularity of FA has increased recently due to its effectiveness in handling various optimization problems. To enhance the performance of the FA even further, an adaptive FA is proposed in this paper to solve mechanical design optimization problems, and the adaptivity is focused on the search mechanism and adaptive parameter settings. Moreover, chaotic maps are also embedded into AFA for performance improvement. It is shown through experimental tests that some of the best known results are improved by the proposed algorithm.
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paper_title: Evolutionary discrete firefly algorithm for travelling salesman problem

paper_content:

This paper addresses how to apply firefly algorithm (FA) for travelling salesman problem (TSP). Two schemes are studied, i.e. discrete distance between two fireflies and the movement scheme. Computer simulation shows that the simple form of FA without combination with other methods performs very well to solve some TSP instances, but it can be trapped into local optimum solutions for some other instances.
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paper_title: An improved firefly algorithm for solving dynamic multidimensional knapsack problems

paper_content:

There is a wide range of publications reported in the literature, considering optimization problems where the entire problem related data remains stationary throughout optimization. However, most of the real-life problems have indeed a dynamic nature arising from the uncertainty of future events. Optimization in dynamic environments is a relatively new and hot research area and has attracted notable attention of the researchers in the past decade. Firefly Algorithm (FA), Genetic Algorithm (GA) and Differential Evolution (DE) have been widely used for static optimization problems, but the applications of those algorithms in dynamic environments are relatively lacking. In the present study, an effective FA introducing diversity with partial random restarts and with an adaptive move procedure is developed and proposed for solving dynamic multidimensional knapsack problems. To the best of our knowledge this paper constitutes the first study on the performance of FA on a dynamic combinatorial problem. In order to evaluate the performance of the proposed algorithm the same problem is also modeled and solved by GA, DE and original FA. Based on the computational results and convergence capabilities we concluded that improved FA is a very powerful algorithm for solving the multidimensional knapsack problems for both static and dynamic environments.
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paper_title: An Evolutionary Discrete Firefly Algorithm with Novel Operators for Solving the Vehicle Routing Problem with Time Windows

paper_content:

An evolutionary discrete version of the Firefly Algorithm (EDFA) is presented in this chapter for solving the well-known Vehicle Routing Problem with Time Windows (VRPTW). The contribution of this work is not only the adaptation of the EDFA to the VRPTW, but also with some novel route optimization operators. These operators incorporate the process of minimizing the number of routes for a solution in the search process where node selective extractions and subsequent reinsertion are performed. The new operators analyze all routes of the current solution and thus increase the diversification capacity of the search process (in contrast with the traditional node and arc exchange based operators). With the aim of proving that the proposed EDFA and operators are effective, some different versions of the EDFA are compared. The present work includes the experimentation with all the 56 instances of the well-known VRPTW set. In order to obtain rigorous and fair conclusions, two different statistical tests have been conducted.
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Title: Firefly Algorithm for Optimization Problems with Non-Continuous Variables: A Review and Analysis

Section 1: Introduction
Description 1: Provide an overview of optimization problems, metaheuristic algorithms, swarm-based algorithms, and specifically introduce the Firefly Algorithm, its strengths, challenges, and the purpose of this paper.

Section 2: Optimization problems
Description 2: Discuss the general framework of optimization problems, including decision variables, objective functions, and the concept of feasible regions, addressing both continuous and non-continuous variables.

Section 3: Firefly Algorithm
Description 3: Detailed explanation of the Firefly Algorithm, its biological inspiration, working principles, key equations, and rules guiding firefly interactions and movements in the solution space.

Section 4: Modified firefly algorithms for discrete optimization problems
Description 4: Explore the various modifications of the Firefly Algorithm to handle discrete optimization problems, categorizing them based on whether updating is done in continuous or discrete space.

Section 4.1: Updating in the continuous space
Description 4.1: Discuss modifications where the Firefly Algorithm updates the continuous space and then converts results to discrete values, including various techniques such as sigmoid functions and rounding.

Section 4.2: Updating in the discrete space
Description 4.2: Explain modifications that involve updating directly in the discrete space, including techniques like Hamming distance and specific problem-based approaches.

Section 5: Discussion
Description 5: Analyze the strengths and weaknesses of the various modifications, the effectiveness of parameter tuning, and highlight potential areas for future research.

Section 6: Conclusion
Description 6: Summarize the key points covered in the review, the significance of the modifications for discrete optimization problems, and final thoughts on future research directions.