Search results for: Ant colony optimization algorithm

Authors: Sasadhar Bera, Indrajit Mukherjee

Abstract:

Ant colony optimization (ACO) and its variants are applied extensively to resolve various continuous optimization problems. As per the various diversification and intensification schemes of ACO for continuous function optimization, researchers generally consider components of multidimensional state space to generate the new search point(s). However, diversifying to a new search space by updating only components of the multidimensional vector may not ensure that the new point is at a significant distance from the current solution. If a minimum distance is not ensured during diversification, then there is always a possibility that the search will end up with reaching only local optimum. Therefore, to overcome such situations, a Mahalanobis distance-based diversification with Nelder-Mead simplex-based search scheme for each ant is proposed for the ACO strategy. A comparative computational run results, based on nine nonlinear standard test problems, confirms that the performance of ACO is improved significantly with the integration of the proposed schemes in the ACO.

Keywords: Ant Colony Optimization, Diversification Scheme, Intensification, Mahalanobis Distance, Nelder-Mead Simplex.

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Authors: Gaohuizi Guo, Ning Zhang

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Firefly algorithm (FA) and Sine Cosine algorithm (SCA) are two very popular and advanced metaheuristic algorithms. However, these algorithms applied to multi-objective optimization problems have some shortcomings, respectively, such as premature convergence and limited exploration capability. Combining the privileges of FA and SCA while avoiding their deficiencies may improve the accuracy and efficiency of the algorithm. This paper proposes a hybridization of FA and SCA algorithms, named multi-objective firefly-sine cosine algorithm (MFA-SCA), to develop a more efficient meta-heuristic algorithm than FA and SCA.

Keywords: Firefly algorithm, hybrid algorithm, multi-objective optimization, Sine Cosine algorithm.

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Authors: Panpan Xu, Shulin Sui

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The crossover probability and mutation probability are the two important factors in genetic algorithm. The adaptive genetic algorithm can improve the convergence performance of genetic algorithm, in which the crossover probability and mutation probability are adaptively designed with the changes of fitness value. We apply adaptive genetic algorithm into a function optimization problem. The numerical experiment represents that adaptive genetic algorithm improves the convergence speed and avoids local convergence.

Keywords: Genetic algorithm, Adaptive genetic algorithm, Function optimization.

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Authors: Minsoo Lee, Yearn Jeong Kim, Yun-mi Kim, Sujeung Cheong, Sookyung Song

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Bio-chips are used for experiments on genes and contain various information such as genes, samples and so on. The two-dimensional bio-chips, in which one axis represent genes and the other represent samples, are widely being used these days. Instead of experimenting with real genes which cost lots of money and much time to get the results, bio-chips are being used for biological experiments. And extracting data from the bio-chips with high accuracy and finding out the patterns or useful information from such data is very important. Bio-chip analysis systems extract data from various kinds of bio-chips and mine the data in order to get useful information. One of the commonly used methods to mine the data is classification. The algorithm that is used to classify the data can be various depending on the data types or number characteristics and so on. Considering that bio-chip data is extremely large, an algorithm that imitates the ecosystem such as the ant algorithm is suitable to use as an algorithm for classification. This paper focuses on finding the classification rules from the bio-chip data using the Ant Colony algorithm which imitates the ecosystem. The developed system takes in consideration the accuracy of the discovered rules when it applies it to the bio-chip data in order to predict the classes.

Keywords: Ant Colony System, DNA chip data, Classification.

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Authors: Adel Sabry Eesa, Adnan Mohsin Abdulazeez Brifcani, Zeynep Orman

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This paper presents a new meta-heuristic bio-inspired optimization algorithm which is called Cuttlefish Algorithm (CFA). The algorithm mimics the mechanism of color changing behavior of the cuttlefish to solve numerical global optimization problems. The colors and patterns of the cuttlefish are produced by reflected light from three different layers of cells. The proposed algorithm considers mainly two processes: reflection and visibility. Reflection process simulates light reflection mechanism used by these layers, while visibility process simulates visibility of matching patterns of the cuttlefish. To show the effectiveness of the algorithm, it is tested with some other popular bio-inspired optimization algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Bees Algorithm (BA) that have been previously proposed in the literature. Simulations and obtained results indicate that the proposed CFA is superior when compared with these algorithms.

Keywords: Cuttlefish Algorithm, bio-inspired algorithms, optimization.

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Authors: W. Wongthatsanekorn, N. Matheekrieangkrai

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This research proposes Bee Algorithm (BA) to optimize Ready Mixed Concrete (RMC) truck scheduling problem from single batch plant to multiple construction sites. This problem is considered as an NP-hard constrained combinatorial optimization problem. This paper provides the details of the RMC dispatching process and its related constraints. BA was then developed to minimize total waiting time of RMC trucks while satisfying all constraints. The performance of BA is then evaluated on two benchmark problems (3 and 5construction sites) according to previous researchers. The simulation results of BA are compared in term of efficiency and accuracy with Genetic Algorithm (GA) and all problems show that BA approach outperforms GA in term of efficiency and accuracy to obtain optimal solution. Hence, BA approach could be practically implemented to obtain the best schedule.

Keywords: Bee Colony Optimization, Ready Mixed Concrete Problem.

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Authors: Farhad Kolahan, M. Hossein Abolbashari, Samaeddin Mohitzadeh

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Several methods are available for weight and shape optimization of structures, among which Evolutionary Structural Optimization (ESO) is one of the most widely used methods. In ESO, however, the optimization criterion is completely case-dependent. Moreover, only the improving solutions are accepted during the search. In this paper a Simulated Annealing (SA) algorithm is used for structural optimization problem. This algorithm differs from other random search methods by accepting non-improving solutions. The implementation of SA algorithm is done through reducing the number of finite element analyses (function evaluations). Computational results show that SA can efficiently and effectively solve such optimization problems within short search time.

Keywords: Simulated annealing, Structural optimization, Compliance, C.V. product.

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Authors: A. Safari, R. Jahani, H. A. Shayanfar, J. Olamaei

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This paper shows the results obtained in the analysis of the impact of distributed generation (DG) on distribution losses and presents a new algorithm to the optimal allocation of distributed generation resources in distribution networks. The optimization is based on a Hybrid Genetic Algorithm and Particle Swarm Optimization (HGAPSO) aiming to optimal DG allocation in distribution network. Through this algorithm a significant improvement in the optimization goal is achieved. With a numerical example the superiority of the proposed algorithm is demonstrated in comparison with the simple genetic algorithm.

Keywords: Distributed Generation, Distribution Networks, Genetic Algorithm, Particle Swarm Optimization.

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Authors: Yahya H. Zweiri

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The back-propagation algorithm calculates the weight changes of an artificial neural network, and a two-term algorithm with a dynamically optimal learning rate and a momentum factor is commonly used. Recently the addition of an extra term, called a proportional factor (PF), to the two-term BP algorithm was proposed. The third term increases the speed of the BP algorithm. However, the PF term also reduces the convergence of the BP algorithm, and optimization approaches for evaluating the learning parameters are required to facilitate the application of the three terms BP algorithm. This paper considers the optimization of the new back-propagation algorithm by using derivative information. A family of approaches exploiting the derivatives with respect to the learning rate, momentum factor and proportional factor is presented. These autonomously compute the derivatives in the weight space, by using information gathered from the forward and backward procedures. The three-term BP algorithm and the optimization approaches are evaluated using the benchmark XOR problem.

Keywords: Neural Networks, Backpropagation, Optimization.

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Authors: S. Adhirai, R. P. Mahapatra, Paramjit Singh

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Optimization is an important tool in making decisions and in analysing physical systems. In mathematical terms, an optimization problem is the problem of finding the best solution from among the set of all feasible solutions. The paper discusses the Whale Optimization Algorithm (WOA), and its applications in different fields. The algorithm is tested using MATLAB because of its unique and powerful features. The benchmark functions used in WOA algorithm are grouped as: unimodal (F1-F7), multimodal (F8-F13), and fixed-dimension multimodal (F14-F23). Out of these benchmark functions, we show the experimental results for F7, F11, and F19 for different number of iterations. The search space and objective space for the selected function are drawn, and finally, the best solution as well as the best optimal value of the objective function found by WOA is presented. The algorithmic results demonstrate that the WOA performs better than the state-of-the-art meta-heuristic and conventional algorithms.

Keywords: Optimization, optimal value, objective function, optimization problems, meta-heuristic optimization algorithms, Whale Optimization Algorithm, Implementation, MATLAB.

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Authors: Tomohiro Hachino, Hitoshi Takata, Shigeru Nakayama, Ichiro Iimura, Seiji Fukushima, Yasutaka Igarashi

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This paper presents a nonparametric identification of continuous-time nonlinear systems by using a Gaussian process (GP) model. The GP prior model is trained by artificial bee colony algorithm. The nonlinear function of the objective system is estimated as the predictive mean function of the GP, and the confidence measure of the estimated nonlinear function is given by the predictive covariance of the GP. The proposed identification method is applied to modeling of a simplified electric power system. Simulation results are shown to demonstrate the effectiveness of the proposed method.

Keywords: Artificial bee colony algorithm, Gaussian process model, identification, nonlinear system, electric power system.

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Authors: O. Hasançebi, S. Kazemzadeh Azad

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In the present study the efficiency of Big Bang-Big Crunch (BB-BC) algorithm is investigated in discrete structural design optimization. It is shown that a standard version of the BB-BC algorithm is sometimes unable to produce reasonable solutions to problems from discrete structural design optimization. Two reformulations of the algorithm, which are referred to as modified BB-BC (MBB-BC) and exponential BB-BC (EBB-BC), are introduced to enhance the capability of the standard algorithm in locating good solutions for steel truss and frame type structures, respectively. The performances of the proposed algorithms are experimented and compared to its standard version as well as some other algorithms over several practical design examples. In these examples, steel structures are sized for minimum weight subject to stress, stability and displacement limitations according to the provisions of AISC-ASD.

Keywords: Structural optimization, discrete optimization, metaheuristics, big bang-big crunch (BB-BC) algorithm, design optimization of steel trusses and frames.

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Authors: Li Ni, Pen ManMan, Li KenLi

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Clustering is an intensive research for some years because of its multifaceted applications, such as biology, information retrieval, medicine, business and so on. The expectation maximization (EM) is a kind of algorithm framework in clustering methods, one of the ten algorithms of machine learning. Traditionally, optimization of objective function has been the standard approach in EM. Hence, research has investigated the utility of evolutionary computing and related techniques in the regard. Chemical Reaction Optimization (CRO) is a recently established method. So the property embedded in CRO is used to solve optimization problems. This paper presents an algorithm framework (EM-CRO) with modified CRO operators based on EM cluster problems. The hybrid algorithm is mainly to solve the problem of initial value sensitivity of the objective function optimization clustering algorithm. Our experiments mainly take the EM classic algorithm:k-means and fuzzy k-means as an example, through the CRO algorithm to optimize its initial value, get K-means-CRO and FKM-CRO algorithm. The experimental results of them show that there is improved efficiency for solving objective function optimization clustering problems.

Keywords: Chemical reaction optimization, expectation maximization, initial, objective function clustering.

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Authors: Neveen I. Ghali, Nahed El-Dessouki, Mervat A. N., Lamiaa Bakrawi

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In this paper we use exponential particle swarm optimization (EPSO) to cluster data. Then we compare between (EPSO) clustering algorithm which depends on exponential variation for the inertia weight and particle swarm optimization (PSO) clustering algorithm which depends on linear inertia weight. This comparison is evaluated on five data sets. The experimental results show that EPSO clustering algorithm increases the possibility to find the optimal positions as it decrease the number of failure. Also show that (EPSO) clustering algorithm has a smaller quantization error than (PSO) clustering algorithm, i.e. (EPSO) clustering algorithm more accurate than (PSO) clustering algorithm.

Keywords: Particle swarm optimization, data clustering, exponential PSO.

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Authors: Lada-On Lertsuwanakul, Herwig Unger

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This paper objects to extend Jon Kleinberg-s research. He introduced the structure of small-world in a grid and shows with a greedy algorithm using only local information able to find route between source and target in delivery time O(log2n). His fundamental model for distributed system uses a two-dimensional grid with longrange random links added between any two node u and v with a probability proportional to distance d(u,v)-2. We propose with an additional information of the long link nearby, we can find the shorter path. We apply the ant colony system as a messenger distributed their pheromone, the long-link details, in surrounding area. The subsequence forwarding decision has more option to move to, select among local neighbors or send to node has long link closer to its target. Our experiment results sustain our approach, the average routing time by Color Pheromone faster than greedy method.

Keywords: Routing algorithm, Small-World network, Ant Colony Optimization, and Peer-to-peer System.

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Authors: Hyun-Chool Shin

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In this paper we propose a simple adaptive algorithm iteratively solving the unit-norm constrained optimization problem. Instead of conventional parameter norm based normalization, the proposed algorithm incorporates scalar normalization which is computationally much simpler. The analysis of stationary point is presented to show that the proposed algorithm indeed solves the constrained optimization problem. The simulation results illustrate that the proposed algorithm performs as good as conventional ones while being computationally simpler.

Keywords: constrained optimization, unit-norm, LMS, principle component analysis.

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Authors: Radhwan Yousif Sedik Al-Jawadi

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Optimization is necessary for finding appropriate solutions to a range of real-life problems. In particular, genetic (or more generally, evolutionary) algorithms have proved very useful in solving many problems for which analytical solutions are not available. In this paper, we present an optimization algorithm called Dynamic Schema with Dissimilarity and Similarity of Chromosomes (DSDSC) which is a variant of the classical genetic algorithm. This approach constructs new chromosomes from a schema and pairs of existing ones by exploring their dissimilarities and similarities. To show the effectiveness of the algorithm, it is tested and compared with the classical GA, on 15 two-dimensional optimization problems taken from literature. We have found that, in most cases, our method is better than the classical genetic algorithm.

Keywords: Genetic algorithm, similarity and dissimilarity, chromosome injection, dynamic schema.

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Authors: Hao Wu, Jonathan L. Shapiro

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The Bayesian Optimization Algorithm (BOA) is an algorithm based on the estimation of distributions. It uses techniques from modeling data by Bayesian networks to estimating the joint distribution of promising solutions. To obtain the structure of Bayesian network, different search algorithms can be used. The key point that BOA addresses is whether the constructed Bayesian network could generate new and useful solutions (strings), which could lead the algorithm in the right direction to solve the problem. Undoubtedly, this ability is a crucial factor of the efficiency of BOA. Varied search algorithms can be used in BOA, but their performances are different. For choosing better ones, certain suitable method to present their ability difference is needed. In this paper, a greedy search algorithm and a stochastic search algorithm are used in BOA to solve certain optimization problem. A method using Kullback-Leibler (KL) Divergence to reflect their difference is described.

Keywords: Bayesian optimization algorithm, greedy search, KL divergence, stochastic search.

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Authors: C. Rajan, N. Shanthi, C. Rasi Priya, K. Geetha

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Routing in MANET is extremely challenging because of MANETs dynamic features, its limited bandwidth, frequent topology changes caused by node mobility and power energy consumption. In order to efficiently transmit data to destinations, the applicable routing algorithms must be implemented in mobile ad-hoc networks. Thus we can increase the efficiency of the routing by satisfying the Quality of Service (QoS) parameters by developing routing algorithms for MANETs. The algorithms that are inspired by the principles of natural biological evolution and distributed collective behavior of social colonies have shown excellence in dealing with complex optimization problems and are becoming more popular. This paper presents a survey on few meta-heuristic algorithms and naturally-inspired algorithms.

Keywords: Ant colony optimization, genetic algorithm, Naturally-inspired algorithms and particle swarm optimization.

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Authors: Tao Zhao, Xin Wang

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With the increasing complexity of engineering problems, the traditional, single-objective and deterministic optimization method can not meet people-s requirements. A multi-objective fuzzy optimization model of resource input is built for M chlor-alkali chemical eco-industrial park in this paper. First, the model is changed into the form that can be solved by genetic algorithm using fuzzy theory. And then, a fitness function is constructed for genetic algorithm. Finally, a numerical example is presented to show that the method compared with traditional single-objective optimization method is more practical and efficient.

Keywords: Fitness function, genetic algorithm, multi-objectivefuzzy optimization, satisfaction degree membership function.

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Authors: Minsoo Lee, Yun-mi Kim, Yearn Jeong Kim, Yoon-kyung Lee, Hyejung Yoon

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Biological data has several characteristics that strongly differentiate it from typical business data. It is much more complex, usually large in size, and continuously changes. Until recently business data has been the main target for discovering trends, patterns or future expectations. However, with the recent rise in biotechnology, the powerful technology that was used for analyzing business data is now being applied to biological data. With the advanced technology at hand, the main trend in biological research is rapidly changing from structural DNA analysis to understanding cellular functions of the DNA sequences. DNA chips are now being used to perform experiments and DNA analysis processes are being used by researchers. Clustering is one of the important processes used for grouping together similar entities. There are many clustering algorithms such as hierarchical clustering, self-organizing maps, K-means clustering and so on. In this paper, we propose a clustering algorithm that imitates the ecosystem taking into account the features of biological data. We implemented the system using an Ant-Colony clustering algorithm. The system decides the number of clusters automatically. The system processes the input biological data, runs the Ant-Colony algorithm, draws the Topic Map, assigns clusters to the genes and displays the output. We tested the algorithm with a test data of 100 to1000 genes and 24 samples and show promising results for applying this algorithm to clustering DNA chip data.

Keywords: Ant colony system, biological data, clustering, DNA chip.

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Authors: B. Bahmani Firouzi, T. Niknam, M. Nayeripour

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With Power system movement toward restructuring along with factors such as life environment pollution, problems of transmission expansion and with advancement in construction technology of small generation units, it is expected that small units like wind turbines, fuel cells, photovoltaic, ... that most of the time connect to the distribution networks play a very essential role in electric power industry. With increase in developing usage of small generation units, management of distribution networks should be reviewed. The target of this paper is to present a new method for optimal management of active and reactive power in distribution networks with regard to costs pertaining to various types of dispersed generations, capacitors and cost of electric energy achieved from network. In other words, in this method it-s endeavored to select optimal sources of active and reactive power generation and controlling equipments such as dispersed generations, capacitors, under load tapchanger transformers and substations in a way that firstly costs in relation to them are minimized and secondly technical and physical constraints are regarded. Because the optimal management of distribution networks is an optimization problem with continuous and discrete variables, the new evolutionary method based on Ant Colony Algorithm has been applied. The simulation results of the method tested on two cases containing 23 and 34 buses exist and will be shown at later sections.

Keywords: Distributed Generation, Optimal Operation Management of distribution networks, Ant Colony Optimization(ACO).

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Authors: P. Suryakumari, P. Kantarao

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Optimal Power Flow (OPF) problem in electrical power system is considered as a static, non-linear, multi-objective or a single objective optimization problem. This paper presents an algorithm for solving the voltage stability objective reactive power dispatch problem in a power system .The proposed approach employs cat swarm optimization algorithm for optimal settings of RPD control variables. Generator terminal voltages, reactive power generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables. CSO algorithm is tested on standard IEEE 30 bus system and the results are compared with other methods to prove the effectiveness of the new algorithm. As a result, the proposed method is the best for solving optimal reactive power dispatch problem.

Keywords: RPD problem, voltage stability enhancement, CSO algorithm.

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Authors: Ahcene Habbi, Yassine Boudouaoui

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This paper deals with the problem of automatic rule generation for fuzzy systems design. The proposed approach is based on hybrid artificial bee colony (ABC) optimization and weighted least squares (LS) method and aims to find the structure and parameters of fuzzy systems simultaneously. More precisely, two ABC based fuzzy modeling strategies are presented and compared. The first strategy uses global optimization to learn fuzzy models, the second one hybridizes ABC and weighted least squares estimate method. The performances of the proposed ABC and ABC-LS fuzzy modeling strategies are evaluated on complex modeling problems and compared to other advanced modeling methods.

Keywords: Automatic design, learning, fuzzy rules, hybrid, swarm optimization.

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Authors: Hassan Azarkish, Said Farahat, S.Masoud H. Sarvari

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In the present work, the performance of the particle swarm optimization and the genetic algorithm compared as a typical geometry design problem. The design maximizes the heat transfer rate from a given fin volume. The analysis presumes that a linear temperature distribution along the fin. The fin profile generated using the B-spline curves and controlled by the change of control point coordinates. An inverse method applied to find the appropriate fin geometry yield the linear temperature distribution along the fin corresponds to optimum design. The numbers of the populations, the count of iterations and time to convergence measure efficiency. Results show that the particle swarm optimization is most efficient for geometry optimization.

Keywords: Genetic Algorithm, Geometry Optimization, longitudinal Fin, Particle Swarm Optimization

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Authors: R. Rajabpour, N. Talebbeydokhti, M. H. Ahmadi

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Carefully scheduling the operations of pumps can be resulted to significant energy savings. Schedules can be defined either implicit, in terms of other elements of the network such as tank levels, or explicit by specifying the time during which each pump is on/off. In this study, two new explicit representations based on timecontrolled triggers were analyzed, where the maximum number of pump switches was established beforehand, and the schedule may contain fewer switches than the maximum. The optimal operation of pumping stations was determined using a Jumping Particle Swarm Optimization (JPSO) algorithm to achieve the minimum energy cost. The model integrates JPSO optimizer and EPANET hydraulic network solver. The optimal pump operation schedule of VanZyl water distribution system was determined using the proposed model and compared with those from Genetic and Ant Colony algorithms. The results indicate that the proposed model utilizing the JPSO algorithm is a versatile management model for the operation of realworld water distribution system.

Keywords: JPSO, operation, optimization, water distribution system.

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Authors: D. Uma Devi, P. Seetha Ramaiah

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Voting algorithms are extensively used to make decisions in fault tolerant systems where each redundant module gives inconsistent outputs. Popular voting algorithms include majority voting, weighted voting, and inexact majority voters. Each of these techniques suffers from scenarios where agreements do not exist for the given voter inputs. This has been successfully overcome in literature using fuzzy theory. Our previous work concentrated on a neuro-fuzzy algorithm where training using the neuro system substantially improved the prediction result of the voting system. Weight training of Neural Network is sub-optimal. This study proposes to optimize the weights of the Neural Network using Artificial Bee Colony algorithm. Experimental results show the proposed system improves the decision making of the voting algorithms.

Keywords: Voting algorithms, Fault tolerance, Fault masking, Neuro-Fuzzy System (NFS), Artificial Bee Colony (ABC)

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Authors: Younis R. Elhaddad

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Combinatorial optimization problems arise in many scientific and practical applications. Therefore many researchers try to find or improve different methods to solve these problems with high quality results and in less time. Genetic Algorithm (GA) and Simulated Annealing (SA) have been used to solve optimization problems. Both GA and SA search a solution space throughout a sequence of iterative states. However, there are also significant differences between them. The GA mechanism is parallel on a set of solutions and exchanges information using the crossover operation. SA works on a single solution at a time. In this work SA and GA are combined using new technique in order to overcome the disadvantages' of both algorithms.

Keywords: Genetic Algorithm, Optimization problems, Simulated Annealing, Traveling Salesman Problem

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Authors: B.Bahmani Firouzi, T. Niknam, M. Nayeripour

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Clustering is a very well known technique in data mining. One of the most widely used clustering techniques is the kmeans algorithm. Solutions obtained from this technique depend on the initialization of cluster centers and the final solution converges to local minima. In order to overcome K-means algorithm shortcomings, this paper proposes a hybrid evolutionary algorithm based on the combination of PSO, SA and K-means algorithms, called PSO-SA-K, which can find better cluster partition. The performance is evaluated through several benchmark data sets. The simulation results show that the proposed algorithm outperforms previous approaches, such as PSO, SA and K-means for partitional clustering problem.

Keywords: Data clustering, Hybrid evolutionary optimization algorithm, K-means algorithm, Simulated Annealing (SA), Particle Swarm Optimization (PSO).

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Authors: Ludovic Favre, Thibaut M. Schafer, Jean-Luc Robyr, Elena-Lavinia Niederhäuser

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This paper presents an optimization method based on genetic algorithm for the energy management inside buildings developed in the frame of the project Smart Living Lab (SLL) in Fribourg (Switzerland). This algorithm optimizes the interaction between renewable energy production, storage systems and energy consumers. In comparison with standard algorithms, the innovative aspect of this project is the extension of the smart regulation over three simultaneous criteria: the energy self-consumption, the decrease of greenhouse gas emissions and operating costs. The genetic algorithm approach was chosen due to the large quantity of optimization variables and the non-linearity of the optimization function. The optimization process includes also real time data of the building as well as weather forecast and users habits. This information is used by a physical model of the building energy resources to predict the future energy production and needs, to select the best energetic strategy, to combine production or storage of energy in order to guarantee the demand of electrical and thermal energy. The principle of operation of the algorithm as well as typical output example of the algorithm is presented.

Keywords: Building’s energy, control system, energy management, modelling, genetic optimization algorithm, renewable energy, greenhouse gases, energy storage.

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