Journal articles: 'Ackley's function'

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Agibalov, O., T. Blinovskaya, and N. Ventsov. "On the issue of using intuitionistic fuzzy sets for describing the expediency of solving optimization problems by genetic algorithms with given parameters." E3S Web of Conferences 224 (2020): 01008. http://dx.doi.org/10.1051/e3sconf/202022401008.

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The paper analyses a possible option for preparing data on the results of the genetic algorithm for transfer to another subject area. It was shown that the complexity of modern target functions requires the development of new approaches to determining the parameters of search procedures. A set of experiments, each stage of which consisted of performing 100 runs of the genetic algorithm on a CPU or GPU architecture, which determines the optimal solution of the Ackley’s function within a given time interval, was carried out. After the specified time interval expired, the operation of the algorithm was correctly completed by fixing the results obtained at the final iteration. The values of the absolute error were set to Δ={0.5, 0.15, 0.1, 0.05}. For each error value the number of algorithm runs, as a result of which the deviation was greater than Δ, was determined. On the basis of the experiment carried out, fuzzy estimates of the inexpediency of searching for the optimum of the Ackley’s function by the genetic algorithm on the CPU architecture in a time from 100 ms ...1800 ms were determined. The possibility of using intuitionistic fuzzy sets for describing the expediency of solving optimization problems by genetic algorithms with given parameters was shown.

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Zambrano Zambrano, Dannyll Michellc, Darío Vélez, Yohanna Daza, and José Manuel Palomares. "Parametric Analysis of BFOA for Minimization Problems Using a Benchmark Function." Enfoque UTE 10, no. 3 (September 30, 2019): 67–80. http://dx.doi.org/10.29019/enfoque.v10n3.490.

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This paper presents the social foraging behavior of Escherichia coli (E. Coli) bacteria based on Bacteria Foraging Optimization algorithms (BFOA) to find optimization and distributed control values. The search strategy for E. coli is very complex to express and the dynamics of the simulated chemotaxis stage in BFOA is analyzed with the help of a simple mathematical model. The methodology starts from a detailed analysis of the parameters of bacterial swimming and tumbling (C) and the probability of elimination and dispersion (Ped), then an adaptive variant of BFOA is proposed, in which the size of the chemotherapeutic step is adjusted according to the current suitability of a virtual bacterium. To evaluate the performance of the algorithm in obtaining optimal values, the resolution was applied to one of the benchmark functions, in this case the Ackley minimization function, a comparative analysis of the BFOA is then performed. The simulation results have shown the validity of the optimal values (minimum or maximum) obtained on a specific function for real world problems, with a function belonging to the benchmark group of optimization functions.

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Negrin Diaz, Iván Antonio, Ernesto Luciano Chagoyén Méndez, and Alejandro Negrin Montecelo. "Parameter tuning in the process of optimization of reinforced concrete structures." DYNA 88, no. 216 (February 22, 2021): 87–95. http://dx.doi.org/10.15446/dyna.v88n216.87169.

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Parameter tuning deals with finding the best parameter configuration of an optimization method in a given problem. In structural optimization, it could be an extensive and high-computing cost process. One way to avoid this drawback is to use analytical functions (or benchmark functions), for simulating main features of objective functions in real problems. In this paper, Biogeography-Based Optimization is applied during structural optimization of reinforced concrete frame structures, and Ackley function for parameter tuning in real cases simulation. The tuned method outperformed other meta-heuristics in the actual optimization problem. Structural results show that by not including static soil-structure interaction, differences in direct cost of the superstructure of up to 4.42% are obtained for predominantly cohesive soils and 11.55% for predominantly frictional ones. In beams, L/h ratios around 15 and high reinforcement ratios are highly recommended. In columns and shallow foundations, best rectangularity reaches values of 1.15 and 2.00 respectively.

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Ewald, Dawid, Hubert Zarzycki, Łukasz Apiecionek, and Jacek Czerniak. "Ordered Fuzzy Numbers Applied in Bee Swarm Optimization Systems." JUCS - Journal of Universal Computer Science 26, no. 11 (November 28, 2020): 1475–94. http://dx.doi.org/10.3897/jucs.2020.078.

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The paper presents an innovative OFNBee optimization method based on combining the swarm intelligence with the use of directed fuzzy numers OFN. In the introduction, the issues related to the subject of the study, including bee algorithms and OFN numbers, were reviewed. The innovative OFNBee algorithm was presented and verified against a set of known benchmarks functions such as Sphere, Rastrigin, Griewank, Rosenbrock, Schwefel and Ackley. These functions have been applied due to their reliability in the literature. In the further part of the study, the configuration of the algorithm parameters is carried out, including the launch of each mathematical function several dozen times for different data, such as different population sizes. The key part of the research and analysis was to compare OFNBee with six standard ABC, MBO, IMBO, TLBO, HBMO, BBMO bee algorithms. The article ends with a summary and an indication of the possible future works.

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Mirfenderesgi, Golnazalsadat, and S. Jamshid Mousavi. "Adaptive meta-modeling-based simulation optimization in basin-scale optimum water allocation: a comparative analysis of meta-models." Journal of Hydroinformatics 18, no. 3 (December 4, 2015): 446–65. http://dx.doi.org/10.2166/hydro.2015.157.

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Incorporating river basin simulation models in heuristic optimization algorithms can help modelers address complex, basin-scale water resource problems. We have developed a hybrid optimization-simulation model by linking a stretching particle swarm optimization (SPSO) algorithm and the MODSIM river basin decision support system (DSS), and have used the SPSO-MODSIM model to optimize water allocation at basin scale. Due to high computational cost of the SPSO-MODSIM model, we have, subsequently, used four meta-model types of artificial neural networks (ANN), support vector machines (SVM), kriging and polynomial response functions, replacing the MODSIM DSS, in an adaptively learning meta-modeling approach. The performances of the meta-models are first compared in two Ackley and Dejong benchmark functions optimization problems, and the meta-models are then evaluated by solving the Atrak river basin water allocation optimization problem in Iran. The results demonstrate that independent of the meta-model type, the sequentially space-filling meta-modeling approach can improve the performance of meta-models in the course of optimization by adaptively locating the promising regions of the search space where more samples need to be generated. However, the ANN and SVM meta-models perform better than others in saving the number of costly, original objective function evaluations.

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Carmona Cortes, Omar Andres, and Josenildo Costa da Silva. "Unconstrained numerical optimization using real-coded genetic algorithms: a study case using benchmark functions in R from Scratch." Revista Brasileira de Computação Aplicada 11, no. 3 (September 25, 2019): 1–11. http://dx.doi.org/10.5335/rbca.v11i3.9047.

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Unconstrained numerical problems are common in solving practical applications that, due to its nature, are usually devised by several design variables, narrowing the kind of technique or algorithm that can deal with them. An interesting way of tackling this kind of issue is to use an evolutionary algorithm named Genetic Algorithm. In this context, this work is a tutorial on using real-coded genetic algorithms for solving unconstrained numerical optimization problems. We present the theory and the implementation in R language. Five benchmarks functions (Rosenbrock, Griewank, Ackley, Schwefel, and Alpine) are used as a study case. Further, four different crossover operators (simple, arithmetical, non-uniform arithmetical, and Linear), two selection mechanisms (roulette wheel and tournament), and two mutation operators (uniform and non-uniform) are shown. Results indicate that non-uniform mutation and tournament selection tend to present better outcomes.

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Houcine, Lassad, Mohamed Bouzbida, and Abdelkader Chaari. "Improved Adaptive Particle Swarm Optimization for Optimization Functions and Clustering Fuzzy Modeling System." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 26, no. 05 (September 28, 2018): 717–39. http://dx.doi.org/10.1142/s0218488518500332.

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In this paper, a new PSO algorithm with a new adaptive weight of inertia and time acceleration coefficients (TVAC) is proposed; this algorithm called IAPSO is introduced for global optimization. The objective of this proposition is to initialize the weight of inertia to a high value, giving priority to the global exploration of the research space and gradually decreasing the new inertia adaptable to the weight in order to obtain refined solutions. The test of our algorithm is performed on three standard reference functions (Schwefel’s (unimodal), Ackley (multimodal) and Griewank (Multimodal)). The proposed IAPSO algorithm combined with the Fuzzy Clustering NPCM algorithm for modeling and identifying a non-linear system. The new NPCM-IAPSO grouping algorithm also solves the problems of the classical clustering algorithm (FCM, GK, PCM, EPCM, FCM-PSO, EPCM-PSO …etc.), such as convergence towards local optimization and sensitivity to initialization. The effectiveness of the proposed NPCM-IAPSO algorithm was tested on the furnace gas Box and Jenkins, dryer system and two other nonlinear systems described by differential equations.

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Han, Wen Hua. "A New Simple Micro-PSO for High Dimensional Optimization Problem." Applied Mechanics and Materials 236-237 (November 2012): 1195–200. http://dx.doi.org/10.4028/www.scientific.net/amm.236-237.1195.

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The particle swarm optimization (PSO) algorithm is a population-based intelligent stochastic search optimization technique, which has already been widely used to various of fields. In this paper, a simple micro-PSO is proposed for high dimensional optimization problem, which is resulted from being introduced escape boundary and perturbation for global optimum. The advantages of the simple micro-PSO are more simple and easily implemented than the previous micro-PSO. Experiments were conducted using Griewank, Rosenbrock, Ackley, Tablets functions. The experimental results demonstrate that the simple micro-PSO are higher optimization precision and faster convergence rate than PSO and robust for the dimension of the optimization problem.

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Asadieh, Behzad, and Abbas Afshar. "Optimization of Water-Supply and Hydropower Reservoir Operation Using the Charged System Search Algorithm." Hydrology 6, no. 1 (January 8, 2019): 5. http://dx.doi.org/10.3390/hydrology6010005.

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The Charged System Search (CSS) metaheuristic algorithm is introduced to the field of water resources management and applied to derive water-supply and hydro-power operating policies for a large-scale real-world reservoir system. The optimum algorithm parameters for each reservoir operation problems are also obtained via a tuning procedure. The CSS algorithm is a metaheuristic optimization method inspired by the governing laws of electrostatics in physics and motion from the Newtonian mechanics. In this study, the CSS algorithm’s performance has been tested with benchmark problems, consisting of highly non-linear constrained and/or unconstrained real-valued mathematical models, such as the Ackley’s function and Fletcher–Powell function. The CSS algorithm is then used to optimally solve the water-supply and hydropower operation of “Dez” reservoir in southern Iran over three different operation periods of 60, 240, and 480 months, and the results are presented and compared with those obtained by other available optimization approaches including Genetic Algorithm (GA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO) and Constrained Big Bang–Big Crunch (CBB–BC) algorithm, as well as those obtained by gradient-based Non-Linear Programming (NLP) approach. The results demonstrate the robustness and superiority of the CSS algorithm in solving long term reservoir operation problems, compared to alternative methods. The CSS algorithm is used for the first time in the field of water resources management, and proves to be a robust, accurate, and fast convergent method in handling complex problems in this filed. The application of this approach in other water management problems such as multi-reservoir operation and conjunctive surface/ground water resources management remains to be studied.

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de la Fraga, Luis Gerardo. "Differential Evolution under Fixed Point Arithmetic and FP16 Numbers." Mathematical and Computational Applications 26, no. 1 (February 4, 2021): 13. http://dx.doi.org/10.3390/mca26010013.

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In this work, the differential evolution algorithm behavior under a fixed point arithmetic is analyzed also using half-precision floating point (FP) numbers of 16 bits, and these last numbers are known as FP16. In this paper, it is considered that it is important to analyze differential evolution (DE) in these circumstances with the goal of reducing its consumption power, storage size of the variables, and improve its speed behavior. All these aspects become important if one needs to design a dedicated hardware, as an embedded DE within a circuit chip, that performs optimization. With these conditions DE is tested using three common multimodal benchmark functions: Rosenbrock, Rastrigin, and Ackley, in 10 dimensions. Results are obtained in software by simulating all numbers using C programming language.

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Haznedar, Bulent, Rabia Bayraktar, Melih Yayla, and Mustafa Diyar Demirkol. "Training of ANFIS with simulated annealing algorithm on flexural buckling load prediction of aluminium alloy columns." New Trends and Issues Proceedings on Advances in Pure and Applied Sciences, no. 12 (April 30, 2020): 15–23. http://dx.doi.org/10.18844/gjpaas.v0i12.4982.

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In this study, we propose a simulated annealing algorithm (SA) to train an adaptive neurofuzzy inference system (ANFIS). We performed different types of optimization algorithms such as genetic algorithm (GA), SA and artificial bee colony algorithm on two different problem types. Then, we measured the performance of these algorithms. First, we applied optimization algorithms on eight numerical benchmark functions which are sphere, axis parallel hyper-ellipsoid, Rosenbrock, Rastrigin, Schwefel, Griewank, sum of different powers and Ackley functions. After that, the training of ANFIS is carried out by mentioned optimization algorithms to predict the strength of heat-treated fine-drawn aluminium composite columns defeated by flexural bending. In summary, the accuracy of the proposed soft computing model was compared with the accuracy of the results of existing methods in the literature. It is seen that the training of ANFIS with the SA has more accuracy. Keywords: Soft computing, ANFIS, simulated annealing, flexural buckling, aluminium alloy columns.

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Sharma, Bhanu, and Amar Singh. "Robust approach for optimized path selection in Monarch Butterfly Optimization." Journal of University of Shanghai for Science and Technology 23, no. 09 (September 1, 2021): 19–28. http://dx.doi.org/10.51201/jusst/21/08502.

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Nature Inspired Computing or (NIC) strives to develop new computing technologies by observing how nature can inspired to solve complex problems under various environmental conditions. This has produced unconventional research in new fields such as neural networks, swarm intelligence, evolutionary computing, and artificial immune systems. NIC technology is used in almost every branch of physics, biology, engineering, economics and even management. In this paper, one of the nature-inspired approach namely Monarch Butterfly Optimization (MBO)is used for modifying the chromosome parameter in it. The new conditional path selection criteria are developed for the movement of individual subpopulation along with the amplitude parameter. Ackley function is implemented by using conditional path selection mathematical model and the effect of amplitude parameter with adjusting ratio has been identified. The results show better performance among the conditional path selection criteria in terms of route optimization selection.

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Yong, Wang, Li Jing-yang, and Li Chun-lei. "Double Flight-Modes Particle Swarm Optimization." Journal of Optimization 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/356420.

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Getting inspiration from the real birds in flight, we propose a new particle swarm optimization algorithm that we call the double flight modes particle swarm optimization (DMPSO) in this paper. In the DMPSO, each bird (particle) can use both rotational flight mode and nonrotational flight mode to fly, while it is searching for food in its search space. There is a King in the swarm of birds, and the King controls each bird’s flight behavior in accordance with certain rules all the time. Experiments were conducted on benchmark functions such as Schwefel, Rastrigin, Ackley, Step, Griewank, and Sphere. The experimental results show that the DMPSO not only has marked advantage of global convergence property but also can effectively avoid the premature convergence problem and has good performance in solving the complex and high-dimensional optimization problems.

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Ferrari, Allan Christian Krainski, Leandro dos Santos Coelho, Gideon Villar Leandro, Cristiano Osinski, and Carlos Alexandre Gouvea da Silva. "Meta-heuristic inspired by the behavior of the humpback whale tuned by a fuzzy inference system." Journal of Intelligent & Fuzzy Systems 39, no. 5 (November 19, 2020): 7993–8000. http://dx.doi.org/10.3233/jifs-201459.

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The Whale Optimization Algorithm (WOA) is a recent meta-heuristic that can be explored in global optimization problems. This paper proposes a new parameter adjustment mechanism that influences the probability of the food recognition process in the whale algorithm. The adjustment is performed using a fuzzy inference system that uses the current iteration number as input information. Our simulation results are compared with other meta-heuristics such as the conventional version of WOA, Particle Swarm Optimization (PSO) and Differential Evolution (DE). All algorithms are used to optimize ten test functions (Sphere, Schwefel 2.22, Quartic, Rosenbrock, Ackley, Rastrigin, Penalty 1, Schwefel 2.21, Six hump camel back and Shekel 1) in order to obtain their respective optimal values for be used as criteria for analysis and comparison. The results of the simulations show that the proposed fuzzy inference system improves the convergence of WOA and also is competitive in relation to the other algorithms, i.e., classical WOA, PSO and DE.

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Zaharov, D. O., and A. P. Karpenko. "Study of League Championship Algorithm Efficiency for Global Optimization Problem." Mathematics and Mathematical Modeling, no. 2 (June 9, 2020): 25–45. http://dx.doi.org/10.24108/mathm.0220.0000217.

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The article objective is to study a new League Championship Algorithm (LCA) algorithm efficiency by its comparing with the efficiency of the Particle Swarm optimization (PSO) algorithm.The article presents a brief description of the terms used in the League Championship algorithm, describes the basic rules of the algorithm, on the basis of which the iterative process for solving the global optimization problem is built.Gives a detailed description of the League Championship algorithm, which comprises a flowchart of the algorithm, as well as a formalization of all its main steps.Depicts an exhaustive description of the software developed to implement the League Championship algorithm to solve global optimization problems.Briefly describes the modified particle swarm algorithm. Presents the values of all free parameters of the algorithm and the algorithm modifications, which make it different from the classical version, as well.The main part of the article shows the results of a great deal of computational experiments using two abovementioned algorithms. All the performance criteria, used for assessment of the algorithms efficiency, are given.Computational experiments were performed using the spherical function, as well as the Rosenbrock, Rastrigin, and Ackley functions. The results of the experiments are summarized in Tables, and also illustrated in Figures. Experiments were performed for the vector dimension of the variable parameters that is equal to 2, 4, 8, 16, 32, and 64.An analysis of the results of computational experiments involves a full assessment of the efficiency of the League Championship algorithm, and also provides an answer about expediency for further algorithm development.It is shown that the League Championship algorithm presented in the article has a high development potential and needs further work for its study.

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LUO, Zi-Qiang, Peng CAO, Bin WEN, and Yu ZHANG. "A Novel Cloud Evolutionary Strategy for Ackley's Function." DEStech Transactions on Engineering and Technology Research, sste (March 27, 2017). http://dx.doi.org/10.12783/dtetr/sste2016/6518.

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Alsaadi, Areej Ahmad, Wadee Alhalabi, and Elena-Niculina Dragoi. "Performance analysis." Data Technologies and Applications ahead-of-print, ahead-of-print (July 16, 2019). http://dx.doi.org/10.1108/dta-05-2018-0043.

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Purpose Differential search algorithm (DSA) is a new optimization, meta-heuristic algorithm. It simulates the Brownian-like, random-walk movement of an organism by migrating to a better position. The purpose of this paper is to analyze the performance analysis of DSA into two key parts: six random number generators (RNGs) and Benchmark functions (BMF) from IEEE World Congress on Evolutionary Computation (CEC, 2015). Noting that this study took problem dimensionality and maximum function evaluation (MFE) into account, various configurations were executed to check the parameters’ influence. Shifted rotated Rastrigin’s functions provided the best outcomes for the majority of RNGs, and minimum dimensionality offered the best average. Among almost all BMFs studied, Weibull and Beta RNGs concluded with the best and worst averages, respectively. In sum, 50,000 MFE provided the best results with almost RNGs and BMFs. Design/methodology/approach DSA was tested under six randomizers (Bernoulli, Beta, Binomial, Chisquare, Rayleigh, Weibull), two unimodal functions (rotated high conditioned elliptic function, rotated cigar function), three simple multi-modal functions (shifted rotated Ackley’s, shifted rotated Rastrigin’s, shifted rotated Schwefel’s functions) and three hybrid Functions (Hybrid Function 1 (n=3), Hybrid Function 2 (n=4,and Hybrid Function 3 (n=5)) at four problem dimensionalities (10D, 30D, 50D and 100D). According to the protocol of the CEC (2015) testbed, the stopping criteria are the MFEs, which are set to 10,000, 50,000 and 100,000. All algorithms mentioned were implemented on PC running Windows 8.1, i5 CPU at 1.60 GHz, 2.29 GHz and a 64-bit operating system. Findings The authors concluded the results based on RNGs as follows: F3 gave the best average results with Bernoulli, whereas F4 resulted in the best outcomes with all other RNGs; minimum and maximum dimensionality offered the best and worst averages, respectively; and Bernoulli and Binomial RNGs retained the best and worst averages, respectively, when all other parameters were fixed. In addition, the authors’ results concluded, based on BMFs: Weibull and Beta RNGs produced the best and worst averages with most BMFs; shifted and rotated Rastrigin’s function and Hybrid Function 2 gave rise to the best and worst averages. In both parts, 50,000 MFEs offered the best average results with most RNGs and BMFs. Originality/value Being aware of the advantages and drawbacks of DS enlarges knowledge about the class in which differential evolution belongs. Application of that knowledge, to specific problems, ensures that the possible improvements are not randomly applied. Strengths and weaknesses influenced by the characteristics of the problem being solved (e.g. linearity, dimensionality) and by the internal approaches being used (e.g. stop criteria, parameter control settings, initialization procedure) are not studied in detail. In-depth study of performance under various conditions is a “must” if one desires to efficiently apply DS algorithms to help solve specific problems. In this work, all the functions were chosen from the 2015 IEEE World Congress on Evolutionary Computation (CEC, 2015).

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Ackley, Tyler W., Dayna McManus, Jeffrey E. Topal, Brian Cicali, and Sunish Shah. "Correction for Ackley et al., “A Valid Warning or Clinical Lore: an Evaluation of Safety Outcomes of Remdesivir in Patients with Impaired Renal Function from a Multicenter Matched Cohort”." Antimicrobial Agents and Chemotherapy 65, no. 7 (June 17, 2021). http://dx.doi.org/10.1128/aac.00943-21.

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Journal articles on the topic 'Ackley's function'

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